LMFDB - Space of Modular Forms of Level 288 and Weight 2

Defining parameters

Level:	$ N $	=	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	=	$ 2 $
Nonzero newspaces:			$ 12 $
Newform subspaces:			$ 28 $
Sturm bound:			$9216$
Trace bound:			$17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(288))$.

	Total	New	Old
Modular forms	2560	1071	1489
Cusp forms	2049	981	1068
Eisenstein series	511	90	421

Trace form

$ 981q - 12q^{2} - 12q^{3} - 12q^{4} - 14q^{5} - 16q^{6} - 10q^{7} - 12q^{8} - 24q^{9} + O(q^{10}) $

\( 981q - 12q^{2} - 12q^{3} - 12q^{4} - 14q^{5} - 16q^{6} - 10q^{7} - 12q^{8} - 24q^{9} - 28q^{10} - 6q^{11} - 16q^{12} - 6q^{13} + 4q^{14} - 6q^{15} + 8q^{16} + 14q^{17} - 16q^{18} - 12q^{19} + 4q^{20} + 18q^{23} - 16q^{24} + 15q^{25} - 32q^{26} - 56q^{28} + 10q^{29} - 32q^{30} + 26q^{31} - 32q^{32} - 44q^{33} - 24q^{34} + 12q^{35} - 40q^{36} - 70q^{37} - 116q^{38} - 18q^{39} - 128q^{40} - 70q^{41} - 96q^{42} - 34q^{43} - 148q^{44} - 64q^{45} - 132q^{46} - 66q^{47} - 120q^{48} - 75q^{49} - 180q^{50} - 44q^{51} - 132q^{52} - 78q^{53} - 104q^{54} - 72q^{55} - 160q^{56} - 72q^{57} - 144q^{58} - 74q^{59} - 72q^{60} - 6q^{61} - 48q^{62} - 66q^{63} - 72q^{64} - 112q^{65} - 16q^{66} - 34q^{67} - 56q^{68} - 80q^{69} - 24q^{70} - 68q^{71} - 16q^{72} - 10q^{73} + 4q^{74} - 124q^{75} - 12q^{76} - 28q^{77} + 8q^{78} - 70q^{79} + 112q^{80} - 88q^{81} + 124q^{82} - 186q^{83} + 96q^{84} + 20q^{85} + 176q^{86} - 170q^{87} + 152q^{88} - 78q^{89} + 128q^{90} - 192q^{91} + 256q^{92} - 16q^{93} + 160q^{94} - 248q^{95} + 120q^{96} - 74q^{97} + 208q^{98} - 154q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(288))$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $ S_k^{\mathrm{new}}(N, \chi) $ we list the newforms together with their dimension.

Label	$\chi$	Newforms	Dimension	$\chi$ degree
288.2.a	$\chi_{288}(1, \cdot)$	288.2.a.a	1	1
		288.2.a.b	1
		288.2.a.c	1
		288.2.a.d	1
		288.2.a.e	1
288.2.c	$\chi_{288}(287, \cdot)$	288.2.c.a	4	1
288.2.d	$\chi_{288}(145, \cdot)$	288.2.d.a	2	1
288.2.d	$\chi_{288}(145, \cdot)$	288.2.d.b	2	1
288.2.f	$\chi_{288}(143, \cdot)$	288.2.f.a	4	1
288.2.i	$\chi_{288}(97, \cdot)$	288.2.i.a	2	2
		288.2.i.b	2
		288.2.i.c	4
		288.2.i.d	4
		288.2.i.e	4
		288.2.i.f	8
288.2.k	$\chi_{288}(73, \cdot)$	None	0	2
288.2.l	$\chi_{288}(71, \cdot)$	None	0	2
288.2.p	$\chi_{288}(47, \cdot)$	288.2.p.a	4	2
288.2.p	$\chi_{288}(47, \cdot)$	288.2.p.b	16	2
288.2.r	$\chi_{288}(49, \cdot)$	288.2.r.a	4	2
288.2.r	$\chi_{288}(49, \cdot)$	288.2.r.b	16	2
288.2.s	$\chi_{288}(95, \cdot)$	288.2.s.a	24	2
288.2.v	$\chi_{288}(37, \cdot)$	288.2.v.a	4	4
		288.2.v.b	8
		288.2.v.c	32
		288.2.v.d	32
288.2.w	$\chi_{288}(35, \cdot)$	288.2.w.a	32	4
288.2.w	$\chi_{288}(35, \cdot)$	288.2.w.b	32	4
288.2.y	$\chi_{288}(23, \cdot)$	None	0	4
288.2.bb	$\chi_{288}(25, \cdot)$	None	0	4
288.2.bc	$\chi_{288}(13, \cdot)$	288.2.bc.a	368	8
288.2.bf	$\chi_{288}(11, \cdot)$	288.2.bf.a	368	8

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(288))$ into lower level spaces

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	()()()()()()()()()()()()()()()()()()()($ ( 1 + 2 T^{2} )^{2} $)($ 1 - 4 T + 6 T^{2} - 4 T^{3} + 2 T^{4} - 8 T^{5} + 24 T^{6} - 32 T^{7} + 16 T^{8} $)
$3$	()()()()()()()()()($ 1 + 3 T + 3 T^{2} $)($ 1 - 3 T + 3 T^{2} $)($ ( 1 + 2 T + 3 T^{2} )^{2} $)($ ( 1 - 3 T^{2} )^{2} $)($ ( 1 - 2 T + 3 T^{2} )^{2} $)($ 1 + 3 T^{2} + 12 T^{4} + 27 T^{6} + 81 T^{8} $)($ 1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4} $)($ ( 1 - 3 T + 6 T^{2} - 15 T^{3} + 30 T^{4} - 45 T^{5} + 54 T^{6} - 81 T^{7} + 81 T^{8} )^{2} $)($ 1 + 3 T^{2} + 9 T^{4} $)($ 1 - T^{2} - 2 T^{4} + 9 T^{6} + 18 T^{8} + 81 T^{10} - 162 T^{12} - 729 T^{14} + 6561 T^{16} $)()()
$5$	($ 1 + 4 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ ( 1 - 8 T^{2} + 25 T^{4} )^{2} $)($ 1 - 2 T^{2} + 25 T^{4} $)($ ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) $)($ ( 1 + 4 T^{2} + 25 T^{4} )^{2} $)($ 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} $)($ ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} $)($ ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} $)($ ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} $)($ ( 1 - T - T^{2} + 8 T^{3} - 26 T^{4} + 40 T^{5} - 25 T^{6} - 125 T^{7} + 625 T^{8} )^{2} $)($ ( 1 - 5 T^{2} + 25 T^{4} )^{2} $)($ 1 - 13 T^{2} + 48 T^{4} + 103 T^{6} - 1099 T^{8} + 3648 T^{10} - 5222 T^{12} - 177298 T^{14} + 1667616 T^{16} - 4432450 T^{18} - 3263750 T^{20} + 57000000 T^{22} - 429296875 T^{24} + 1005859375 T^{26} + 11718750000 T^{28} - 79345703125 T^{30} + 152587890625 T^{32} $)($ ( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} )( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} ) $)($ 1 + 19 T^{2} + 176 T^{4} + 1031 T^{6} + 3893 T^{8} + 4928 T^{10} - 61926 T^{12} - 631122 T^{14} - 3717344 T^{16} - 15778050 T^{18} - 38703750 T^{20} + 77000000 T^{22} + 1520703125 T^{24} + 10068359375 T^{26} + 42968750000 T^{28} + 115966796875 T^{30} + 152587890625 T^{32} $)($ ( 1 - 2 T + 5 T^{2} )^{2}( 1 - 8 T^{2} + 25 T^{4} ) $)($ ( 1 + 2 T^{2} - 16 T^{3} + 2 T^{4} - 80 T^{5} + 50 T^{6} + 625 T^{8} )^{2} $)
$7$	($ 1 + 7 T^{2} $)($ 1 + 4 T + 7 T^{2} $)($ 1 - 4 T + 7 T^{2} $)($ 1 + 7 T^{2} $)($ 1 + 7 T^{2} $)($ ( 1 + 2 T^{2} + 49 T^{4} )^{2} $)($ ( 1 + 2 T + 7 T^{2} )^{2} $)($ ( 1 - 2 T + 7 T^{2} )^{2} $)($ ( 1 - 4 T + 7 T^{2} )^{2}( 1 + 4 T + 7 T^{2} )^{2} $)($ 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} $)($ 1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4} $)($ 1 - 2 T - 5 T^{2} + 10 T^{3} + 4 T^{4} + 70 T^{5} - 245 T^{6} - 686 T^{7} + 2401 T^{8} $)($ ( 1 - 13 T^{2} + 49 T^{4} )( 1 + 2 T^{2} + 49 T^{4} ) $)($ 1 + 2 T - 5 T^{2} - 10 T^{3} + 4 T^{4} - 70 T^{5} - 245 T^{6} + 686 T^{7} + 2401 T^{8} $)($ 1 - T^{2} - 23 T^{4} + 74 T^{6} - 1874 T^{8} + 3626 T^{10} - 55223 T^{12} - 117649 T^{14} + 5764801 T^{16} $)($ ( 1 + 7 T^{2} + 49 T^{4} )^{2} $)($ 1 + 23 T^{2} + 204 T^{4} + 1399 T^{6} + 12029 T^{8} + 45000 T^{10} - 343382 T^{12} - 4039462 T^{14} - 24407256 T^{16} - 197933638 T^{18} - 824460182 T^{20} + 5294205000 T^{22} + 69344791229 T^{24} + 395182873351 T^{26} + 2823622589004 T^{28} + 15599130675527 T^{30} + 33232930569601 T^{32} $)($ ( 1 - 5 T + 7 T^{2} )^{2}( 1 + T + 7 T^{2} )^{2} $)($ ( 1 + 3 T - 14 T^{2} - 39 T^{3} + 139 T^{4} + 252 T^{5} - 1208 T^{6} - 666 T^{7} + 9424 T^{8} - 4662 T^{9} - 59192 T^{10} + 86436 T^{11} + 333739 T^{12} - 655473 T^{13} - 1647086 T^{14} + 2470629 T^{15} + 5764801 T^{16} )^{2} $)($ ( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} )^{2} $)($ 1 + 8 T + 32 T^{2} + 104 T^{3} + 252 T^{4} + 392 T^{5} + 480 T^{6} + 168 T^{7} - 1274 T^{8} + 1176 T^{9} + 23520 T^{10} + 134456 T^{11} + 605052 T^{12} + 1747928 T^{13} + 3764768 T^{14} + 6588344 T^{15} + 5764801 T^{16} $)
$11$	($ 1 + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ ( 1 - 10 T^{2} + 121 T^{4} )^{2} $)($ 1 + 10 T^{2} + 121 T^{4} $)($ ( 1 - 11 T^{2} )^{2} $)($ ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} $)($ 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} $)($ 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} $)($ 1 + 2 T - 13 T^{2} - 10 T^{3} + 124 T^{4} - 110 T^{5} - 1573 T^{6} + 2662 T^{7} + 14641 T^{8} $)($ 1 - 19 T^{2} + 240 T^{4} - 2299 T^{6} + 14641 T^{8} $)($ 1 - 2 T - 13 T^{2} + 10 T^{3} + 124 T^{4} + 110 T^{5} - 1573 T^{6} - 2662 T^{7} + 14641 T^{8} $)($ 1 - 8 T^{2} + 103 T^{4} + 2248 T^{6} - 20864 T^{8} + 272008 T^{10} + 1508023 T^{12} - 14172488 T^{14} + 214358881 T^{16} $)($ ( 1 - 6 T + 11 T^{2} )^{2}( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} ) $)($ ( 1 - 3 T + 38 T^{2} - 87 T^{3} + 606 T^{4} - 957 T^{5} + 4598 T^{6} - 3993 T^{7} + 14641 T^{8} )^{2}( 1 + 9 T + 41 T^{2} + 108 T^{3} + 276 T^{4} + 1188 T^{5} + 4961 T^{6} + 11979 T^{7} + 14641 T^{8} )^{2} $)($ 1 + 13 T^{2} + 48 T^{4} + 1573 T^{6} + 14641 T^{8} $)($ 1 + 48 T^{2} + 1090 T^{4} + 17592 T^{6} + 242041 T^{8} + 2632140 T^{10} + 21031138 T^{12} + 158095260 T^{14} + 1558598596 T^{16} + 19129526460 T^{18} + 307916891458 T^{20} + 4662996570540 T^{22} + 51883637916121 T^{24} + 456291173580792 T^{26} + 3420886930625890 T^{28} + 18227992011995568 T^{30} + 45949729863572161 T^{32} $)($ ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} ) $)($ 1 + 4 T + 8 T^{2} - 68 T^{3} - 304 T^{4} - 804 T^{5} + 1304 T^{6} + 7396 T^{7} + 43982 T^{8} + 81356 T^{9} + 157784 T^{10} - 1070124 T^{11} - 4450864 T^{12} - 10951468 T^{13} + 14172488 T^{14} + 77948684 T^{15} + 214358881 T^{16} $)
$13$	($ 1 + 6 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ ( 1 - 4 T + 13 T^{2} )^{4} $)($ ( 1 - 13 T^{2} )^{2} $)($ ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) $)($ ( 1 - 14 T^{2} + 169 T^{4} )^{2} $)($ ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) $)($ ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) $)($ 1 + 2 T + T^{2} - 46 T^{3} - 212 T^{4} - 598 T^{5} + 169 T^{6} + 4394 T^{7} + 28561 T^{8} $)($ ( 1 - 3 T - 4 T^{2} - 39 T^{3} + 169 T^{4} )^{2} $)($ 1 + 2 T + T^{2} - 46 T^{3} - 212 T^{4} - 598 T^{5} + 169 T^{6} + 4394 T^{7} + 28561 T^{8} $)($ ( 1 + 3 T - 11 T^{2} - 18 T^{3} + 114 T^{4} - 234 T^{5} - 1859 T^{6} + 6591 T^{7} + 28561 T^{8} )^{2} $)($ ( 1 + 13 T^{2} + 169 T^{4} )^{2} $)($ 1 + 47 T^{2} + 1116 T^{4} + 17239 T^{6} + 168353 T^{8} + 463056 T^{10} - 26916578 T^{12} - 784598686 T^{14} - 12569281176 T^{16} - 132597177934 T^{18} - 768764384258 T^{20} + 2235082868304 T^{22} + 137330714072513 T^{24} + 2376542540984911 T^{26} + 26000662996688796 T^{28} + 185056690127866583 T^{30} + 665416609183179841 T^{32} $)($ ( 1 - T^{2} + 169 T^{4} )( 1 + 23 T^{2} + 169 T^{4} ) $)($ 1 + 51 T^{2} + 1288 T^{4} + 16911 T^{6} + 73645 T^{8} - 1059264 T^{10} - 5456606 T^{12} + 411982806 T^{14} + 9084740848 T^{16} + 69625094214 T^{18} - 155846123966 T^{20} - 5112865008576 T^{22} + 60074488948045 T^{24} + 2331324955658439 T^{26} + 30007933637755528 T^{28} + 200806195670663739 T^{30} + 665416609183179841 T^{32} $)($ 1 - 4 T + 6 T^{2} - 4 T^{3} + 2 T^{4} - 52 T^{5} + 1014 T^{6} - 8788 T^{7} + 28561 T^{8} $)($ 1 + 8 T + 36 T^{2} + 104 T^{3} + 200 T^{4} - 72 T^{5} - 4084 T^{6} - 34216 T^{7} - 153618 T^{8} - 444808 T^{9} - 690196 T^{10} - 158184 T^{11} + 5712200 T^{12} + 38614472 T^{13} + 173765124 T^{14} + 501988136 T^{15} + 815730721 T^{16} $)
$17$	($ 1 + 8 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ ( 1 - 16 T^{2} + 289 T^{4} )^{2} $)($ ( 1 + 17 T^{2} )^{2} $)($ ( 1 - 2 T + 17 T^{2} )^{2} $)($ ( 1 - 32 T^{2} + 289 T^{4} )^{2} $)($ ( 1 + 3 T + 17 T^{2} )^{2} $)($ ( 1 + 3 T + 17 T^{2} )^{2} $)($ ( 1 + 10 T^{2} + 289 T^{4} )^{2} $)($ ( 1 - 4 T + 17 T^{2} )^{4} $)($ ( 1 + 10 T^{2} + 289 T^{4} )^{2} $)($ ( 1 - T + 26 T^{2} - 17 T^{3} + 289 T^{4} )^{4} $)($ ( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} )( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} ) $)($ ( 1 - 101 T^{2} + 4882 T^{4} - 146891 T^{6} + 2998666 T^{8} - 42451499 T^{10} + 407749522 T^{12} - 2437894469 T^{14} + 6975757441 T^{16} )^{2} $)($ ( 1 - 5 T + 17 T^{2} )^{4} $)($ ( 1 + 7 T + 66 T^{2} + 309 T^{3} + 1702 T^{4} + 5253 T^{5} + 19074 T^{6} + 34391 T^{7} + 83521 T^{8} )^{4} $)($ ( 1 - 26 T^{2} + 289 T^{4} )^{2} $)($ 1 - 72 T^{2} + 2620 T^{4} - 64376 T^{6} + 1215110 T^{8} - 18604664 T^{10} + 218825020 T^{12} - 1737904968 T^{14} + 6975757441 T^{16} $)
$19$	($ 1 + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + 19 T^{2} $)($ ( 1 - 19 T^{2} )^{4} $)($ ( 1 - 19 T^{2} )^{2} $)($ 1 - 22 T^{2} + 361 T^{4} $)($ ( 1 - 4 T + 19 T^{2} )^{4} $)($ ( 1 + T + 19 T^{2} )^{2} $)($ ( 1 - T + 19 T^{2} )^{2} $)($ ( 1 + 4 T + 19 T^{2} )^{4} $)($ ( 1 - 10 T^{2} + 361 T^{4} )^{2} $)($ ( 1 - 4 T + 19 T^{2} )^{4} $)($ ( 1 + 31 T^{2} + 888 T^{4} + 11191 T^{6} + 130321 T^{8} )^{2} $)($ ( 1 - 2 T - 15 T^{2} - 38 T^{3} + 361 T^{4} )^{2} $)($ ( 1 - T + 64 T^{2} - 49 T^{3} + 1726 T^{4} - 931 T^{5} + 23104 T^{6} - 6859 T^{7} + 130321 T^{8} )^{4} $)($ ( 1 - 37 T^{2} + 361 T^{4} )^{2} $)($ ( 1 - 69 T^{2} + 2306 T^{4} - 53763 T^{6} + 1069146 T^{8} - 19408443 T^{10} + 300520226 T^{12} - 3246165789 T^{14} + 16983563041 T^{16} )^{2} $)($ 1 + 8 T + 18 T^{2} - 160 T^{3} - 1246 T^{4} - 3040 T^{5} + 6498 T^{6} + 54872 T^{7} + 130321 T^{8} $)($ 1 - 4 T - 8 T^{2} - 28 T^{3} + 336 T^{4} - 1308 T^{5} + 14056 T^{6} - 28228 T^{7} - 115058 T^{8} - 536332 T^{9} + 5074216 T^{10} - 8971572 T^{11} + 43787856 T^{12} - 69330772 T^{13} - 376367048 T^{14} - 3575486956 T^{15} + 16983563041 T^{16} $)
$23$	($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ ( 1 + 14 T^{2} + 529 T^{4} )^{2} $)($ ( 1 + 23 T^{2} )^{2} $)($ ( 1 - 4 T + 23 T^{2} )^{2} $)($ ( 1 + 22 T^{2} + 529 T^{4} )^{2} $)($ 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} $)($ 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} $)($ 1 + 6 T - 13 T^{2} + 18 T^{3} + 1044 T^{4} + 414 T^{5} - 6877 T^{6} + 73002 T^{7} + 279841 T^{8} $)($ 1 + 29 T^{2} + 312 T^{4} + 15341 T^{6} + 279841 T^{8} $)($ 1 - 6 T - 13 T^{2} - 18 T^{3} + 1044 T^{4} - 414 T^{5} - 6877 T^{6} - 73002 T^{7} + 279841 T^{8} $)($ 1 - 65 T^{2} + 2185 T^{4} - 63830 T^{6} + 1646734 T^{8} - 33766070 T^{10} + 611452585 T^{12} - 9622332785 T^{14} + 78310985281 T^{16} $)($ ( 1 - 23 T^{2} + 529 T^{4} )^{2} $)($ 1 - 85 T^{2} + 3432 T^{4} - 80441 T^{6} + 1017209 T^{8} + 1764696 T^{10} - 386280290 T^{12} + 9323832998 T^{14} - 183562178736 T^{16} + 4932307655942 T^{18} - 108097062633890 T^{20} + 261238341174744 T^{22} + 79658639026700729 T^{24} - 3332389988537139209 T^{26} + 75210991050693741672 T^{28} - $$98\!\cdots\!65$$ T^{30} + $$61\!\cdots\!61$$ T^{32} $)($ ( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} )^{2} $)($ ( 1 - 5 T - 32 T^{2} - 45 T^{3} + 1385 T^{4} + 3040 T^{5} - 11142 T^{6} - 48640 T^{7} - 123716 T^{8} - 1118720 T^{9} - 5894118 T^{10} + 36987680 T^{11} + 387579785 T^{12} - 289635435 T^{13} - 4737148448 T^{14} - 17024127235 T^{15} + 78310985281 T^{16} )^{2} $)($ 1 + 12 T + 72 T^{2} + 300 T^{3} + 1246 T^{4} + 6900 T^{5} + 38088 T^{6} + 146004 T^{7} + 279841 T^{8} $)($ 1 - 8 T + 32 T^{2} - 200 T^{3} + 2108 T^{4} - 11560 T^{5} + 45024 T^{6} - 277224 T^{7} + 1704454 T^{8} - 6376152 T^{9} + 23817696 T^{10} - 140650520 T^{11} + 589904828 T^{12} - 1287268600 T^{13} + 4737148448 T^{14} - 27238603576 T^{15} + 78310985281 T^{16} $)
$29$	($ 1 - 4 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ ( 1 - 56 T^{2} + 841 T^{4} )^{2} $)($ 1 - 50 T^{2} + 841 T^{4} $)($ 1 - 22 T^{2} + 841 T^{4} $)($ ( 1 + 52 T^{2} + 841 T^{4} )^{2} $)($ 1 - 2 T - 25 T^{2} - 58 T^{3} + 841 T^{4} $)($ 1 - 2 T - 25 T^{2} - 58 T^{3} + 841 T^{4} $)($ 1 + 10 T + 41 T^{2} + 10 T^{3} - 260 T^{4} + 290 T^{5} + 34481 T^{6} + 243890 T^{7} + 707281 T^{8} $)($ ( 1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4} )^{2} $)($ 1 + 10 T + 41 T^{2} + 10 T^{3} - 260 T^{4} + 290 T^{5} + 34481 T^{6} + 243890 T^{7} + 707281 T^{8} $)($ ( 1 - 5 T - 31 T^{2} + 10 T^{3} + 1570 T^{4} + 290 T^{5} - 26071 T^{6} - 121945 T^{7} + 707281 T^{8} )^{2} $)($ ( 1 - 29 T^{2} + 841 T^{4} )^{2} $)($ 1 - 97 T^{2} + 3780 T^{4} - 80561 T^{6} + 1632089 T^{8} - 54786000 T^{10} + 1038848902 T^{12} + 18974156858 T^{14} - 1329857348520 T^{16} + 15957265917578 T^{18} + 734758090255462 T^{20} - 32587990464306000 T^{22} + 816446667883105529 T^{24} - 33892595421897492761 T^{26} + $$13\!\cdots\!80$$ T^{28} - $$28\!\cdots\!57$$ T^{30} + $$25\!\cdots\!21$$ T^{32} $)($ ( 1 + 29 T^{2} + 841 T^{4} )^{2} $)($ 1 + 123 T^{2} + 7912 T^{4} + 340647 T^{6} + 10067965 T^{8} + 144056448 T^{10} - 3705324014 T^{12} - 328820871018 T^{14} - 12137186779472 T^{16} - 276538352526138 T^{18} - 2620705273945934 T^{20} + 85688134810823808 T^{22} + 5036463377066894365 T^{24} + $$14\!\cdots\!47$$ T^{26} + $$27\!\cdots\!92$$ T^{28} + $$36\!\cdots\!63$$ T^{30} + $$25\!\cdots\!21$$ T^{32} $)($ 1 - 4 T + 6 T^{2} + 204 T^{3} - 830 T^{4} + 5916 T^{5} + 5046 T^{6} - 97556 T^{7} + 707281 T^{8} $)($ 1 - 12 T^{2} + 64 T^{3} + 72 T^{4} - 4416 T^{5} + 14140 T^{6} + 57344 T^{7} - 693650 T^{8} + 1662976 T^{9} + 11891740 T^{10} - 107701824 T^{11} + 50924232 T^{12} + 1312713536 T^{13} - 7137879852 T^{14} + 500246412961 T^{16} $)
$31$	($ 1 + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 31 T^{2} $)($ ( 1 - 46 T^{2} + 961 T^{4} )^{2} $)($ ( 1 - 10 T + 31 T^{2} )^{2} $)($ ( 1 + 2 T + 31 T^{2} )^{2} $)($ ( 1 - 50 T^{2} + 961 T^{4} )^{2} $)($ ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) $)($ ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) $)($ 1 - 10 T + 19 T^{2} - 190 T^{3} + 2500 T^{4} - 5890 T^{5} + 18259 T^{6} - 297910 T^{7} + 923521 T^{8} $)($ 1 - 35 T^{2} + 264 T^{4} - 33635 T^{6} + 923521 T^{8} $)($ 1 + 10 T + 19 T^{2} + 190 T^{3} + 2500 T^{4} + 5890 T^{5} + 18259 T^{6} + 297910 T^{7} + 923521 T^{8} $)($ 1 + 11 T^{2} - 1163 T^{4} - 7018 T^{6} + 608854 T^{8} - 6744298 T^{10} - 1074054923 T^{12} + 9762540491 T^{14} + 852891037441 T^{16} $)($ ( 1 + 31 T^{2} + 961 T^{4} )^{2} $)($ 1 + 131 T^{2} + 7152 T^{4} + 312151 T^{6} + 16524593 T^{8} + 706250232 T^{10} + 22761450214 T^{12} + 818587141454 T^{14} + 29243993208000 T^{16} + 786662242937294 T^{18} + 21020677263083494 T^{20} + 626799680607103992 T^{22} + 14093677267060286513 T^{24} + $$25\!\cdots\!51$$ T^{26} + $$56\!\cdots\!72$$ T^{28} + $$99\!\cdots\!51$$ T^{30} + $$72\!\cdots\!81$$ T^{32} $)($ ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} $)($ ( 1 - 5 T - 48 T^{2} + 155 T^{3} + 1121 T^{4} + 2040 T^{5} - 44678 T^{6} - 79040 T^{7} + 1805724 T^{8} - 2450240 T^{9} - 42935558 T^{10} + 60773640 T^{11} + 1035267041 T^{12} + 4437518405 T^{13} - 42600176688 T^{14} - 137563070555 T^{15} + 852891037441 T^{16} )^{2} $)($ ( 1 + 4 T + 31 T^{2} )^{4} $)($ ( 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} )^{4} $)
$37$	($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ ( 1 + 6 T + 37 T^{2} )^{4} $)($ ( 1 - 37 T^{2} )^{2} $)($ 1 - 10 T^{2} + 1369 T^{4} $)($ ( 1 - 37 T^{2} )^{4} $)($ ( 1 + 8 T + 37 T^{2} )^{2} $)($ ( 1 + 8 T + 37 T^{2} )^{2} $)($ ( 1 - 8 T + 66 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} $)($ ( 1 + 8 T + 37 T^{2} )^{4} $)($ ( 1 - 8 T + 66 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} $)($ ( 1 - 4 T + 37 T^{2} )^{8} $)($ ( 1 - 37 T^{2} )^{4} $)($ ( 1 - 140 T^{2} + 8596 T^{4} - 317540 T^{6} + 10470934 T^{8} - 434712260 T^{10} + 16110287956 T^{12} - 359201697260 T^{14} + 3512479453921 T^{16} )^{2} $)($ ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} $)($ ( 1 - 144 T^{2} + 12668 T^{4} - 733824 T^{6} + 31784838 T^{8} - 1004605056 T^{10} + 23741871548 T^{12} - 369464602896 T^{14} + 3512479453921 T^{16} )^{2} $)($ 1 - 4 T + 6 T^{2} - 4 T^{3} + 2 T^{4} - 148 T^{5} + 8214 T^{6} - 202612 T^{7} + 1874161 T^{8} $)($ 1 + 8 T - 44 T^{2} - 760 T^{3} - 1272 T^{4} + 22872 T^{5} + 112156 T^{6} - 219496 T^{7} - 4000082 T^{8} - 8121352 T^{9} + 153541564 T^{10} + 1158535416 T^{11} - 2383932792 T^{12} - 52701407320 T^{13} - 112891961996 T^{14} + 759455017064 T^{15} + 3512479453921 T^{16} $)
$41$	($ 1 - 8 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ ( 1 + 16 T^{2} + 1681 T^{4} )^{2} $)($ ( 1 + 41 T^{2} )^{2} $)($ ( 1 + 2 T + 41 T^{2} )^{2} $)($ ( 1 - 80 T^{2} + 1681 T^{4} )^{2} $)($ 1 + T - 40 T^{2} + 41 T^{3} + 1681 T^{4} $)($ 1 + T - 40 T^{2} + 41 T^{3} + 1681 T^{4} $)($ 1 - 14 T + 89 T^{2} - 350 T^{3} + 1732 T^{4} - 14350 T^{5} + 149609 T^{6} - 964894 T^{7} + 2825761 T^{8} $)($ ( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} )^{2} $)($ 1 - 14 T + 89 T^{2} - 350 T^{3} + 1732 T^{4} - 14350 T^{5} + 149609 T^{6} - 964894 T^{7} + 2825761 T^{8} $)($ ( 1 + T - 40 T^{2} + 41 T^{3} + 1681 T^{4} )^{4} $)($ ( 1 - 6 T + 41 T^{2} )^{2}( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} ) $)($ ( 1 + 18 T + 292 T^{2} + 3312 T^{3} + 34963 T^{4} + 303732 T^{5} + 2503888 T^{6} + 17908938 T^{7} + 122450608 T^{8} + 734266458 T^{9} + 4209035728 T^{10} + 20933513172 T^{11} + 98797081843 T^{12} + 383715737712 T^{13} + 1387030438372 T^{14} + 3505576929858 T^{15} + 7984925229121 T^{16} )^{2} $)($ ( 1 - 5 T - 16 T^{2} - 205 T^{3} + 1681 T^{4} )^{2} $)($ ( 1 + 4 T - 74 T^{2} + 288 T^{3} + 4517 T^{4} - 22796 T^{5} - 11538 T^{6} + 738968 T^{7} - 2462804 T^{8} + 30297688 T^{9} - 19395378 T^{10} - 1571123116 T^{11} + 12763962437 T^{12} + 33366585888 T^{13} - 351507713834 T^{14} + 779017095524 T^{15} + 7984925229121 T^{16} )^{2} $)($ 1 - 12 T + 72 T^{2} - 516 T^{3} + 3694 T^{4} - 21156 T^{5} + 121032 T^{6} - 827052 T^{7} + 2825761 T^{8} $)($ 1 + 8 T + 32 T^{2} + 88 T^{3} + 1788 T^{4} + 23048 T^{5} + 131040 T^{6} + 748824 T^{7} + 3829318 T^{8} + 30701784 T^{9} + 220278240 T^{10} + 1588491208 T^{11} + 5052460668 T^{12} + 10195345688 T^{13} + 152003335712 T^{14} + 1558034191048 T^{15} + 7984925229121 T^{16} $)
$43$	($ 1 + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 + 43 T^{2} $)($ ( 1 - 22 T^{2} + 1849 T^{4} )^{2} $)($ ( 1 - 43 T^{2} )^{2} $)($ 1 - 70 T^{2} + 1849 T^{4} $)($ ( 1 + 8 T + 43 T^{2} )^{4} $)($ 1 + 7 T + 6 T^{2} + 301 T^{3} + 1849 T^{4} $)($ 1 - 7 T + 6 T^{2} - 301 T^{3} + 1849 T^{4} $)($ ( 1 - 10 T + 43 T^{2} )^{2}( 1 + 10 T + 57 T^{2} + 430 T^{3} + 1849 T^{4} ) $)($ 1 - 11 T^{2} - 1728 T^{4} - 20339 T^{6} + 3418801 T^{8} $)($ ( 1 + 10 T + 43 T^{2} )^{2}( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} ) $)($ 1 - 136 T^{2} + 10471 T^{4} - 588472 T^{6} + 26782720 T^{8} - 1088084728 T^{10} + 35798265271 T^{12} - 859705374664 T^{14} + 11688200277601 T^{16} $)($ ( 1 - 10 T + 43 T^{2} )^{2}( 1 + 10 T + 57 T^{2} + 430 T^{3} + 1849 T^{4} ) $)($ ( 1 + 4 T - 96 T^{2} - 868 T^{3} + 4061 T^{4} + 55182 T^{5} + 78652 T^{6} - 1341518 T^{7} - 8451684 T^{8} - 57685274 T^{9} + 145427548 T^{10} + 4387355274 T^{11} + 13883750861 T^{12} - 127603328524 T^{13} - 606850852704 T^{14} + 1087274444428 T^{15} + 11688200277601 T^{16} )^{2} $)($ 1 - 35 T^{2} - 624 T^{4} - 64715 T^{6} + 3418801 T^{8} $)($ 1 + 324 T^{2} + 58258 T^{4} + 7305024 T^{6} + 705172105 T^{8} + 54954910764 T^{10} + 3558033934834 T^{12} + 194436327001344 T^{14} + 9048929543300068 T^{16} + 359512768625485056 T^{18} + 12164209974444414034 T^{20} + $$34\!\cdots\!36$$ T^{22} + $$82\!\cdots\!05$$ T^{24} + $$15\!\cdots\!76$$ T^{26} + $$23\!\cdots\!58$$ T^{28} + $$23\!\cdots\!76$$ T^{30} + $$13\!\cdots\!01$$ T^{32} $)($ 1 - 16 T + 162 T^{2} - 1384 T^{3} + 10178 T^{4} - 59512 T^{5} + 299538 T^{6} - 1272112 T^{7} + 3418801 T^{8} $)($ 1 + 12 T + 56 T^{2} - 604 T^{3} - 8560 T^{4} - 59644 T^{5} - 32984 T^{6} + 2234540 T^{7} + 25213774 T^{8} + 96085220 T^{9} - 60987416 T^{10} - 4742115508 T^{11} - 29264936560 T^{12} - 88793099572 T^{13} + 353996330744 T^{14} + 3261823333284 T^{15} + 11688200277601 T^{16} $)
$47$	($ 1 + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 47 T^{2} $)($ ( 1 + 62 T^{2} + 2209 T^{4} )^{2} $)($ ( 1 + 47 T^{2} )^{2} $)($ ( 1 + 12 T + 47 T^{2} )^{2} $)($ ( 1 + 70 T^{2} + 2209 T^{4} )^{2} $)($ 1 - 2 T - 43 T^{2} - 94 T^{3} + 2209 T^{4} $)($ 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} $)($ 1 - 2 T - 37 T^{2} + 106 T^{3} - 716 T^{4} + 4982 T^{5} - 81733 T^{6} - 207646 T^{7} + 4879681 T^{8} $)($ 1 + 53 T^{2} + 600 T^{4} + 117077 T^{6} + 4879681 T^{8} $)($ 1 + 2 T - 37 T^{2} - 106 T^{3} - 716 T^{4} - 4982 T^{5} - 81733 T^{6} + 207646 T^{7} + 4879681 T^{8} $)($ 1 - 161 T^{2} + 15097 T^{4} - 1031366 T^{6} + 55019806 T^{8} - 2278287494 T^{10} + 73668544057 T^{12} - 1735453667969 T^{14} + 23811286661761 T^{16} $)($ ( 1 - 47 T^{2} + 2209 T^{4} )^{2} $)($ 1 - 265 T^{2} + 38172 T^{4} - 3663305 T^{6} + 256619789 T^{8} - 13483362840 T^{10} + 543517455226 T^{12} - 17957421673750 T^{14} + 672442507889160 T^{16} - 39667944477313750 T^{18} + 2652191799434662906 T^{20} - $$14\!\cdots\!60$$ T^{22} + $$61\!\cdots\!29$$ T^{24} - $$19\!\cdots\!45$$ T^{26} + $$44\!\cdots\!52$$ T^{28} - $$68\!\cdots\!85$$ T^{30} + $$56\!\cdots\!21$$ T^{32} $)($ ( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} )^{2} $)($ ( 1 + 3 T - 98 T^{2} - 219 T^{3} + 3523 T^{4} - 1116 T^{5} - 253856 T^{6} + 226218 T^{7} + 18909448 T^{8} + 10632246 T^{9} - 560767904 T^{10} - 115866468 T^{11} + 17191116163 T^{12} - 50226556533 T^{13} - 1056363102242 T^{14} + 1519869361389 T^{15} + 23811286661761 T^{16} )^{2} $)($ 1 - 52 T^{2} + 486 T^{4} - 114868 T^{6} + 4879681 T^{8} $)($ 1 - 312 T^{2} + 44348 T^{4} - 3794696 T^{6} + 215798406 T^{8} - 8382483464 T^{10} + 216404092988 T^{12} - 3363115182648 T^{14} + 23811286661761 T^{16} $)
$53$	($ 1 - 4 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 + 14 T + 53 T^{2} $)($ 1 + 4 T + 53 T^{2} $)($ ( 1 - 88 T^{2} + 2809 T^{4} )^{2} $)($ 1 + 94 T^{2} + 2809 T^{4} $)($ 1 - 70 T^{2} + 2809 T^{4} $)($ ( 1 + 52 T^{2} + 2809 T^{4} )^{2} $)($ ( 1 + 4 T + 53 T^{2} )^{2} $)($ ( 1 + 4 T + 53 T^{2} )^{2} $)($ ( 1 - 8 T + 98 T^{2} - 424 T^{3} + 2809 T^{4} )^{2} $)($ ( 1 + 8 T + 53 T^{2} )^{4} $)($ ( 1 - 8 T + 98 T^{2} - 424 T^{3} + 2809 T^{4} )^{2} $)($ ( 1 + 4 T + 53 T^{2} )^{8} $)($ ( 1 + 53 T^{2} )^{4} $)($ ( 1 + 196 T^{2} + 21556 T^{4} + 1665484 T^{6} + 98315734 T^{8} + 4678344556 T^{10} + 170087208436 T^{12} + 4344214781284 T^{14} + 62259690411361 T^{16} )^{2} $)($ ( 1 - 53 T^{2} )^{4} $)($ ( 1 - 264 T^{2} + 35516 T^{4} - 3123720 T^{6} + 194863110 T^{8} - 8774529480 T^{10} + 280238323196 T^{12} - 5851391338056 T^{14} + 62259690411361 T^{16} )^{2} $)($ 1 + 4 T + 54 T^{2} + 708 T^{3} + 3490 T^{4} + 37524 T^{5} + 151686 T^{6} + 595508 T^{7} + 7890481 T^{8} $)($ 1 + 8 T + 100 T^{2} + 424 T^{3} + 3016 T^{4} + 19768 T^{5} + 118540 T^{6} + 2296472 T^{7} + 11779502 T^{8} + 121713016 T^{9} + 332978860 T^{10} + 2943000536 T^{11} + 23797690696 T^{12} + 177314889032 T^{13} + 2216436112900 T^{14} + 9397689118696 T^{15} + 62259690411361 T^{16} $)
$59$	($ 1 + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 59 T^{2} $)($ ( 1 - 10 T^{2} + 3481 T^{4} )^{2} $)($ 1 + 10 T^{2} + 3481 T^{4} $)($ 1 - 102 T^{2} + 3481 T^{4} $)($ ( 1 + 10 T^{2} + 3481 T^{4} )^{2} $)($ 1 - 5 T - 34 T^{2} - 295 T^{3} + 3481 T^{4} $)($ 1 + 5 T - 34 T^{2} + 295 T^{3} + 3481 T^{4} $)($ 1 - 14 T + 83 T^{2} + 70 T^{3} - 2276 T^{4} + 4130 T^{5} + 288923 T^{6} - 2875306 T^{7} + 12117361 T^{8} $)($ 1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8} $)($ 1 + 14 T + 83 T^{2} - 70 T^{3} - 2276 T^{4} - 4130 T^{5} + 288923 T^{6} + 2875306 T^{7} + 12117361 T^{8} $)($ 1 - 56 T^{2} - 4313 T^{4} - 27272 T^{6} + 32453824 T^{8} - 94933832 T^{10} - 52262177993 T^{12} - 2362109883896 T^{14} + 146830437604321 T^{16} $)($ ( 1 + 6 T + 59 T^{2} )^{2}( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} ) $)($ ( 1 + 6 T + 178 T^{2} + 996 T^{3} + 15871 T^{4} + 89238 T^{5} + 1194346 T^{6} + 6437052 T^{7} + 79012984 T^{8} + 379786068 T^{9} + 4157518426 T^{10} + 18327611202 T^{11} + 192314636431 T^{12} + 712064601804 T^{13} + 7508134988098 T^{14} + 14931908908914 T^{15} + 146830437604321 T^{16} )^{2} $)($ 1 + 117 T^{2} + 10208 T^{4} + 407277 T^{6} + 12117361 T^{8} $)($ 1 + 364 T^{2} + 70130 T^{4} + 9549968 T^{6} + 1028964713 T^{8} + 92991430988 T^{10} + 7291973853618 T^{12} + 506327334867240 T^{14} + 31497451193778532 T^{16} + 1762525452672862440 T^{18} + 88359479586850462098 T^{20} + $$39\!\cdots\!08$$ T^{22} + $$15\!\cdots\!73$$ T^{24} + $$48\!\cdots\!68$$ T^{26} + $$12\!\cdots\!30$$ T^{28} + $$22\!\cdots\!04$$ T^{30} + $$21\!\cdots\!41$$ T^{32} $)($ 1 - 16 T + 114 T^{2} - 696 T^{3} + 4834 T^{4} - 41064 T^{5} + 396834 T^{6} - 3286064 T^{7} + 12117361 T^{8} $)($ 1 - 20 T + 136 T^{2} + 1124 T^{3} - 27632 T^{4} + 217412 T^{5} - 194408 T^{6} - 12195572 T^{7} + 142178894 T^{8} - 719538748 T^{9} - 676734248 T^{10} + 44651859148 T^{11} - 334826919152 T^{12} + 803574912076 T^{13} + 5736552575176 T^{14} - 49773029696380 T^{15} + 146830437604321 T^{16} $)
$61$	($ 1 + 10 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ ( 1 + 2 T + 61 T^{2} )^{4} $)($ ( 1 - 61 T^{2} )^{2} $)($ ( 1 - 61 T^{2} )^{2} $)($ ( 1 + 70 T^{2} + 3721 T^{4} )^{2} $)($ 1 - 61 T^{2} + 3721 T^{4} $)($ 1 - 61 T^{2} + 3721 T^{4} $)($ 1 - 6 T - 71 T^{2} + 90 T^{3} + 5532 T^{4} + 5490 T^{5} - 264191 T^{6} - 1361886 T^{7} + 13845841 T^{8} $)($ ( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} )^{2} $)($ 1 - 6 T - 71 T^{2} + 90 T^{3} + 5532 T^{4} + 5490 T^{5} - 264191 T^{6} - 1361886 T^{7} + 13845841 T^{8} $)($ ( 1 + 13 T + 79 T^{2} - 416 T^{3} - 5930 T^{4} - 25376 T^{5} + 293959 T^{6} + 2950753 T^{7} + 13845841 T^{8} )^{2} $)($ ( 1 + 61 T^{2} + 3721 T^{4} )^{2} $)($ 1 + 299 T^{2} + 43416 T^{4} + 4465735 T^{6} + 393470093 T^{8} + 31461221184 T^{10} + 2332722797890 T^{12} + 164022774523334 T^{14} + 10603540284680400 T^{16} + 610328744001325814 T^{18} + 32298508956660075490 T^{20} + $$16\!\cdots\!24$$ T^{22} + $$75\!\cdots\!33$$ T^{24} + $$31\!\cdots\!35$$ T^{26} + $$11\!\cdots\!36$$ T^{28} + $$29\!\cdots\!59$$ T^{30} + $$36\!\cdots\!61$$ T^{32} $)($ ( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} )( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} ) $)($ 1 + 323 T^{2} + 52152 T^{4} + 6035887 T^{6} + 584536925 T^{8} + 49803739968 T^{10} + 3801157073266 T^{12} + 264102902456582 T^{14} + 16823476283802768 T^{16} + 982726900040941622 T^{18} + 52630216452466386706 T^{20} + $$25\!\cdots\!48$$ T^{22} + $$11\!\cdots\!25$$ T^{24} + $$43\!\cdots\!87$$ T^{26} + $$13\!\cdots\!92$$ T^{28} + $$31\!\cdots\!43$$ T^{30} + $$36\!\cdots\!61$$ T^{32} $)($ 1 - 4 T + 6 T^{2} - 4 T^{3} + 2 T^{4} - 244 T^{5} + 22326 T^{6} - 907924 T^{7} + 13845841 T^{8} $)($ 1 - 24 T + 132 T^{2} + 648 T^{3} + 72 T^{4} - 138600 T^{5} + 1067820 T^{6} - 2497416 T^{7} + 88430 T^{8} - 152342376 T^{9} + 3973358220 T^{10} - 31459566600 T^{11} + 996900552 T^{12} + 547298403048 T^{13} + 6800689415652 T^{14} - 75425828064504 T^{15} + 191707312997281 T^{16} $)
$67$	($ 1 + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 + 67 T^{2} $)($ ( 1 - 70 T^{2} + 4489 T^{4} )^{2} $)($ ( 1 - 67 T^{2} )^{2} $)($ 1 + 10 T^{2} + 4489 T^{4} $)($ ( 1 - 4 T + 67 T^{2} )^{4} $)($ 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} $)($ 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} $)($ 1 - 10 T - 5 T^{2} + 290 T^{3} - 164 T^{4} + 19430 T^{5} - 22445 T^{6} - 3007630 T^{7} + 20151121 T^{8} $)($ 1 - 59 T^{2} - 1008 T^{4} - 264851 T^{6} + 20151121 T^{8} $)($ 1 + 10 T - 5 T^{2} - 290 T^{3} - 164 T^{4} - 19430 T^{5} - 22445 T^{6} + 3007630 T^{7} + 20151121 T^{8} $)($ 1 - 88 T^{2} - 2873 T^{4} - 144232 T^{6} + 57806752 T^{8} - 647457448 T^{10} - 57894170633 T^{12} - 7960337630872 T^{14} + 406067677556641 T^{16} $)($ ( 1 + 14 T + 67 T^{2} )^{2}( 1 - 14 T + 129 T^{2} - 938 T^{3} + 4489 T^{4} ) $)($ ( 1 - 8 T - 138 T^{2} + 1052 T^{3} + 11279 T^{4} - 57198 T^{5} - 930218 T^{6} + 1298482 T^{7} + 71382744 T^{8} + 86998294 T^{9} - 4175748602 T^{10} - 17203042074 T^{11} + 227284493759 T^{12} + 1420331612564 T^{13} - 12483256739322 T^{14} - 48485692842584 T^{15} + 406067677556641 T^{16} )^{2} $)($ 1 + 125 T^{2} + 11136 T^{4} + 561125 T^{6} + 20151121 T^{8} $)($ 1 + 296 T^{2} + 39450 T^{4} + 3796936 T^{6} + 362561921 T^{8} + 33090030780 T^{10} + 2631719645962 T^{12} + 193036342550180 T^{14} + 13423375489686516 T^{16} + 866540141707758020 T^{18} + 53032101023857423402 T^{20} + $$29\!\cdots\!20$$ T^{22} + $$14\!\cdots\!61$$ T^{24} + $$69\!\cdots\!64$$ T^{26} + $$32\!\cdots\!50$$ T^{28} + $$10\!\cdots\!84$$ T^{30} + $$16\!\cdots\!81$$ T^{32} $)($ 1 + 8 T + 18 T^{2} - 736 T^{3} - 5854 T^{4} - 49312 T^{5} + 80802 T^{6} + 2406104 T^{7} + 20151121 T^{8} $)($ 1 + 36 T + 504 T^{2} + 2652 T^{3} - 10800 T^{4} - 217380 T^{5} - 1006488 T^{6} - 637596 T^{7} + 11635982 T^{8} - 42718932 T^{9} - 4518124632 T^{10} - 65379860940 T^{11} - 217632106800 T^{12} + 3580531783764 T^{13} + 45591024613176 T^{14} + 218185617791628 T^{15} + 406067677556641 T^{16} $)
$71$	($ 1 + 71 T^{2} $)($ 1 - 16 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ ( 1 + 110 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 + 71 T^{2} )^{2} $)($ ( 1 - 12 T + 71 T^{2} )^{2} $)($ ( 1 - 74 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 + 8 T + 71 T^{2} )^{2} $)($ ( 1 - 8 T + 71 T^{2} )^{2} $)($ ( 1 - 4 T + 50 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} $)($ ( 1 + 130 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 + 4 T + 50 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} $)($ ( 1 + 176 T^{2} + 16638 T^{4} + 887216 T^{6} + 25411681 T^{8} )^{2} $)($ ( 1 + 71 T^{2} )^{4} $)($ ( 1 + 400 T^{2} + 73324 T^{4} + 8374048 T^{6} + 685441990 T^{8} + 42213575968 T^{10} + 1863286097644 T^{12} + 51240113568400 T^{14} + 645753531245761 T^{16} )^{2} $)($ ( 1 - 6 T + 71 T^{2} )^{4} $)($ ( 1 + 18 T + 332 T^{2} + 3582 T^{3} + 36198 T^{4} + 254322 T^{5} + 1673612 T^{6} + 6442398 T^{7} + 25411681 T^{8} )^{4} $)($ 1 - 12 T + 72 T^{2} - 876 T^{3} + 10654 T^{4} - 62196 T^{5} + 362952 T^{6} - 4294932 T^{7} + 25411681 T^{8} $)($ 1 - 24 T + 288 T^{2} - 2904 T^{3} + 21308 T^{4} - 62712 T^{5} - 415008 T^{6} + 11818440 T^{7} - 144298362 T^{8} + 839109240 T^{9} - 2092055328 T^{10} - 22445314632 T^{11} + 541472098748 T^{12} - 5239482035304 T^{13} + 36892881769248 T^{14} - 218282883801384 T^{15} + 645753531245761 T^{16} $)
$73$	($ 1 - 6 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ ( 1 + 73 T^{2} )^{4} $)($ ( 1 - 14 T + 73 T^{2} )^{2} $)($ ( 1 + 6 T + 73 T^{2} )^{2} $)($ ( 1 + 4 T + 73 T^{2} )^{4} $)($ ( 1 - 3 T + 73 T^{2} )^{2} $)($ ( 1 - 3 T + 73 T^{2} )^{2} $)($ ( 1 + 122 T^{2} + 5329 T^{4} )^{2} $)($ ( 1 + 12 T + 73 T^{2} )^{4} $)($ ( 1 + 122 T^{2} + 5329 T^{4} )^{2} $)($ ( 1 - 15 T + 194 T^{2} - 1095 T^{3} + 5329 T^{4} )^{4} $)($ ( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} )^{2} $)($ ( 1 + T + 214 T^{2} - 5 T^{3} + 20758 T^{4} - 365 T^{5} + 1140406 T^{6} + 389017 T^{7} + 28398241 T^{8} )^{4} $)($ ( 1 - 9 T + 73 T^{2} )^{4} $)($ ( 1 + 11 T + 278 T^{2} + 2325 T^{3} + 29966 T^{4} + 169725 T^{5} + 1481462 T^{6} + 4279187 T^{7} + 28398241 T^{8} )^{4} $)($ ( 1 - 14 T + 98 T^{2} - 1022 T^{3} + 5329 T^{4} )^{2} $)($ 1 + 32 T + 512 T^{2} + 7008 T^{3} + 95708 T^{4} + 1109024 T^{5} + 11042304 T^{6} + 107800160 T^{7} + 989395590 T^{8} + 7869411680 T^{9} + 58844438016 T^{10} + 431429189408 T^{11} + 2717938849628 T^{12} + 14528085723744 T^{13} + 77483123859968 T^{14} + 353516752611104 T^{15} + 806460091894081 T^{16} $)
$79$	($ 1 + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 + 79 T^{2} $)($ ( 1 - 142 T^{2} + 6241 T^{4} )^{2} $)($ ( 1 - 10 T + 79 T^{2} )^{2} $)($ ( 1 + 10 T + 79 T^{2} )^{2} $)($ ( 1 - 146 T^{2} + 6241 T^{4} )^{2} $)($ 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 - 22 T + 211 T^{2} - 2530 T^{3} + 30052 T^{4} - 199870 T^{5} + 1316851 T^{6} - 10846858 T^{7} + 38950081 T^{8} $)($ ( 1 - 142 T^{2} + 6241 T^{4} )( 1 + 11 T^{2} + 6241 T^{4} ) $)($ 1 + 22 T + 211 T^{2} + 2530 T^{3} + 30052 T^{4} + 199870 T^{5} + 1316851 T^{6} + 10846858 T^{7} + 38950081 T^{8} $)($ 1 - 181 T^{2} + 12757 T^{4} - 1361482 T^{6} + 156748534 T^{8} - 8497009162 T^{10} + 496886183317 T^{12} - 43998829449301 T^{14} + 1517108809906561 T^{16} $)($ ( 1 + 79 T^{2} + 6241 T^{4} )^{2} $)($ 1 + 383 T^{2} + 74724 T^{4} + 9593503 T^{6} + 916548293 T^{8} + 73505234952 T^{10} + 5745220732498 T^{12} + 475438917658202 T^{14} + 38877973133064792 T^{16} + 2967214285104838682 T^{18} + $$22\!\cdots\!38$$ T^{20} + $$17\!\cdots\!92$$ T^{22} + $$13\!\cdots\!73$$ T^{24} + $$90\!\cdots\!03$$ T^{26} + $$44\!\cdots\!84$$ T^{28} + $$14\!\cdots\!23$$ T^{30} + $$23\!\cdots\!21$$ T^{32} $)($ ( 1 + 14 T + 117 T^{2} + 1106 T^{3} + 6241 T^{4} )^{2} $)($ ( 1 - 15 T - 80 T^{2} + 1305 T^{3} + 13273 T^{4} - 59400 T^{5} - 1907150 T^{6} + 913560 T^{7} + 190569148 T^{8} + 72171240 T^{9} - 11902523150 T^{10} - 29286516600 T^{11} + 516984425113 T^{12} + 4015558600695 T^{13} - 19446996441680 T^{14} - 288058634792385 T^{15} + 1517108809906561 T^{16} )^{2} $)($ ( 1 - 122 T^{2} + 6241 T^{4} )^{2} $)($ 1 - 120 T^{2} + 10940 T^{4} + 170552 T^{6} - 23710074 T^{8} + 1064415032 T^{10} + 426113886140 T^{12} - 29170494662520 T^{14} + 1517108809906561 T^{16} $)
$83$	($ 1 + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 83 T^{2} $)($ ( 1 + 134 T^{2} + 6889 T^{4} )^{2} $)($ 1 - 134 T^{2} + 6889 T^{4} $)($ 1 + 90 T^{2} + 6889 T^{4} $)($ ( 1 + 34 T^{2} + 6889 T^{4} )^{2} $)($ 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 + 6 T - 133 T^{2} + 18 T^{3} + 18684 T^{4} + 1494 T^{5} - 916237 T^{6} + 3430722 T^{7} + 47458321 T^{8} $)($ 1 - 91 T^{2} + 1392 T^{4} - 626899 T^{6} + 47458321 T^{8} $)($ 1 - 6 T - 133 T^{2} - 18 T^{3} + 18684 T^{4} - 1494 T^{5} - 916237 T^{6} - 3430722 T^{7} + 47458321 T^{8} $)($ 1 - 125 T^{2} + 6925 T^{4} + 634750 T^{6} - 79408946 T^{8} + 4372792750 T^{10} + 328648872925 T^{12} - 40867546671125 T^{14} + 2252292232139041 T^{16} $)($ ( 1 - 18 T + 241 T^{2} - 1494 T^{3} + 6889 T^{4} )( 1 + 18 T + 241 T^{2} + 1494 T^{3} + 6889 T^{4} ) $)($ ( 1 + 27 T + 544 T^{2} + 8127 T^{3} + 107593 T^{4} + 1304076 T^{5} + 14403022 T^{6} + 148987620 T^{7} + 1398163588 T^{8} + 12365972460 T^{9} + 99222418558 T^{10} + 745653703812 T^{11} + 5106183131353 T^{12} + 32012583305661 T^{13} + 177855563112736 T^{14} + 732673376719929 T^{15} + 2252292232139041 T^{16} )^{2} $)($ 1 + 150 T^{2} + 15611 T^{4} + 1033350 T^{6} + 47458321 T^{8} $)($ 1 + 559 T^{2} + 168260 T^{4} + 35967119 T^{6} + 6055752221 T^{8} + 843016361960 T^{10} + 99713806040442 T^{12} + 10182388433060610 T^{14} + 904920089638581976 T^{16} + 70146473915354542290 T^{18} + $$47\!\cdots\!82$$ T^{20} + $$27\!\cdots\!40$$ T^{22} + $$13\!\cdots\!61$$ T^{24} + $$55\!\cdots\!31$$ T^{26} + $$17\!\cdots\!60$$ T^{28} + $$41\!\cdots\!11$$ T^{30} + $$50\!\cdots\!81$$ T^{32} $)($ 1 + 16 T + 114 T^{2} + 792 T^{3} + 6370 T^{4} + 65736 T^{5} + 785346 T^{6} + 9148592 T^{7} + 47458321 T^{8} $)($ 1 + 20 T + 184 T^{2} + 2684 T^{3} + 37008 T^{4} + 337916 T^{5} + 3624872 T^{6} + 38211284 T^{7} + 335969678 T^{8} + 3171536572 T^{9} + 24971743208 T^{10} + 193215975892 T^{11} + 1756337543568 T^{12} + 10572385085812 T^{13} + 60157028699896 T^{14} + 542721019792540 T^{15} + 2252292232139041 T^{16} $)
$89$	($ 1 + 16 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 16 T + 89 T^{2} $)($ ( 1 - 160 T^{2} + 7921 T^{4} )^{2} $)($ ( 1 + 89 T^{2} )^{2} $)($ ( 1 - 10 T + 89 T^{2} )^{2} $)($ ( 1 - 128 T^{2} + 7921 T^{4} )^{2} $)($ ( 1 + 10 T + 89 T^{2} )^{2} $)($ ( 1 + 10 T + 89 T^{2} )^{2} $)($ ( 1 + 16 T + 218 T^{2} + 1424 T^{3} + 7921 T^{4} )^{2} $)($ ( 1 + 4 T + 89 T^{2} )^{4} $)($ ( 1 + 16 T + 218 T^{2} + 1424 T^{3} + 7921 T^{4} )^{2} $)($ ( 1 - 14 T + 194 T^{2} - 1246 T^{3} + 7921 T^{4} )^{4} $)($ ( 1 - 18 T + 89 T^{2} )^{2}( 1 + 18 T + 89 T^{2} )^{2} $)($ ( 1 - 440 T^{2} + 100348 T^{4} - 14946776 T^{6} + 1566592486 T^{8} - 118393412696 T^{10} + 6296058399868 T^{12} - 218671768022840 T^{14} + 3936588805702081 T^{16} )^{2} $)($ ( 1 + 14 T + 89 T^{2} )^{4} $)($ ( 1 - 16 T + 408 T^{2} - 4116 T^{3} + 56278 T^{4} - 366324 T^{5} + 3231768 T^{6} - 11279504 T^{7} + 62742241 T^{8} )^{4} $)($ 1 + 12 T + 72 T^{2} + 516 T^{3} + 1582 T^{4} + 45924 T^{5} + 570312 T^{6} + 8459628 T^{7} + 62742241 T^{8} $)($ 1 - 16 T + 128 T^{2} - 2096 T^{3} + 18652 T^{4} + 22640 T^{5} - 553088 T^{6} + 12396240 T^{7} - 224072442 T^{8} + 1103265360 T^{9} - 4381010048 T^{10} + 15960498160 T^{11} + 1170268279132 T^{12} - 11704188605104 T^{13} + 63613605243008 T^{14} - 707701358328464 T^{15} + 3936588805702081 T^{16} $)
$97$	($ 1 + 18 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ ( 1 + 8 T + 97 T^{2} )^{4} $)($ ( 1 - 2 T + 97 T^{2} )^{2} $)($ ( 1 + 2 T + 97 T^{2} )^{2} $)($ ( 1 - 8 T + 97 T^{2} )^{4} $)($ 1 - 11 T + 24 T^{2} - 1067 T^{3} + 9409 T^{4} $)($ 1 - 11 T + 24 T^{2} - 1067 T^{3} + 9409 T^{4} $)($ 1 + 2 T - 167 T^{2} - 46 T^{3} + 19444 T^{4} - 4462 T^{5} - 1571303 T^{6} + 1825346 T^{7} + 88529281 T^{8} $)($ ( 1 - 3 T - 88 T^{2} - 291 T^{3} + 9409 T^{4} )^{2} $)($ 1 + 2 T - 167 T^{2} - 46 T^{3} + 19444 T^{4} - 4462 T^{5} - 1571303 T^{6} + 1825346 T^{7} + 88529281 T^{8} $)($ ( 1 + 9 T - 16 T^{2} + 873 T^{3} + 9409 T^{4} )^{4} $)($ ( 1 + 10 T + 97 T^{2} )^{2}( 1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4} ) $)($ ( 1 - 4 T - 198 T^{2} - 320 T^{3} + 21017 T^{4} + 106308 T^{5} - 1078406 T^{6} - 6931984 T^{7} + 64836612 T^{8} - 672402448 T^{9} - 10146722054 T^{10} + 97024441284 T^{11} + 1860619898777 T^{12} - 2747948882240 T^{13} - 164928456975942 T^{14} - 323193137912452 T^{15} + 7837433594376961 T^{16} )^{2} $)($ ( 1 + T - 96 T^{2} + 97 T^{3} + 9409 T^{4} )^{2} $)($ ( 1 - 254 T^{2} + 1560 T^{3} + 35209 T^{4} - 273780 T^{5} - 2055806 T^{6} + 15575820 T^{7} + 104325124 T^{8} + 1510854540 T^{9} - 19343078654 T^{10} - 249871613940 T^{11} + 3117027454729 T^{12} + 13396250800920 T^{13} - 211574889251966 T^{14} + 7837433594376961 T^{16} )^{2} $)($ ( 1 + 20 T + 222 T^{2} + 1940 T^{3} + 9409 T^{4} )^{2} $)($ ( 1 - 16 T + 428 T^{2} - 4368 T^{3} + 63222 T^{4} - 423696 T^{5} + 4027052 T^{6} - 14602768 T^{7} + 88529281 T^{8} )^{2} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(9216\)
Trace bound:			\(17\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

Hecke Characteristic Polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	288.2

Level	288
Weight	2
Dimension	981
Nonzero newspaces	12
Newform subspaces	28
Sturm bound	9216
Trace bound	17

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
288.2.a	\(\chi_{288}(1, \cdot)\)	288.2.a.a	1	1
		288.2.a.b	1
		288.2.a.c	1
		288.2.a.d	1
		288.2.a.e	1
288.2.c	\(\chi_{288}(287, \cdot)\)	288.2.c.a	4	1
288.2.d	\(\chi_{288}(145, \cdot)\)	288.2.d.a	2	1
288.2.d	\(\chi_{288}(145, \cdot)\)	288.2.d.b	2	1
288.2.f	\(\chi_{288}(143, \cdot)\)	288.2.f.a	4	1
288.2.i	\(\chi_{288}(97, \cdot)\)	288.2.i.a	2	2
		288.2.i.b	2
		288.2.i.c	4
		288.2.i.d	4
		288.2.i.e	4
		288.2.i.f	8
288.2.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.2.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.2.p	\(\chi_{288}(47, \cdot)\)	288.2.p.a	4	2
288.2.p	\(\chi_{288}(47, \cdot)\)	288.2.p.b	16	2
288.2.r	\(\chi_{288}(49, \cdot)\)	288.2.r.a	4	2
288.2.r	\(\chi_{288}(49, \cdot)\)	288.2.r.b	16	2
288.2.s	\(\chi_{288}(95, \cdot)\)	288.2.s.a	24	2
288.2.v	\(\chi_{288}(37, \cdot)\)	288.2.v.a	4	4
		288.2.v.b	8
		288.2.v.c	32
		288.2.v.d	32
288.2.w	\(\chi_{288}(35, \cdot)\)	288.2.w.a	32	4
288.2.w	\(\chi_{288}(35, \cdot)\)	288.2.w.b	32	4
288.2.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.2.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.2.bc	\(\chi_{288}(13, \cdot)\)	288.2.bc.a	368	8
288.2.bf	\(\chi_{288}(11, \cdot)\)	288.2.bf.a	368	8