Properties

Label 1287.2
Level 1287
Weight 2
Dimension 45630
Nonzero newspaces 60
Sturm bound 241920
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(241920\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1287))\).

Total New Old
Modular forms 62400 47414 14986
Cusp forms 58561 45630 12931
Eisenstein series 3839 1784 2055

Trace form

\( 45630 q - 114 q^{2} - 152 q^{3} - 114 q^{4} - 114 q^{5} - 152 q^{6} - 100 q^{7} - 76 q^{8} - 152 q^{9} + O(q^{10}) \) \( 45630 q - 114 q^{2} - 152 q^{3} - 114 q^{4} - 114 q^{5} - 152 q^{6} - 100 q^{7} - 76 q^{8} - 152 q^{9} - 282 q^{10} - 116 q^{11} - 352 q^{12} - 100 q^{13} - 204 q^{14} - 152 q^{15} - 14 q^{16} - 66 q^{17} - 152 q^{18} - 272 q^{19} - 58 q^{20} - 152 q^{21} - 42 q^{22} - 250 q^{23} - 260 q^{24} - 92 q^{25} - 104 q^{26} - 404 q^{27} - 436 q^{28} - 226 q^{29} - 368 q^{30} - 214 q^{31} - 490 q^{32} - 312 q^{33} - 440 q^{34} - 380 q^{35} - 484 q^{36} - 440 q^{37} - 496 q^{38} - 298 q^{39} - 568 q^{40} - 246 q^{41} - 416 q^{42} - 124 q^{43} - 226 q^{44} - 492 q^{45} - 236 q^{46} - 104 q^{47} - 376 q^{48} - 256 q^{50} - 220 q^{51} - 22 q^{52} - 212 q^{53} - 312 q^{54} - 370 q^{55} - 408 q^{56} - 312 q^{57} - 114 q^{58} - 210 q^{59} - 552 q^{60} - 70 q^{61} - 480 q^{62} - 408 q^{63} - 684 q^{64} - 360 q^{65} - 772 q^{66} - 534 q^{67} - 842 q^{68} - 456 q^{69} - 624 q^{70} - 558 q^{71} - 764 q^{72} - 620 q^{73} - 870 q^{74} - 532 q^{75} - 460 q^{76} - 408 q^{77} - 948 q^{78} - 320 q^{79} - 522 q^{80} - 344 q^{81} - 670 q^{82} - 248 q^{83} - 308 q^{84} - 182 q^{85} - 196 q^{86} - 144 q^{87} - 86 q^{88} - 130 q^{89} - 64 q^{90} - 388 q^{91} - 40 q^{92} - 96 q^{93} + 36 q^{94} + 300 q^{95} + 740 q^{96} + 126 q^{97} + 454 q^{98} + 216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1287))\)

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
1287.2.a \(\chi_{1287}(1, \cdot)\) 1287.2.a.a 1 1
1287.2.a.b 1
1287.2.a.c 1
1287.2.a.d 1
1287.2.a.e 1
1287.2.a.f 2
1287.2.a.g 2
1287.2.a.h 3
1287.2.a.i 3
1287.2.a.j 3
1287.2.a.k 4
1287.2.a.l 4
1287.2.a.m 4
1287.2.a.n 4
1287.2.a.o 5
1287.2.a.p 5
1287.2.a.q 6
1287.2.b \(\chi_{1287}(298, \cdot)\) 1287.2.b.a 10 1
1287.2.b.b 12
1287.2.b.c 14
1287.2.b.d 20
1287.2.e \(\chi_{1287}(1286, \cdot)\) 1287.2.e.a 4 1
1287.2.e.b 4
1287.2.e.c 4
1287.2.e.d 4
1287.2.e.e 40
1287.2.f \(\chi_{1287}(989, \cdot)\) 1287.2.f.a 48 1
1287.2.i \(\chi_{1287}(430, \cdot)\) n/a 240 2
1287.2.j \(\chi_{1287}(529, \cdot)\) n/a 280 2
1287.2.k \(\chi_{1287}(100, \cdot)\) n/a 120 2
1287.2.l \(\chi_{1287}(133, \cdot)\) n/a 280 2
1287.2.m \(\chi_{1287}(980, \cdot)\) 1287.2.m.a 4 2
1287.2.m.b 40
1287.2.m.c 44
1287.2.p \(\chi_{1287}(109, \cdot)\) n/a 136 2
1287.2.q \(\chi_{1287}(235, \cdot)\) n/a 240 4
1287.2.r \(\chi_{1287}(329, \cdot)\) n/a 328 2
1287.2.u \(\chi_{1287}(1024, \cdot)\) n/a 280 2
1287.2.w \(\chi_{1287}(692, \cdot)\) n/a 112 2
1287.2.z \(\chi_{1287}(659, \cdot)\) n/a 328 2
1287.2.bb \(\chi_{1287}(131, \cdot)\) n/a 288 2
1287.2.bf \(\chi_{1287}(199, \cdot)\) n/a 116 2
1287.2.bh \(\chi_{1287}(428, \cdot)\) n/a 328 2
1287.2.bj \(\chi_{1287}(725, \cdot)\) n/a 328 2
1287.2.bk \(\chi_{1287}(166, \cdot)\) n/a 280 2
1287.2.bm \(\chi_{1287}(727, \cdot)\) n/a 280 2
1287.2.bo \(\chi_{1287}(296, \cdot)\) n/a 112 2
1287.2.bs \(\chi_{1287}(230, \cdot)\) n/a 328 2
1287.2.bv \(\chi_{1287}(404, \cdot)\) n/a 192 4
1287.2.bw \(\chi_{1287}(116, \cdot)\) n/a 224 4
1287.2.bz \(\chi_{1287}(64, \cdot)\) n/a 272 4
1287.2.ca \(\chi_{1287}(175, \cdot)\) n/a 656 4
1287.2.cd \(\chi_{1287}(353, \cdot)\) n/a 560 4
1287.2.cf \(\chi_{1287}(122, \cdot)\) n/a 560 4
1287.2.ch \(\chi_{1287}(76, \cdot)\) n/a 656 4
1287.2.cj \(\chi_{1287}(505, \cdot)\) n/a 272 4
1287.2.ck \(\chi_{1287}(89, \cdot)\) n/a 192 4
1287.2.cm \(\chi_{1287}(254, \cdot)\) n/a 560 4
1287.2.co \(\chi_{1287}(538, \cdot)\) n/a 656 4
1287.2.cq \(\chi_{1287}(16, \cdot)\) n/a 1312 8
1287.2.cr \(\chi_{1287}(289, \cdot)\) n/a 544 8
1287.2.cs \(\chi_{1287}(295, \cdot)\) n/a 1312 8
1287.2.ct \(\chi_{1287}(157, \cdot)\) n/a 1152 8
1287.2.cv \(\chi_{1287}(125, \cdot)\) n/a 448 8
1287.2.cw \(\chi_{1287}(73, \cdot)\) n/a 544 8
1287.2.cy \(\chi_{1287}(29, \cdot)\) n/a 1312 8
1287.2.dc \(\chi_{1287}(17, \cdot)\) n/a 448 8
1287.2.de \(\chi_{1287}(25, \cdot)\) n/a 1312 8
1287.2.dg \(\chi_{1287}(49, \cdot)\) n/a 1312 8
1287.2.dh \(\chi_{1287}(140, \cdot)\) n/a 1312 8
1287.2.dj \(\chi_{1287}(194, \cdot)\) n/a 1312 8
1287.2.dl \(\chi_{1287}(82, \cdot)\) n/a 544 8
1287.2.dp \(\chi_{1287}(248, \cdot)\) n/a 1152 8
1287.2.dr \(\chi_{1287}(68, \cdot)\) n/a 1312 8
1287.2.du \(\chi_{1287}(35, \cdot)\) n/a 448 8
1287.2.dw \(\chi_{1287}(4, \cdot)\) n/a 1312 8
1287.2.dz \(\chi_{1287}(95, \cdot)\) n/a 1312 8
1287.2.ea \(\chi_{1287}(5, \cdot)\) n/a 2624 16
1287.2.ec \(\chi_{1287}(19, \cdot)\) n/a 1088 16
1287.2.ee \(\chi_{1287}(7, \cdot)\) n/a 2624 16
1287.2.eh \(\chi_{1287}(20, \cdot)\) n/a 2624 16
1287.2.ej \(\chi_{1287}(71, \cdot)\) n/a 896 16
1287.2.el \(\chi_{1287}(112, \cdot)\) n/a 2624 16
1287.2.en \(\chi_{1287}(85, \cdot)\) n/a 2624 16
1287.2.eo \(\chi_{1287}(59, \cdot)\) n/a 2624 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 2}\)