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

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

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

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