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Properties

Label 287.4
Level 287
Weight 4
Dimension 9454
Nonzero newspaces 16
Sturm bound 26880
Trace bound 3

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(26880\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(287))\).

Total New Old
Modular forms 10320 9846 474
Cusp forms 9840 9454 386
Eisenstein series 480 392 88

Trace form

\( 9454 q - 74 q^{2} - 62 q^{3} - 74 q^{4} - 98 q^{5} - 140 q^{6} - 142 q^{7} - 134 q^{8} + 10 q^{9} + O(q^{10}) \) \( 9454 q - 74 q^{2} - 62 q^{3} - 74 q^{4} - 98 q^{5} - 140 q^{6} - 142 q^{7} - 134 q^{8} + 10 q^{9} - 20 q^{10} - 74 q^{11} - 164 q^{12} - 80 q^{13} - 142 q^{14} - 332 q^{15} - 194 q^{16} - 230 q^{17} - 38 q^{18} + 238 q^{19} + 256 q^{20} + 362 q^{21} - 176 q^{22} - 494 q^{23} - 356 q^{24} - 494 q^{25} - 80 q^{26} - 140 q^{27} - 478 q^{28} - 212 q^{29} + 5652 q^{30} + 2190 q^{31} + 5042 q^{32} + 1738 q^{33} + 396 q^{34} - 374 q^{35} - 5770 q^{36} - 2510 q^{37} - 2824 q^{38} - 6244 q^{39} - 10456 q^{40} - 2562 q^{41} - 7036 q^{42} - 1320 q^{43} - 6872 q^{44} - 2236 q^{45} - 1420 q^{46} + 562 q^{47} + 5012 q^{48} + 886 q^{49} + 5670 q^{50} + 8242 q^{51} + 13304 q^{52} + 5490 q^{53} + 11340 q^{54} + 316 q^{55} + 1454 q^{56} - 2012 q^{57} - 68 q^{58} - 1910 q^{59} - 920 q^{60} + 70 q^{61} - 1232 q^{62} - 730 q^{63} - 1658 q^{64} + 2648 q^{65} + 25252 q^{66} + 15742 q^{67} + 21044 q^{68} + 16564 q^{69} + 10856 q^{70} + 7704 q^{71} + 2794 q^{72} - 2342 q^{73} - 5696 q^{74} - 13100 q^{75} - 31436 q^{76} - 5442 q^{77} - 27128 q^{78} - 13166 q^{79} - 32896 q^{80} - 30100 q^{81} - 38078 q^{82} - 14564 q^{83} - 17352 q^{84} - 24800 q^{85} - 24720 q^{86} - 7868 q^{87} - 15200 q^{88} - 6198 q^{89} - 7448 q^{90} + 2516 q^{91} + 4888 q^{92} + 10186 q^{93} + 29668 q^{94} + 20286 q^{95} + 53116 q^{96} + 28300 q^{97} + 16942 q^{98} + 26872 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(287))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
287.4.a \(\chi_{287}(1, \cdot)\) 287.4.a.a 1 1
287.4.a.b 11
287.4.a.c 12
287.4.a.d 17
287.4.a.e 19
287.4.c \(\chi_{287}(204, \cdot)\) 287.4.c.a 62 1
287.4.e \(\chi_{287}(165, \cdot)\) 287.4.e.a 72 2
287.4.e.b 88
287.4.f \(\chi_{287}(50, \cdot)\) n/a 128 2
287.4.h \(\chi_{287}(57, \cdot)\) n/a 248 4
287.4.j \(\chi_{287}(81, \cdot)\) n/a 164 2
287.4.l \(\chi_{287}(27, \cdot)\) n/a 328 4
287.4.n \(\chi_{287}(64, \cdot)\) n/a 248 4
287.4.r \(\chi_{287}(9, \cdot)\) n/a 328 4
287.4.s \(\chi_{287}(16, \cdot)\) n/a 656 8
287.4.u \(\chi_{287}(8, \cdot)\) n/a 512 8
287.4.w \(\chi_{287}(3, \cdot)\) n/a 656 8
287.4.z \(\chi_{287}(4, \cdot)\) n/a 656 8
287.4.bb \(\chi_{287}(6, \cdot)\) n/a 1312 16
287.4.bc \(\chi_{287}(2, \cdot)\) n/a 1312 16
287.4.be \(\chi_{287}(12, \cdot)\) n/a 2624 32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(287))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(287)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 1}\)