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Properties

Label 476.4
Level 476
Weight 4
Dimension 11360
Nonzero newspaces 20
Sturm bound 55296
Trace bound 5

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Defining parameters

Level: \( N \) = \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(55296\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(476))\).

Total New Old
Modular forms 21216 11656 9560
Cusp forms 20256 11360 8896
Eisenstein series 960 296 664

Trace form

\( 11360 q - 26 q^{2} + 12 q^{3} - 26 q^{4} - 76 q^{5} - 32 q^{6} - 48 q^{7} - 170 q^{8} - 136 q^{9} + O(q^{10}) \) \( 11360 q - 26 q^{2} + 12 q^{3} - 26 q^{4} - 76 q^{5} - 32 q^{6} - 48 q^{7} - 170 q^{8} - 136 q^{9} - 8 q^{10} + 392 q^{11} + 304 q^{12} + 172 q^{13} + 278 q^{14} - 288 q^{15} + 126 q^{16} - 380 q^{17} - 106 q^{18} - 796 q^{19} - 32 q^{20} - 1268 q^{21} - 332 q^{22} + 248 q^{23} - 2552 q^{24} + 376 q^{25} - 2296 q^{26} + 792 q^{27} - 1186 q^{28} + 2160 q^{29} + 856 q^{30} + 1056 q^{31} + 774 q^{32} + 216 q^{33} + 4192 q^{34} - 4 q^{35} + 5398 q^{36} + 200 q^{37} + 4248 q^{38} + 3824 q^{39} + 1912 q^{40} + 3096 q^{41} + 2096 q^{42} - 1656 q^{43} - 796 q^{44} - 3276 q^{45} - 1652 q^{46} - 2464 q^{47} + 400 q^{48} - 2312 q^{49} - 2994 q^{50} - 3956 q^{51} - 5248 q^{52} - 8568 q^{53} - 408 q^{54} - 8512 q^{55} - 4514 q^{56} - 11800 q^{57} - 2484 q^{58} - 492 q^{59} - 6736 q^{60} + 4796 q^{61} - 4176 q^{62} + 6696 q^{63} - 1826 q^{64} + 17584 q^{65} - 5136 q^{66} + 3488 q^{67} - 5740 q^{68} + 16408 q^{69} + 9216 q^{70} + 3888 q^{71} + 2174 q^{72} + 13184 q^{73} + 1396 q^{74} + 5076 q^{75} + 528 q^{76} + 4304 q^{77} + 1616 q^{78} - 3352 q^{79} - 6128 q^{80} - 25872 q^{81} - 3976 q^{82} - 16988 q^{83} - 21384 q^{84} - 26572 q^{85} - 37004 q^{86} - 17016 q^{87} - 17540 q^{88} + 2120 q^{89} - 5472 q^{90} + 1428 q^{91} + 9116 q^{92} + 15072 q^{93} + 22168 q^{94} + 12952 q^{95} + 45120 q^{96} + 7808 q^{97} + 31582 q^{98} + 11288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(476))\)

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
476.4.a \(\chi_{476}(1, \cdot)\) 476.4.a.a 6 1
476.4.a.b 6
476.4.a.c 6
476.4.a.d 6
476.4.b \(\chi_{476}(169, \cdot)\) 476.4.b.a 28 1
476.4.e \(\chi_{476}(475, \cdot)\) n/a 212 1
476.4.f \(\chi_{476}(307, \cdot)\) n/a 192 1
476.4.i \(\chi_{476}(137, \cdot)\) 476.4.i.a 28 2
476.4.i.b 36
476.4.k \(\chi_{476}(55, \cdot)\) n/a 424 2
476.4.l \(\chi_{476}(225, \cdot)\) 476.4.l.a 56 2
476.4.p \(\chi_{476}(103, \cdot)\) n/a 384 2
476.4.q \(\chi_{476}(271, \cdot)\) n/a 424 2
476.4.t \(\chi_{476}(305, \cdot)\) 476.4.t.a 72 2
476.4.u \(\chi_{476}(253, \cdot)\) n/a 104 4
476.4.w \(\chi_{476}(83, \cdot)\) n/a 848 4
476.4.z \(\chi_{476}(47, \cdot)\) n/a 848 4
476.4.ba \(\chi_{476}(81, \cdot)\) n/a 144 4
476.4.bd \(\chi_{476}(71, \cdot)\) n/a 1296 8
476.4.be \(\chi_{476}(41, \cdot)\) n/a 288 8
476.4.bh \(\chi_{476}(9, \cdot)\) n/a 288 8
476.4.bj \(\chi_{476}(19, \cdot)\) n/a 1696 8
476.4.bl \(\chi_{476}(5, \cdot)\) n/a 576 16
476.4.bm \(\chi_{476}(11, \cdot)\) n/a 3392 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(476))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(476)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 1}\)