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Properties

Label 456.4
Level 456
Weight 4
Dimension 7184
Nonzero newspaces 18
Sturm bound 46080
Trace bound 6

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Defining parameters

Level: \( N \) = \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(46080\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(456))\).

Total New Old
Modular forms 17712 7320 10392
Cusp forms 16848 7184 9664
Eisenstein series 864 136 728

Trace form

\( 7184 q - 4 q^{2} - 20 q^{3} - 76 q^{4} - 28 q^{5} + 10 q^{6} - 44 q^{7} + 152 q^{8} + 58 q^{9} + O(q^{10}) \) \( 7184 q - 4 q^{2} - 20 q^{3} - 76 q^{4} - 28 q^{5} + 10 q^{6} - 44 q^{7} + 152 q^{8} + 58 q^{9} - 108 q^{10} + 56 q^{11} + 94 q^{12} + 148 q^{13} + 200 q^{14} + 18 q^{15} + 156 q^{16} - 268 q^{17} - 350 q^{18} - 100 q^{19} - 112 q^{20} + 144 q^{21} - 932 q^{22} - 672 q^{23} - 1082 q^{24} - 94 q^{25} - 112 q^{26} + 853 q^{27} - 388 q^{28} + 1536 q^{29} + 486 q^{30} + 1256 q^{31} + 496 q^{32} - 658 q^{33} + 2628 q^{34} - 1560 q^{35} + 2038 q^{36} - 1392 q^{37} + 776 q^{38} - 2106 q^{39} + 1996 q^{40} - 1936 q^{41} - 1530 q^{42} - 1404 q^{43} - 2304 q^{44} + 774 q^{45} - 3572 q^{46} + 2244 q^{47} - 4610 q^{48} + 2106 q^{49} - 3940 q^{50} - 709 q^{51} - 3524 q^{52} + 260 q^{53} + 4210 q^{54} - 1300 q^{55} + 3728 q^{56} - 260 q^{57} + 4880 q^{58} - 1192 q^{59} + 1626 q^{60} - 4424 q^{61} - 15044 q^{62} - 540 q^{63} - 13348 q^{64} + 1780 q^{65} - 4882 q^{66} + 4756 q^{67} - 1164 q^{68} - 48 q^{69} + 9308 q^{70} + 7636 q^{71} - 1142 q^{72} + 10766 q^{73} + 17888 q^{74} + 12904 q^{75} + 25100 q^{76} + 6540 q^{77} + 16578 q^{78} + 15992 q^{79} + 20064 q^{80} - 1478 q^{81} + 28528 q^{82} + 5068 q^{83} + 13062 q^{84} - 2296 q^{85} - 7300 q^{86} - 7434 q^{87} - 18212 q^{88} - 10624 q^{89} - 12006 q^{90} - 33684 q^{91} - 38916 q^{92} - 4638 q^{93} - 33036 q^{94} - 6392 q^{95} - 12884 q^{96} + 3188 q^{97} - 6708 q^{98} - 13849 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.4.a \(\chi_{456}(1, \cdot)\) 456.4.a.a 2 1
456.4.a.b 2
456.4.a.c 3
456.4.a.d 4
456.4.a.e 4
456.4.a.f 4
456.4.a.g 4
456.4.a.h 5
456.4.d \(\chi_{456}(191, \cdot)\) None 0 1
456.4.e \(\chi_{456}(379, \cdot)\) n/a 120 1
456.4.f \(\chi_{456}(113, \cdot)\) 456.4.f.a 30 1
456.4.f.b 30
456.4.g \(\chi_{456}(229, \cdot)\) n/a 108 1
456.4.j \(\chi_{456}(419, \cdot)\) n/a 216 1
456.4.k \(\chi_{456}(151, \cdot)\) None 0 1
456.4.p \(\chi_{456}(341, \cdot)\) n/a 236 1
456.4.q \(\chi_{456}(49, \cdot)\) 456.4.q.a 14 2
456.4.q.b 14
456.4.q.c 16
456.4.q.d 16
456.4.t \(\chi_{456}(31, \cdot)\) None 0 2
456.4.u \(\chi_{456}(11, \cdot)\) n/a 472 2
456.4.v \(\chi_{456}(221, \cdot)\) n/a 472 2
456.4.y \(\chi_{456}(259, \cdot)\) n/a 240 2
456.4.z \(\chi_{456}(239, \cdot)\) None 0 2
456.4.be \(\chi_{456}(277, \cdot)\) n/a 240 2
456.4.bf \(\chi_{456}(65, \cdot)\) n/a 120 2
456.4.bg \(\chi_{456}(25, \cdot)\) n/a 180 6
456.4.bj \(\chi_{456}(29, \cdot)\) n/a 1416 6
456.4.bk \(\chi_{456}(61, \cdot)\) n/a 720 6
456.4.bm \(\chi_{456}(41, \cdot)\) n/a 360 6
456.4.bp \(\chi_{456}(67, \cdot)\) n/a 720 6
456.4.br \(\chi_{456}(23, \cdot)\) None 0 6
456.4.bs \(\chi_{456}(79, \cdot)\) None 0 6
456.4.bu \(\chi_{456}(35, \cdot)\) n/a 1416 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)