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Properties

Label 116.4
Level 116
Weight 4
Dimension 707
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 3360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(3360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(116))\).

Total New Old
Modular forms 1330 763 567
Cusp forms 1190 707 483
Eisenstein series 140 56 84

Trace form

\( 707 q - 14 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 14 q^{8} - 28 q^{9} + O(q^{10}) \) \( 707 q - 14 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 14 q^{8} - 28 q^{9} - 14 q^{10} - 14 q^{12} - 28 q^{13} - 14 q^{14} - 14 q^{16} - 28 q^{17} - 14 q^{18} - 14 q^{20} - 812 q^{21} - 14 q^{22} - 28 q^{23} - 14 q^{24} + 420 q^{25} - 14 q^{26} + 1092 q^{27} + 756 q^{29} - 28 q^{30} + 616 q^{31} - 14 q^{32} + 308 q^{33} - 14 q^{34} - 392 q^{35} - 14 q^{36} - 644 q^{37} - 14 q^{38} - 2296 q^{39} - 14 q^{40} - 28 q^{41} - 14 q^{42} + 1736 q^{44} + 3437 q^{45} + 5236 q^{46} + 1484 q^{47} + 3682 q^{48} + 812 q^{49} - 112 q^{50} - 840 q^{51} - 3038 q^{52} - 2359 q^{53} - 5684 q^{54} - 5712 q^{55} - 5404 q^{56} - 3192 q^{57} - 9590 q^{58} - 1540 q^{59} - 8582 q^{60} - 2548 q^{61} - 3640 q^{62} - 3024 q^{63} - 1904 q^{64} - 91 q^{65} + 1666 q^{66} + 1848 q^{67} + 5180 q^{68} + 4172 q^{69} + 11074 q^{70} - 2968 q^{71} + 10696 q^{72} + 3689 q^{73} + 2996 q^{74} - 3220 q^{75} - 14 q^{76} - 308 q^{77} - 14 q^{78} + 840 q^{79} - 14 q^{80} + 6244 q^{81} - 14 q^{82} + 4144 q^{83} - 392 q^{84} + 7028 q^{85} + 6020 q^{87} - 28 q^{88} + 5572 q^{89} + 364 q^{90} + 5544 q^{91} - 14 q^{92} + 2436 q^{93} - 14 q^{94} + 1568 q^{95} - 11144 q^{96} + 16779 q^{97} - 13384 q^{98} + 3892 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)

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
116.4.a \(\chi_{116}(1, \cdot)\) 116.4.a.a 2 1
116.4.a.b 2
116.4.a.c 3
116.4.c \(\chi_{116}(57, \cdot)\) 116.4.c.a 8 1
116.4.e \(\chi_{116}(75, \cdot)\) 116.4.e.a 2 2
116.4.e.b 84
116.4.g \(\chi_{116}(25, \cdot)\) 116.4.g.a 42 6
116.4.i \(\chi_{116}(5, \cdot)\) 116.4.i.a 48 6
116.4.l \(\chi_{116}(3, \cdot)\) 116.4.l.a 12 12
116.4.l.b 504

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(116))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(116)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)