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Properties

Label 76.8
Level 76
Weight 8
Dimension 717
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 2880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(2880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(76))\).

Total New Old
Modular forms 1305 753 552
Cusp forms 1215 717 498
Eisenstein series 90 36 54

Trace form

\( 717 q - 9 q^{2} - 9 q^{4} - 18 q^{5} - 9 q^{6} - 9 q^{8} - 18 q^{9} + O(q^{10}) \) \( 717 q - 9 q^{2} - 9 q^{4} - 18 q^{5} - 9 q^{6} - 9 q^{8} - 18 q^{9} - 9 q^{10} - 9 q^{12} + 22146 q^{13} - 9 q^{14} - 61722 q^{15} - 9 q^{16} + 29349 q^{17} + 100527 q^{19} - 18 q^{20} - 142335 q^{21} - 9 q^{22} - 98397 q^{23} - 9 q^{24} + 258300 q^{25} - 9 q^{26} + 845649 q^{27} - 756738 q^{28} - 597996 q^{29} - 308772 q^{30} + 424098 q^{31} + 1640556 q^{32} + 1644984 q^{33} + 453546 q^{34} - 583596 q^{35} - 3515319 q^{36} - 911754 q^{37} - 2923020 q^{38} - 1397034 q^{39} + 436518 q^{40} + 793260 q^{41} + 6739821 q^{42} + 1719429 q^{43} + 3304296 q^{44} + 5337261 q^{45} - 2094714 q^{46} - 1214253 q^{47} - 11350530 q^{48} - 4946025 q^{49} + 2607084 q^{50} + 817524 q^{51} - 9 q^{52} + 645354 q^{53} - 19692 q^{54} + 5345964 q^{55} + 7469217 q^{57} - 18 q^{58} + 1825695 q^{59} - 15228576 q^{60} - 7236120 q^{61} + 16542576 q^{62} - 18814716 q^{63} + 14544495 q^{64} - 7442613 q^{65} - 14099841 q^{66} + 14941275 q^{67} - 21818988 q^{68} + 57358971 q^{69} - 20398509 q^{70} + 4319235 q^{71} + 16435296 q^{72} - 29130294 q^{73} + 26838207 q^{74} - 17718750 q^{75} + 36422901 q^{76} - 56619027 q^{77} + 15920073 q^{78} + 12511968 q^{79} - 15381009 q^{80} + 55291761 q^{81} - 75428154 q^{82} + 8066403 q^{83} - 66131973 q^{84} + 44757306 q^{85} - 13190382 q^{86} - 51590052 q^{87} + 40974255 q^{88} - 57553083 q^{89} + 85996116 q^{90} - 13484028 q^{91} + 17289126 q^{92} + 104933412 q^{93} + 51790437 q^{95} - 61682634 q^{96} - 40890105 q^{97} - 137750292 q^{98} - 73473813 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.8.a \(\chi_{76}(1, \cdot)\) 76.8.a.a 5 1
76.8.a.b 6
76.8.d \(\chi_{76}(75, \cdot)\) 76.8.d.a 68 1
76.8.e \(\chi_{76}(45, \cdot)\) 76.8.e.a 22 2
76.8.f \(\chi_{76}(27, \cdot)\) 76.8.f.a 136 2
76.8.i \(\chi_{76}(5, \cdot)\) 76.8.i.a 72 6
76.8.k \(\chi_{76}(3, \cdot)\) 76.8.k.a 408 6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)