Properties

Label 76.7
Level 76
Weight 7
Dimension 608
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 2520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(2520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(76))\).

Total New Old
Modular forms 1125 640 485
Cusp forms 1035 608 427
Eisenstein series 90 32 58

Trace form

\( 608 q - 17 q^{2} + 215 q^{4} - 58 q^{5} - 969 q^{6} + 1399 q^{8} + 906 q^{9} + O(q^{10}) \) \( 608 q - 17 q^{2} + 215 q^{4} - 58 q^{5} - 969 q^{6} + 1399 q^{8} + 906 q^{9} - 89 q^{10} - 3849 q^{12} - 15962 q^{13} + 9591 q^{14} + 11664 q^{15} - 8713 q^{16} + 26246 q^{17} + 1830 q^{18} - 21168 q^{19} + 2222 q^{20} - 79242 q^{21} - 29769 q^{22} + 3960 q^{23} + 46071 q^{24} + 140706 q^{25} - 11737 q^{26} - 124830 q^{27} + 77028 q^{28} + 13910 q^{29} + 333930 q^{30} + 30780 q^{31} - 236762 q^{32} - 185754 q^{33} - 275756 q^{34} - 225432 q^{35} - 388803 q^{36} - 8012 q^{37} + 380034 q^{38} + 427140 q^{39} + 664420 q^{40} + 75134 q^{41} + 695841 q^{42} + 337176 q^{43} - 249774 q^{44} - 889554 q^{45} - 1132464 q^{46} - 886860 q^{47} - 733476 q^{48} - 148174 q^{49} + 917802 q^{50} + 1534410 q^{51} + 328375 q^{52} + 1484198 q^{53} - 471528 q^{54} + 318816 q^{55} - 460818 q^{56} - 894978 q^{57} - 204002 q^{58} - 1134000 q^{59} + 1972902 q^{60} - 2012126 q^{61} + 233796 q^{62} + 555840 q^{63} - 3147889 q^{64} + 2475562 q^{65} - 899169 q^{66} + 879552 q^{67} + 231152 q^{68} - 2243850 q^{69} + 4591491 q^{70} - 1528560 q^{71} + 4956348 q^{72} - 4328912 q^{73} + 1145039 q^{74} - 1065699 q^{76} + 4866744 q^{77} - 5598543 q^{78} + 1866024 q^{79} - 4344049 q^{80} + 4065372 q^{81} - 6378350 q^{82} - 938448 q^{83} + 1651755 q^{84} - 2931874 q^{85} + 2655726 q^{86} + 1179216 q^{87} + 8630991 q^{88} - 4895422 q^{89} + 6438846 q^{90} + 1260864 q^{91} - 3257094 q^{92} + 4508394 q^{93} - 14661870 q^{94} - 6508080 q^{95} - 1465050 q^{96} + 7023670 q^{97} + 12839854 q^{98} + 1394874 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(76))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
76.7.b \(\chi_{76}(39, \cdot)\) 76.7.b.a 54 1
76.7.c \(\chi_{76}(37, \cdot)\) 76.7.c.a 2 1
76.7.c.b 8
76.7.g \(\chi_{76}(7, \cdot)\) 76.7.g.a 116 2
76.7.h \(\chi_{76}(65, \cdot)\) 76.7.h.a 20 2
76.7.j \(\chi_{76}(13, \cdot)\) 76.7.j.a 60 6
76.7.l \(\chi_{76}(23, \cdot)\) 76.7.l.a 348 6

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)