Properties

Label 76.5
Level 76
Weight 5
Dimension 400
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 1800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(1800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(76))\).

Total New Old
Modular forms 765 432 333
Cusp forms 675 400 275
Eisenstein series 90 32 58

Trace form

\( 400 q - q^{2} - 41 q^{4} + 10 q^{5} - 9 q^{6} + 119 q^{8} - 180 q^{9} + O(q^{10}) \) \( 400 q - q^{2} - 41 q^{4} + 10 q^{5} - 9 q^{6} + 119 q^{8} - 180 q^{9} - 121 q^{10} - 9 q^{12} + 398 q^{13} - 9 q^{14} - 1134 q^{15} - 521 q^{16} - 959 q^{17} + 630 q^{18} + 777 q^{19} + 430 q^{20} + 2061 q^{21} - 9 q^{22} + 945 q^{23} - 9 q^{24} + 966 q^{25} - 1913 q^{26} - 7056 q^{27} - 6084 q^{28} - 1046 q^{29} + 4842 q^{30} + 2808 q^{31} + 10814 q^{32} + 10782 q^{33} + 10532 q^{34} + 4752 q^{35} + 3789 q^{36} - 4360 q^{37} - 4734 q^{38} - 7992 q^{39} - 15220 q^{40} + 1306 q^{41} - 26559 q^{42} - 7563 q^{43} - 12294 q^{44} + 225 q^{45} - 4464 q^{46} - 2079 q^{47} + 17316 q^{48} - 2087 q^{49} + 20778 q^{50} - 5481 q^{51} + 7607 q^{52} - 15458 q^{53} + 720 q^{54} - 3924 q^{55} - 18 q^{56} + 5067 q^{57} + 638 q^{58} + 14715 q^{59} + 29070 q^{60} - 12154 q^{61} + 26316 q^{62} + 14220 q^{63} - 13745 q^{64} + 29363 q^{65} - 33057 q^{66} + 23163 q^{67} - 48680 q^{68} + 77229 q^{69} - 62109 q^{70} - 24543 q^{71} - 44316 q^{72} + 12809 q^{73} + 6559 q^{74} + 13581 q^{76} - 17181 q^{77} + 39825 q^{78} - 5766 q^{79} + 55759 q^{80} - 71100 q^{81} + 84362 q^{82} - 28053 q^{83} + 84555 q^{84} - 120638 q^{85} + 35334 q^{86} - 75960 q^{87} + 6543 q^{88} + 12451 q^{89} - 63306 q^{90} + 9732 q^{91} - 80334 q^{92} + 90990 q^{93} - 118350 q^{94} - 81729 q^{95} - 118746 q^{96} - 16909 q^{97} - 23866 q^{98} + 64044 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.5.b \(\chi_{76}(39, \cdot)\) 76.5.b.a 36 1
76.5.c \(\chi_{76}(37, \cdot)\) 76.5.c.a 2 1
76.5.c.b 4
76.5.g \(\chi_{76}(7, \cdot)\) 76.5.g.a 76 2
76.5.h \(\chi_{76}(65, \cdot)\) 76.5.h.a 12 2
76.5.j \(\chi_{76}(13, \cdot)\) 76.5.j.a 42 6
76.5.l \(\chi_{76}(23, \cdot)\) 76.5.l.a 228 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)