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

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

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

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