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Properties

Label 76.11
Level 76
Weight 11
Dimension 1024
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 3960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(3960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(76))\).

Total New Old
Modular forms 1845 1056 789
Cusp forms 1755 1024 731
Eisenstein series 90 32 58

Trace form

\( 1024 q + 15 q^{2} - 41 q^{4} + 3102 q^{5} - 14409 q^{6} + 72567 q^{8} + 57510 q^{9} + O(q^{10}) \) \( 1024 q + 15 q^{2} - 41 q^{4} + 3102 q^{5} - 14409 q^{6} + 72567 q^{8} + 57510 q^{9} - 526489 q^{10} + 1831671 q^{12} + 1258754 q^{13} - 3803529 q^{14} - 2838726 q^{15} + 7224823 q^{16} + 3270261 q^{17} - 9480762 q^{18} - 10958955 q^{19} + 6217902 q^{20} + 4769397 q^{21} + 3992631 q^{22} + 10149525 q^{23} - 35804169 q^{24} - 38265804 q^{25} + 64879335 q^{26} + 23087178 q^{27} + 40727028 q^{28} - 149049138 q^{29} - 102278070 q^{30} + 61388388 q^{31} + 178745910 q^{32} + 289095606 q^{33} - 167892268 q^{34} - 321628392 q^{35} - 562341987 q^{36} - 268817908 q^{37} + 439302114 q^{38} + 789807132 q^{39} + 1173309140 q^{40} + 668349894 q^{41} - 2091051999 q^{42} - 413029263 q^{43} - 269164734 q^{44} - 1260828099 q^{45} + 1025852016 q^{46} + 1756184697 q^{47} + 1445045004 q^{48} - 317429813 q^{49} - 2012219958 q^{50} + 1024698789 q^{51} - 764967241 q^{52} - 1025091054 q^{53} + 1264338792 q^{54} + 1529593596 q^{55} - 2784983058 q^{56} + 399358827 q^{57} + 2699171294 q^{58} - 3942302265 q^{59} + 923325462 q^{60} + 3824339894 q^{61} + 647946516 q^{62} + 1506011580 q^{63} + 12885320719 q^{64} + 7151401527 q^{65} - 6772384737 q^{66} + 2150459223 q^{67} - 11844215328 q^{68} + 3023276373 q^{69} - 2166270909 q^{70} + 9991125477 q^{71} + 38878667820 q^{72} - 18369674953 q^{73} + 6783356751 q^{74} - 6795710019 q^{76} + 34684619799 q^{77} - 44083231983 q^{78} + 4689562890 q^{79} - 11067022449 q^{80} + 20674079568 q^{81} + 31254879554 q^{82} - 5658425577 q^{83} + 59478396651 q^{84} - 59199225974 q^{85} + 14918263134 q^{86} - 10626095304 q^{87} - 58485098673 q^{88} + 38493934203 q^{89} - 11240832114 q^{90} + 9453903636 q^{91} + 21528234186 q^{92} - 4906722582 q^{93} - 108652668078 q^{94} + 42786061515 q^{95} + 95102381862 q^{96} - 49490469025 q^{97} - 41277137058 q^{98} - 124869660210 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(76))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
76.11.b \(\chi_{76}(39, \cdot)\) 76.11.b.a 90 1
76.11.c \(\chi_{76}(37, \cdot)\) 76.11.c.a 2 1
76.11.c.b 14
76.11.g \(\chi_{76}(7, \cdot)\) 76.11.g.a 196 2
76.11.h \(\chi_{76}(65, \cdot)\) 76.11.h.a 32 2
76.11.j \(\chi_{76}(13, \cdot)\) 76.11.j.a 102 6
76.11.l \(\chi_{76}(23, \cdot)\) 76.11.l.a 588 6

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 1}\)