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Properties

Label 77.2
Level 77
Weight 2
Dimension 179
Nonzero newspaces 8
Newform subspaces 16
Sturm bound 960
Trace bound 3

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Defining parameters

Level: \( N \) = \( 77 = 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 16 \)
Sturm bound: \(960\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(77))\).

Total New Old
Modular forms 300 271 29
Cusp forms 181 179 2
Eisenstein series 119 92 27

Trace form

\( 179 q - 23 q^{2} - 24 q^{3} - 27 q^{4} - 26 q^{5} - 22 q^{6} - 21 q^{7} - 45 q^{8} - 13 q^{9} + O(q^{10}) \) \( 179 q - 23 q^{2} - 24 q^{3} - 27 q^{4} - 26 q^{5} - 22 q^{6} - 21 q^{7} - 45 q^{8} - 13 q^{9} - 8 q^{10} - 21 q^{11} - 28 q^{12} - 24 q^{13} - 13 q^{14} - 34 q^{15} + 9 q^{16} - 8 q^{17} + q^{18} - 10 q^{19} + 8 q^{20} - 4 q^{21} - 23 q^{22} - 34 q^{23} + 30 q^{24} + 9 q^{25} + 28 q^{26} + 23 q^{28} - 30 q^{29} + 38 q^{30} - 12 q^{31} + 17 q^{32} + 16 q^{33} - 14 q^{34} + 14 q^{35} + 39 q^{36} + 2 q^{37} + 30 q^{38} + 34 q^{39} + 60 q^{40} + 28 q^{41} + 58 q^{42} - 4 q^{43} + 43 q^{44} + 22 q^{45} + 38 q^{46} + 2 q^{47} + 86 q^{48} + 29 q^{49} + 17 q^{50} + 38 q^{51} + 52 q^{52} + 36 q^{53} + 110 q^{54} + 34 q^{55} + 45 q^{56} + 20 q^{57} + 60 q^{58} + 20 q^{59} - 38 q^{60} - 22 q^{61} + 34 q^{62} - 33 q^{63} - 37 q^{64} - 44 q^{65} - 142 q^{66} - 38 q^{67} - 76 q^{68} - 86 q^{69} - 88 q^{70} - 102 q^{71} - 195 q^{72} - 54 q^{73} - 24 q^{74} - 154 q^{75} - 220 q^{76} - 41 q^{77} - 208 q^{78} - 20 q^{79} - 136 q^{80} - 151 q^{81} - 56 q^{82} - 24 q^{83} - 198 q^{84} - 68 q^{85} - 102 q^{86} - 60 q^{87} - 45 q^{88} - 60 q^{89} - 44 q^{90} - 14 q^{91} - 8 q^{92} + 22 q^{93} + 86 q^{94} + 60 q^{95} - 2 q^{96} + 82 q^{97} + 97 q^{98} + 87 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
77.2.a \(\chi_{77}(1, \cdot)\) 77.2.a.a 1 1
77.2.a.b 1
77.2.a.c 1
77.2.a.d 2
77.2.b \(\chi_{77}(76, \cdot)\) 77.2.b.a 2 1
77.2.b.b 4
77.2.e \(\chi_{77}(23, \cdot)\) 77.2.e.a 6 2
77.2.e.b 6
77.2.f \(\chi_{77}(15, \cdot)\) 77.2.f.a 8 4
77.2.f.b 16
77.2.i \(\chi_{77}(10, \cdot)\) 77.2.i.a 12 2
77.2.l \(\chi_{77}(6, \cdot)\) 77.2.l.a 8 4
77.2.l.b 16
77.2.m \(\chi_{77}(4, \cdot)\) 77.2.m.a 8 8
77.2.m.b 40
77.2.n \(\chi_{77}(17, \cdot)\) 77.2.n.a 48 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(77))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(77)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)