Properties

Label 177.2
Level 177
Weight 2
Dimension 811
Nonzero newspaces 4
Newforms 10
Sturm bound 4640
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 10 \)
Sturm bound: \(4640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(177))\).

Total New Old
Modular forms 1276 927 349
Cusp forms 1045 811 234
Eisenstein series 231 116 115

Trace form

\( 811q - 3q^{2} - 30q^{3} - 65q^{4} - 6q^{5} - 32q^{6} - 66q^{7} - 15q^{8} - 30q^{9} + O(q^{10}) \) \( 811q - 3q^{2} - 30q^{3} - 65q^{4} - 6q^{5} - 32q^{6} - 66q^{7} - 15q^{8} - 30q^{9} - 76q^{10} - 12q^{11} - 36q^{12} - 72q^{13} - 24q^{14} - 35q^{15} - 89q^{16} - 18q^{17} - 32q^{18} - 78q^{19} - 42q^{20} - 37q^{21} - 94q^{22} - 24q^{23} - 44q^{24} - 89q^{25} - 42q^{26} - 30q^{27} - 114q^{28} - 30q^{29} - 47q^{30} - 90q^{31} - 63q^{32} - 41q^{33} - 112q^{34} - 48q^{35} - 36q^{36} - 96q^{37} - 60q^{38} - 43q^{39} - 148q^{40} - 42q^{41} - 53q^{42} - 102q^{43} - 84q^{44} - 6q^{45} - 14q^{46} + 10q^{47} + 114q^{48} + q^{49} + 139q^{50} + 69q^{51} + 76q^{52} + 62q^{53} + 171q^{54} + 44q^{55} + 344q^{56} + 96q^{57} + 26q^{58} + 57q^{59} + 248q^{60} - 4q^{61} + 20q^{62} + 108q^{63} + 279q^{64} + 90q^{65} + 138q^{66} - 10q^{67} + 106q^{68} + 63q^{69} + 30q^{70} + 44q^{71} + 130q^{72} - 74q^{73} + 2q^{74} - 31q^{75} - 198q^{76} - 96q^{77} - 71q^{78} - 138q^{79} - 186q^{80} - 30q^{81} - 184q^{82} - 84q^{83} - 85q^{84} - 166q^{85} - 132q^{86} - 59q^{87} - 238q^{88} - 90q^{89} - 47q^{90} - 170q^{91} - 168q^{92} - 61q^{93} - 202q^{94} - 120q^{95} - 92q^{96} - 156q^{97} + 3q^{98} - 41q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.2.a \(\chi_{177}(1, \cdot)\) 177.2.a.a 2 1
177.2.a.b 2
177.2.a.c 2
177.2.a.d 3
177.2.d \(\chi_{177}(176, \cdot)\) 177.2.d.a 6 1
177.2.d.b 6
177.2.d.c 6
177.2.e \(\chi_{177}(4, \cdot)\) 177.2.e.a 140 28
177.2.e.b 140
177.2.f \(\chi_{177}(2, \cdot)\) 177.2.f.a 504 28

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)