Properties

Label 177.4
Level 177
Weight 4
Dimension 2552
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 9280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(9280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(177))\).

Total New Old
Modular forms 3596 2668 928
Cusp forms 3364 2552 812
Eisenstein series 232 116 116

Trace form

\( 2552q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} + O(q^{10}) \) \( 2552q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} - 58q^{10} - 29q^{12} - 58q^{13} - 29q^{15} - 58q^{16} - 29q^{18} - 58q^{19} - 29q^{21} - 58q^{22} - 29q^{24} - 58q^{25} - 29q^{27} - 58q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} - 29q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 3567q^{45} + 11310q^{46} + 4292q^{47} + 9019q^{48} + 3654q^{49} + 3248q^{50} - 261q^{51} - 3770q^{52} - 3248q^{53} - 7743q^{54} - 8062q^{55} - 24128q^{56} - 8149q^{57} - 6728q^{58} - 6728q^{59} - 19546q^{60} - 6090q^{61} - 5336q^{62} - 5539q^{63} - 13050q^{64} - 2784q^{65} - 435q^{66} + 1566q^{67} + 7424q^{68} + 6003q^{69} + 17110q^{70} + 11368q^{71} + 21547q^{72} + 8758q^{73} + 21112q^{74} + 6177q^{75} - 58q^{76} - 29q^{78} - 58q^{79} - 29q^{81} - 58q^{82} - 29q^{84} - 58q^{85} - 29q^{87} - 58q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 58q^{94} - 29q^{96} - 58q^{97} + 45762q^{98} - 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.4.a \(\chi_{177}(1, \cdot)\) 177.4.a.a 7 1
177.4.a.b 7
177.4.a.c 8
177.4.a.d 8
177.4.d \(\chi_{177}(176, \cdot)\) 177.4.d.a 2 1
177.4.d.b 4
177.4.d.c 52
177.4.e \(\chi_{177}(4, \cdot)\) 177.4.e.a 420 28
177.4.e.b 420
177.4.f \(\chi_{177}(2, \cdot)\) 177.4.f.a 1624 28

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)