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

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

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

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