Properties

Label 177.5
Level 177
Weight 5
Dimension 3422
Nonzero newspaces 4
Sturm bound 11600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(11600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(177))\).

Total New Old
Modular forms 4756 3534 1222
Cusp forms 4524 3422 1102
Eisenstein series 232 112 120

Trace form

\( 3422q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} + O(q^{10}) \) \( 3422q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} - 58q^{10} - 29q^{12} - 58q^{13} - 29q^{15} - 58q^{16} - 29q^{18} - 58q^{19} - 29q^{21} - 58q^{22} - 29q^{24} - 58q^{25} - 29q^{27} - 58q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} - 29q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} - 29812q^{45} - 72442q^{46} - 17226q^{47} - 6989q^{48} + 17690q^{49} + 66816q^{50} + 43007q^{51} + 94598q^{52} + 46980q^{53} + 74675q^{54} + 52664q^{55} + 100224q^{56} + 16356q^{57} - 116q^{58} - 13572q^{59} - 80794q^{60} - 39382q^{61} - 50112q^{62} - 73254q^{63} - 256186q^{64} - 98658q^{65} - 110461q^{66} - 55390q^{67} - 83520q^{68} - 21721q^{69} + 11078q^{70} + 40716q^{71} + 126643q^{72} + 68672q^{73} + 200448q^{74} + 68498q^{75} - 58q^{76} - 29q^{78} - 58q^{79} - 29q^{81} - 58q^{82} - 29q^{84} - 58q^{85} - 29q^{87} - 58q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 58q^{94} - 29q^{96} - 58q^{97} - 545490q^{98} - 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(177))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
177.5.b \(\chi_{177}(119, \cdot)\) 177.5.b.a 78 1
177.5.c \(\chi_{177}(58, \cdot)\) 177.5.c.a 40 1
177.5.g \(\chi_{177}(10, \cdot)\) n/a 1120 28
177.5.h \(\chi_{177}(5, \cdot)\) n/a 2184 28

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)