Properties

Label 177.7
Level 177
Weight 7
Dimension 5160
Nonzero newspaces 4
Sturm bound 16240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(16240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(177))\).

Total New Old
Modular forms 7076 5272 1804
Cusp forms 6844 5160 1684
Eisenstein series 232 112 120

Trace form

\( 5160q + 25q^{3} - 186q^{4} - 29q^{6} + 514q^{7} - 1487q^{9} + O(q^{10}) \) \( 5160q + 25q^{3} - 186q^{4} - 29q^{6} + 514q^{7} - 1487q^{9} - 58q^{10} + 3427q^{12} - 1070q^{13} - 29q^{15} - 8250q^{16} - 29q^{18} + 21106q^{19} - 15473q^{21} - 58q^{22} - 29q^{24} - 31308q^{25} + 39337q^{27} + 36550q^{28} - 29q^{30} - 70622q^{31} - 29q^{33} - 58q^{34} - 93341q^{36} + 178354q^{37} + 27295q^{39} - 58q^{40} - 29q^{42} - 222830q^{43} - 1589461q^{45} - 818554q^{46} + 944240q^{47} + 4202275q^{48} + 2276576q^{49} + 2234624q^{50} - 168925q^{51} - 2737466q^{52} - 2176160q^{53} - 4505005q^{54} - 3745930q^{55} - 7913984q^{56} - 1951857q^{57} - 116q^{58} + 1184128q^{59} + 6859718q^{60} + 3990322q^{61} + 3628480q^{62} + 4935159q^{63} + 11636166q^{64} + 2845248q^{65} + 435203q^{66} - 2099726q^{67} - 7720960q^{68} - 5706301q^{69} - 13597114q^{70} - 6502496q^{71} - 6041309q^{72} - 482750q^{73} + 11484928q^{74} + 7595849q^{75} + 1354438q^{76} - 29q^{78} + 409186q^{79} - 1062911q^{81} - 58q^{82} - 988445q^{84} - 58q^{85} - 29q^{87} - 58q^{88} - 29q^{90} + 289374q^{91} + 1905199q^{93} - 58q^{94} - 29q^{96} + 112834q^{97} - 58255026q^{98} - 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.7.b \(\chi_{177}(119, \cdot)\) n/a 116 1
177.7.c \(\chi_{177}(58, \cdot)\) 177.7.c.a 60 1
177.7.g \(\chi_{177}(10, \cdot)\) n/a 1680 28
177.7.h \(\chi_{177}(5, \cdot)\) n/a 3304 28

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)