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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

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

Display 100 coefficients 10 coefficients

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 available 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

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