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Properties

Label 177.9
Level 177
Weight 9
Dimension 6898
Nonzero newspaces 4
Sturm bound 20880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(20880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(177))\).

Total New Old
Modular forms 9396 7010 2386
Cusp forms 9164 6898 2266
Eisenstein series 232 112 120

Trace form

\( 6898 q - 209 q^{3} + 934 q^{4} - 6077 q^{6} + 6942 q^{7} + 10015 q^{9} + O(q^{10}) \) \( 6898 q - 209 q^{3} + 934 q^{4} - 6077 q^{6} + 6942 q^{7} + 10015 q^{9} - 20218 q^{10} + 44611 q^{12} - 102978 q^{13} + 60451 q^{15} + 270022 q^{16} - 544349 q^{18} - 75810 q^{19} + 314971 q^{21} + 624902 q^{22} - 48413 q^{24} - 1360958 q^{25} + 2084911 q^{27} - 1736058 q^{28} - 907229 q^{30} + 1405854 q^{31} - 1874909 q^{33} + 6725318 q^{34} - 2490941 q^{36} - 5340738 q^{37} - 4631429 q^{39} - 161338 q^{40} + 10583971 q^{42} + 14104542 q^{43} - 59811382 q^{45} + 68355398 q^{46} + 63546714 q^{47} + 44113891 q^{48} - 69287578 q^{49} - 247486464 q^{50} - 123161305 q^{51} - 48686202 q^{52} + 44302140 q^{53} + 187313027 q^{54} + 212599364 q^{55} + 540407808 q^{56} + 99341466 q^{57} + 41388364 q^{58} - 91298844 q^{59} - 520083514 q^{60} - 212493414 q^{61} - 199245312 q^{62} - 183285204 q^{63} - 132517946 q^{64} + 186364962 q^{65} + 479569187 q^{66} + 332267490 q^{67} + 664151040 q^{68} + 327024095 q^{69} - 73674682 q^{70} - 380816748 q^{71} - 975168797 q^{72} - 414271548 q^{73} + 142718976 q^{74} + 491840888 q^{75} + 18786438 q^{76} - 155615069 q^{78} + 91923870 q^{79} + 121745887 q^{81} + 168416582 q^{82} - 78120029 q^{84} - 67253818 q^{85} - 124165469 q^{87} + 4999622 q^{88} + 50621731 q^{90} + 180109942 q^{91} + 63266011 q^{93} - 366476602 q^{94} + 395974627 q^{96} - 589084098 q^{97} - 4373193330 q^{98} - 168739229 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.9.b \(\chi_{177}(119, \cdot)\) n/a 154 1
177.9.c \(\chi_{177}(58, \cdot)\) 177.9.c.a 80 1
177.9.g \(\chi_{177}(10, \cdot)\) n/a 2240 28
177.9.h \(\chi_{177}(5, \cdot)\) n/a 4424 28

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)