Properties

Label 177.7.c
Level $177$
Weight $7$
Character orbit 177.c
Rep. character $\chi_{177}(58,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $1$
Sturm bound $140$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(140\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(177, [\chi])\).

Total New Old
Modular forms 122 60 62
Cusp forms 118 60 58
Eisenstein series 4 0 4

Trace form

\( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.7.c.a \(60\) \(40.720\) None \(0\) \(0\) \(0\) \(-408\)

Decomposition of \(S_{7}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)