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Properties

Label 177.8.d
Level $177$
Weight $8$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $138$
Sturm bound $160$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Sturm bound: \(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(177, [\chi])\).

Total New Old
Modular forms 142 142 0
Cusp forms 138 138 0
Eisenstein series 4 4 0

Trace form

\( 138 q - 2 q^{3} + 8700 q^{4} + 1344 q^{7} - 1198 q^{9} + O(q^{10}) \) \( 138 q - 2 q^{3} + 8700 q^{4} + 1344 q^{7} - 1198 q^{9} - 5756 q^{12} - 19083 q^{15} + 539588 q^{16} + 4184 q^{19} - 65357 q^{21} + 74836 q^{22} - 1856534 q^{25} - 51923 q^{27} + 470956 q^{28} - 163968 q^{36} + 3681649 q^{45} - 2048724 q^{46} - 1969832 q^{48} + 15016790 q^{49} - 37652 q^{51} - 5669199 q^{57} - 5349224 q^{60} + 6857242 q^{63} + 17847232 q^{64} + 775268 q^{66} + 19635988 q^{75} + 1908512 q^{76} + 16361384 q^{78} - 2195500 q^{79} + 2400690 q^{81} - 26408132 q^{84} - 1936868 q^{85} - 7318277 q^{87} + 28133920 q^{88} + 13665176 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.