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Properties

Label 177.14.d
Level $177$
Weight $14$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $258$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(177, [\chi])\).

Total New Old
Modular forms 262 262 0
Cusp forms 258 258 0
Eisenstein series 4 4 0

Trace form

\( 258 q - 938 q^{3} + 1048572 q^{4} + 162960 q^{7} - 885970 q^{9} + O(q^{10}) \) \( 258 q - 938 q^{3} + 1048572 q^{4} + 162960 q^{7} - 885970 q^{9} - 23082044 q^{12} - 195235311 q^{15} + 4090749188 q^{16} - 574945192 q^{19} - 32042645 q^{21} + 557542420 q^{22} - 59227622918 q^{25} + 6320483593 q^{27} - 852998612 q^{28} + 5008317888 q^{36} + 135012380833 q^{45} + 177156450732 q^{46} - 247150865000 q^{48} + 3622701965846 q^{49} - 375918135188 q^{51} - 1584166714047 q^{57} - 4303542546488 q^{60} - 2411857969598 q^{63} + 14059178690752 q^{64} - 297063744652 q^{66} - 1053363067196 q^{75} - 15365950932928 q^{76} + 998269872584 q^{78} - 7038057197068 q^{79} + 1257606529806 q^{81} - 6171102794852 q^{84} + 10026120621148 q^{85} + 15284203411375 q^{87} - 19729978912736 q^{88} - 29627581129864 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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