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Properties

Label 588.4.e
Level $588$
Weight $4$
Character orbit 588.e
Rep. character $\chi_{588}(491,\cdot)$
Character field $\Q$
Dimension $236$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).

Total New Old
Modular forms 352 256 96
Cusp forms 320 236 84
Eisenstein series 32 20 12

Trace form

\( 236 q - 4 q^{4} - 6 q^{6} - 8 q^{9} + O(q^{10}) \) \( 236 q - 4 q^{4} - 6 q^{6} - 8 q^{9} + 52 q^{10} - 42 q^{12} + 40 q^{13} + 20 q^{16} - 136 q^{18} - 36 q^{22} + 94 q^{24} - 4980 q^{25} + 216 q^{30} - 368 q^{33} + 256 q^{34} - 332 q^{36} - 8 q^{37} + 748 q^{40} + 24 q^{45} + 888 q^{46} - 46 q^{48} - 548 q^{52} + 1034 q^{54} - 348 q^{57} + 28 q^{58} + 1668 q^{60} - 680 q^{61} + 716 q^{64} - 12 q^{66} - 600 q^{69} - 952 q^{72} + 16 q^{73} - 1188 q^{76} - 936 q^{78} + 544 q^{81} + 232 q^{82} - 1000 q^{85} + 84 q^{88} - 2944 q^{90} + 3588 q^{93} - 1920 q^{94} + 946 q^{96} - 3008 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \)