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Properties

Label 588.4.b
Level $588$
Weight $4$
Character orbit 588.b
Rep. character $\chi_{588}(391,\cdot)$
Character field $\Q$
Dimension $120$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 352 120 232
Cusp forms 320 120 200
Eisenstein series 32 0 32

Trace form

\( 120 q - 4 q^{2} - 20 q^{4} - 16 q^{8} + 1080 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{2} - 20 q^{4} - 16 q^{8} + 1080 q^{9} - 52 q^{16} - 36 q^{18} + 476 q^{22} - 3168 q^{25} - 800 q^{29} + 336 q^{30} + 496 q^{32} - 180 q^{36} + 472 q^{37} + 472 q^{44} - 2456 q^{46} + 3892 q^{50} - 720 q^{53} - 504 q^{57} - 100 q^{58} + 1644 q^{60} - 6116 q^{64} - 560 q^{65} - 144 q^{72} - 4332 q^{74} + 1836 q^{78} + 9720 q^{81} + 1056 q^{85} + 6324 q^{86} - 1308 q^{88} - 3640 q^{92} - 2760 q^{93} + O(q^{100}) \)

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

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