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Properties

Label 588.4.n
Level $588$
Weight $4$
Character orbit 588.n
Rep. character $\chi_{588}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464 q + 2 q^{4} - 12 q^{6} + 2 q^{9} + O(q^{10}) \) \( 464 q + 2 q^{4} - 12 q^{6} + 2 q^{9} + 34 q^{10} - 56 q^{13} - 238 q^{16} + 4 q^{18} + 108 q^{22} + 278 q^{24} + 4920 q^{25} - 804 q^{30} - 106 q^{33} - 464 q^{34} + 1004 q^{36} + 256 q^{37} - 2 q^{40} + 282 q^{45} - 924 q^{46} - 488 q^{48} - 224 q^{52} + 286 q^{54} + 1788 q^{57} + 82 q^{58} - 1266 q^{60} - 1076 q^{61} - 2140 q^{64} + 132 q^{66} - 1092 q^{69} + 76 q^{72} + 664 q^{73} + 1416 q^{76} - 5880 q^{78} + 1238 q^{81} - 1700 q^{82} + 3560 q^{85} - 2154 q^{88} - 1964 q^{90} - 270 q^{93} - 1956 q^{94} - 2338 q^{96} - 1016 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)