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Properties

Label 588.3.h
Level $588$
Weight $3$
Character orbit 588.h
Rep. character $\chi_{588}(587,\cdot)$
Character field $\Q$
Dimension $152$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(588, [\chi])\).

Total New Old
Modular forms 240 168 72
Cusp forms 208 152 56
Eisenstein series 32 16 16

Trace form

\( 152 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \) \( 152 q + 4 q^{4} + 4 q^{9} - 12 q^{16} + 68 q^{18} + 76 q^{22} + 592 q^{25} + 4 q^{30} + 108 q^{36} + 88 q^{37} + 48 q^{46} - 4 q^{57} - 372 q^{58} - 68 q^{60} - 260 q^{64} - 600 q^{72} - 232 q^{78} - 76 q^{81} + 152 q^{85} - 156 q^{88} - 228 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)