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Properties

Label 588.4.be
Level $588$
Weight $4$
Character orbit 588.be
Rep. character $\chi_{588}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $672$
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.be (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4104 672 3432
Cusp forms 3960 672 3288
Eisenstein series 144 0 144

Trace form

\( 672 q + 22 q^{7} + 112 q^{9} + O(q^{10}) \) \( 672 q + 22 q^{7} + 112 q^{9} - 84 q^{15} - 36 q^{19} + 54 q^{21} + 1358 q^{25} - 42 q^{27} - 534 q^{31} + 108 q^{33} + 3388 q^{37} + 280 q^{39} + 728 q^{43} - 1142 q^{45} - 1756 q^{49} - 84 q^{51} + 4326 q^{55} + 1232 q^{57} + 5510 q^{61} - 1056 q^{63} - 1232 q^{67} + 1820 q^{69} - 486 q^{73} + 8004 q^{75} + 490 q^{79} - 7420 q^{81} + 1512 q^{85} + 1442 q^{87} + 9036 q^{91} + 12964 q^{93} + 8288 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)