Properties

Label 624.4.bu
Level $624$
Weight $4$
Character orbit 624.bu
Rep. character $\chi_{624}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $168$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).

Total New Old
Modular forms 696 168 528
Cusp forms 648 168 480
Eisenstein series 48 0 48

Trace form

\( 168 q + O(q^{10}) \) \( 168 q - 36 q^{13} - 4200 q^{25} + 288 q^{37} + 3936 q^{49} - 2544 q^{57} + 1476 q^{61} - 1560 q^{69} + 216 q^{73} + 456 q^{81} - 5328 q^{85} - 168 q^{93} - 396 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)