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Properties

Label 624.4.cq
Level $624$
Weight $4$
Character orbit 624.cq
Rep. character $\chi_{624}(175,\cdot)$
Character field $\Q(\zeta_{12})$
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.cq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1392 168 1224
Cusp forms 1296 168 1128
Eisenstein series 96 0 96

Trace form

\( 168 q - 12 q^{5} + 756 q^{9} + O(q^{10}) \) \( 168 q - 12 q^{5} + 756 q^{9} - 120 q^{21} + 108 q^{37} - 360 q^{41} - 216 q^{45} - 1080 q^{49} - 8136 q^{53} - 336 q^{57} - 732 q^{61} + 1464 q^{65} - 228 q^{73} - 6804 q^{81} - 4404 q^{85} - 6324 q^{89} + 1848 q^{93} + 7788 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)