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Properties

Label 576.7.n
Level $576$
Weight $7$
Character orbit 576.n
Rep. character $\chi_{576}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(576, [\chi])\).

Total New Old
Modular forms 1176 288 888
Cusp forms 1128 288 840
Eisenstein series 48 0 48

Trace form

\( 288 q + O(q^{10}) \) \( 288 q - 450000 q^{25} - 264480 q^{33} - 187920 q^{41} - 2420208 q^{49} - 732720 q^{57} - 3582768 q^{81} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)