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Properties

Label 576.4.p
Level $576$
Weight $4$
Character orbit 576.p
Rep. character $\chi_{576}(95,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(576, [\chi])\).

Total New Old
Modular forms 600 144 456
Cusp forms 552 144 408
Eisenstein series 48 0 48

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 1800 q^{25} + 1392 q^{33} - 360 q^{41} + 3528 q^{49} + 1032 q^{57} + 936 q^{81} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

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