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Properties

Label 576.4.y
Level $576$
Weight $4$
Character orbit 576.y
Rep. character $\chi_{576}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $280$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1184 296 888
Cusp forms 1120 280 840
Eisenstein series 64 16 48

Trace form

\( 280 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + O(q^{10}) \) \( 280 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 50 q^{21} + 12 q^{23} - 128 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 608 q^{39} + 2 q^{43} + 246 q^{45} - 5688 q^{49} - 804 q^{51} + 16 q^{55} + 3066 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 58 q^{69} - 3496 q^{75} - 6 q^{77} - 8 q^{81} - 3654 q^{83} + 248 q^{85} + 1296 q^{87} - 1364 q^{91} + 2078 q^{93} - 4 q^{97} + 1202 q^{99} + O(q^{100}) \)

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

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