Properties

Label 576.7.z
Level $576$
Weight $7$
Character orbit 576.z
Rep. character $\chi_{576}(79,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $568$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2336 584 1752
Cusp forms 2272 568 1704
Eisenstein series 64 16 48

Trace form

\( 568 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 568 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 2 q^{11} - 2 q^{13} - 16 q^{17} + 8 q^{19} + 1454 q^{21} + 4 q^{23} + 34324 q^{27} - 2 q^{29} - 8 q^{33} - 62492 q^{35} - 8 q^{37} + 254408 q^{39} + 2 q^{43} - 31254 q^{45} - 4369824 q^{49} + 386520 q^{51} - 8 q^{53} + 16 q^{55} + 403922 q^{59} - 2 q^{61} - 4 q^{65} + 2 q^{67} + 1454 q^{69} + 16 q^{71} + 2794856 q^{75} + 470594 q^{77} - 8 q^{81} + 1537202 q^{83} - 31252 q^{85} + 2029896 q^{87} - 470588 q^{91} + 1173338 q^{93} - 4 q^{97} - 1922458 q^{99} + O(q^{100}) \)

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

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