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Properties

Label 576.3.z
Level $576$
Weight $3$
Character orbit 576.z
Rep. character $\chi_{576}(79,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $184$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 800 200 600
Cusp forms 736 184 552
Eisenstein series 64 16 48

Trace form

\( 184 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 184 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 2 q^{11} - 2 q^{13} - 16 q^{17} + 8 q^{19} + 14 q^{21} + 4 q^{23} + 52 q^{27} - 2 q^{29} - 8 q^{33} - 92 q^{35} - 8 q^{37} - 184 q^{39} + 2 q^{43} - 54 q^{45} - 480 q^{49} + 120 q^{51} - 8 q^{53} + 16 q^{55} - 142 q^{59} - 2 q^{61} - 4 q^{65} + 2 q^{67} + 14 q^{69} + 16 q^{71} + 296 q^{75} + 194 q^{77} - 8 q^{81} - 238 q^{83} - 52 q^{85} + 456 q^{87} - 188 q^{91} + 26 q^{93} - 4 q^{97} + 38 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

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