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Properties

Label 576.7.o
Level $576$
Weight $7$
Character orbit 576.o
Rep. character $\chi_{576}(319,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $284$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
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 292 884
Cusp forms 1128 284 844
Eisenstein series 48 8 40

Trace form

\( 284 q + 2 q^{5} - 4 q^{9} + O(q^{10}) \) \( 284 q + 2 q^{5} - 4 q^{9} + 2 q^{13} - 8 q^{17} + 1462 q^{21} - 418752 q^{25} + 2 q^{29} + 86698 q^{33} + 8 q^{37} - 20882 q^{41} - 289054 q^{45} + 2184908 q^{49} + 602216 q^{53} + 247152 q^{57} + 2 q^{61} + 62498 q^{65} + 797542 q^{69} - 8 q^{73} + 470598 q^{77} - 1194260 q^{81} + 31252 q^{85} + 2350648 q^{89} + 6921190 q^{93} - 2 q^{97} + O(q^{100}) \)

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

\( S_{7}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)