Properties

Label 576.7.m
Level $576$
Weight $7$
Character orbit 576.m
Rep. character $\chi_{576}(271,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $118$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1184 122 1062
Cusp forms 1120 118 1002
Eisenstein series 64 4 60

Trace form

\( 118 q + 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 118 q + 2 q^{5} + 4 q^{7} - 1362 q^{11} - 2 q^{13} + 4 q^{17} + 3938 q^{19} + 13116 q^{23} - 33198 q^{29} + 49916 q^{35} + 3598 q^{37} - 122542 q^{43} + 1781538 q^{49} - 221838 q^{53} - 232700 q^{55} - 846994 q^{59} - 326498 q^{61} + 186420 q^{65} - 481054 q^{67} + 267004 q^{71} + 701780 q^{77} - 2786082 q^{83} - 403252 q^{85} + 3398404 q^{91} - 4 q^{97} + O(q^{100}) \)

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

\( S_{7}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)