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Properties

Label 576.7.bc
Level $576$
Weight $7$
Character orbit 576.bc
Rep. character $\chi_{576}(53,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1536$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.bc (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4640 1536 3104
Cusp forms 4576 1536 3040
Eisenstein series 64 0 64

Trace form

\( 1536 q + O(q^{10}) \) \( 1536 q - 2550240 q^{52} + 930816 q^{55} - 2310336 q^{64} + 2415360 q^{67} - 4544064 q^{70} + 2282592 q^{76} + 3443712 q^{79} - 13933920 q^{82} + 9391200 q^{88} + 5017536 q^{94} + O(q^{100}) \)

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

\( S_{7}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)