Properties

Label 9408.2.et
Level $9408$
Weight $2$
Character orbit 9408.et
Rep. character $\chi_{9408}(55,\cdot)$
Character field $\Q(\zeta_{56})$
Dimension $0$
Newform subspaces $0$
Sturm bound $3584$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9408.et (of order \(56\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1568 \)
Character field: \(\Q(\zeta_{56})\)
Newform subspaces: \( 0 \)
Sturm bound: \(3584\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(9408, [\chi])\).

Total New Old
Modular forms 43200 0 43200
Cusp forms 42816 0 42816
Eisenstein series 384 0 384

Decomposition of \(S_{2}^{\mathrm{old}}(9408, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(9408, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4704, [\chi])\)\(^{\oplus 2}\)