Properties

Label 9216.2.p
Level $9216$
Weight $2$
Character orbit 9216.p
Rep. character $\chi_{9216}(1535,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $752$
Sturm bound $3072$

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Defining parameters

Level: \( N \) \(=\) \( 9216 = 2^{10} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9216.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(3072\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(9216, [\chi])\).

Total New Old
Modular forms 3168 784 2384
Cusp forms 2976 752 2224
Eisenstein series 192 32 160

Decomposition of \(S_{2}^{\mathrm{new}}(9216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(9216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(9216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4608, [\chi])\)\(^{\oplus 2}\)