Properties

Label 72.7.g
Level $72$
Weight $7$
Character orbit 72.g
Rep. character $\chi_{72}(55,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 72.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).

Total New Old
Modular forms 80 0 80
Cusp forms 64 0 64
Eisenstein series 16 0 16

Decomposition of \(S_{7}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)