Properties

Label 304.5.f
Level $304$
Weight $5$
Character orbit 304.f
Rep. character $\chi_{304}(39,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $200$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(200\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(304, [\chi])\).

Total New Old
Modular forms 164 0 164
Cusp forms 156 0 156
Eisenstein series 8 0 8

Decomposition of \(S_{5}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)