Properties

Label 400.4.bh
Level $400$
Weight $4$
Character orbit 400.bh
Rep. character $\chi_{400}(23,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $0$
Newform subspaces $0$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 400.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 0 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

Total New Old
Modular forms 1472 0 1472
Cusp forms 1408 0 1408
Eisenstein series 64 0 64

Decomposition of \(S_{4}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)