Properties

Label 1600.2.cl
Level $1600$
Weight $2$
Character orbit 1600.cl
Rep. character $\chi_{1600}(23,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $0$
Newform subspaces $0$
Sturm bound $480$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.cl (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 0 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

Total New Old
Modular forms 3904 0 3904
Cusp forms 3776 0 3776
Eisenstein series 128 0 128

Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)