Properties

Label 1600.2.ba
Level $1600$
Weight $2$
Character orbit 1600.ba
Rep. character $\chi_{1600}(249,\cdot)$
Character field $\Q(\zeta_{8})$
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.ba (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
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 1008 0 1008
Cusp forms 912 0 912
Eisenstein series 96 0 96

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)