Properties

Label 10000.2.cl
Level $10000$
Weight $2$
Character orbit 10000.cl
Rep. character $\chi_{10000}(41,\cdot)$
Character field $\Q(\zeta_{250})$
Dimension $0$
Newform subspaces $0$
Sturm bound $3000$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10000 = 2^{4} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10000.cl (of order \(250\) and degree \(100\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5000 \)
Character field: \(\Q(\zeta_{250})\)
Newform subspaces: \( 0 \)
Sturm bound: \(3000\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(10000, [\chi])\).

Total New Old
Modular forms 150400 0 150400
Cusp forms 149600 0 149600
Eisenstein series 800 0 800

Decomposition of \(S_{2}^{\mathrm{old}}(10000, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(10000, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(5000, [\chi])\)\(^{\oplus 2}\)