Properties

Label 10000.2.cx
Level $10000$
Weight $2$
Character orbit 10000.cx
Rep. character $\chi_{10000}(23,\cdot)$
Character field $\Q(\zeta_{500})$
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.cx (of order \(500\) and degree \(200\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5000 \)
Character field: \(\Q(\zeta_{500})\)
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 300800 0 300800
Cusp forms 299200 0 299200
Eisenstein series 1600 0 1600

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

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