Properties

Label 10000.2.cg
Level $10000$
Weight $2$
Character orbit 10000.cg
Rep. character $\chi_{10000}(101,\cdot)$
Character field $\Q(\zeta_{100})$
Dimension $35760$
Sturm bound $3000$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 10000 = 2^{4} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10000.cg (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2000 \)
Character field: \(\Q(\zeta_{100})\)
Sturm bound: \(3000\)

Dimensions

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

Total New Old
Modular forms 60400 36240 24160
Cusp forms 59600 35760 23840
Eisenstein series 800 480 320

Decomposition of \(S_{2}^{\mathrm{new}}(10000, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{2}^{\mathrm{old}}(10000, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)