Properties

Label 9800.2.gv
Level $9800$
Weight $2$
Character orbit 9800.gv
Rep. character $\chi_{9800}(9,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $20160$
Sturm bound $3360$

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Defining parameters

Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.gv (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(3360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(9800, [\chi])\).

Total New Old
Modular forms 81024 20160 60864
Cusp forms 80256 20160 60096
Eisenstein series 768 0 768

Decomposition of \(S_{2}^{\mathrm{new}}(9800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(9800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4900, [\chi])\)\(^{\oplus 2}\)