Properties

Label 9800.2.eu
Level $9800$
Weight $2$
Character orbit 9800.eu
Rep. character $\chi_{9800}(551,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $0$
Newform subspaces $0$
Sturm bound $3360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.eu (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 0 \)
Sturm bound: \(3360\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 20448 0 20448
Cusp forms 19872 0 19872
Eisenstein series 576 0 576

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

\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4900, [\chi])\)\(^{\oplus 2}\)