Properties

Label 8450.2.r
Level $8450$
Weight $2$
Character orbit 8450.r
Rep. character $\chi_{8450}(1689,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1536$
Sturm bound $2730$

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Defining parameters

Level: \( N \) \(=\) \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8450.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(2730\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8450, [\chi])\).

Total New Old
Modular forms 5568 1536 4032
Cusp forms 5344 1536 3808
Eisenstein series 224 0 224

Decomposition of \(S_{2}^{\mathrm{new}}(8450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(8450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4225, [\chi])\)\(^{\oplus 2}\)