Properties

Label 7800.2.hx
Level $7800$
Weight $2$
Character orbit 7800.hx
Rep. character $\chi_{7800}(547,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $5760$
Sturm bound $3360$

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Defining parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.hx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(3360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7800, [\chi])\).

Total New Old
Modular forms 13504 5760 7744
Cusp forms 13376 5760 7616
Eisenstein series 128 0 128

Decomposition of \(S_{2}^{\mathrm{new}}(7800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(7800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2600, [\chi])\)\(^{\oplus 2}\)