Properties

Label 7800.2.jh
Level $7800$
Weight $2$
Character orbit 7800.jh
Rep. character $\chi_{7800}(1369,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1696$
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.jh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(3360\)

Dimensions

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

Total New Old
Modular forms 13568 1696 11872
Cusp forms 13312 1696 11616
Eisenstein series 256 0 256

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

\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3900, [\chi])\)\(^{\oplus 2}\)