Properties

Label 7800.2.hd
Level $7800$
Weight $2$
Character orbit 7800.hd
Rep. character $\chi_{7800}(743,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $0$
Newform subspaces $0$
Sturm bound $3360$
Trace bound $0$

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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.hd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 780 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 0 \)
Sturm bound: \(3360\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 6912 0 6912
Cusp forms 6528 0 6528
Eisenstein series 384 0 384

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

\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3900, [\chi])\)\(^{\oplus 2}\)