Properties

Label 7800.2.k
Level $7800$
Weight $2$
Character orbit 7800.k
Rep. character $\chi_{7800}(7151,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $3360$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
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 1728 0 1728
Cusp forms 1632 0 1632
Eisenstein series 96 0 96

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

\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3900, [\chi])\)\(^{\oplus 2}\)