Properties

Label 4200.2.ha
Level $4200$
Weight $2$
Character orbit 4200.ha
Rep. character $\chi_{4200}(247,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $0$
Newform subspaces $0$
Sturm bound $1920$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4200.ha (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 0 \)
Sturm bound: \(1920\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4200, [\chi])\).

Total New Old
Modular forms 15616 0 15616
Cusp forms 15104 0 15104
Eisenstein series 512 0 512

Decomposition of \(S_{2}^{\mathrm{old}}(4200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)