Properties

Label 1216.4.v
Level $1216$
Weight $4$
Character orbit 1216.v
Rep. character $\chi_{1216}(153,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $0$
Newform subspaces $0$
Sturm bound $640$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 0 \)
Sturm bound: \(640\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1216, [\chi])\).

Total New Old
Modular forms 1936 0 1936
Cusp forms 1904 0 1904
Eisenstein series 32 0 32

Decomposition of \(S_{4}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)