Properties

Label 1232.4.df
Level $1232$
Weight $4$
Character orbit 1232.df
Rep. character $\chi_{1232}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1152$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.df (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1232, [\chi])\).

Total New Old
Modular forms 4704 1152 3552
Cusp forms 4512 1152 3360
Eisenstein series 192 0 192

Trace form

\( 1152 q + 1296 q^{9} + O(q^{10}) \) \( 1152 q + 1296 q^{9} - 4104 q^{25} + 108 q^{33} - 2160 q^{49} + 1176 q^{53} + 1800 q^{61} - 840 q^{65} - 2196 q^{77} + 11664 q^{81} + 9312 q^{85} - 3768 q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)