↑

Properties

Label 1232.2.df
Level $1232$
Weight $2$
Character orbit 1232.df
Rep. character $\chi_{1232}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $384$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.df (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

Total New Old
Modular forms 1632 384 1248
Cusp forms 1440 384 1056
Eisenstein series 192 0 192

Trace form

\( 384 q + 48 q^{9} + O(q^{10}) \) \( 384 q + 48 q^{9} - 24 q^{25} + 36 q^{33} + 48 q^{49} - 24 q^{53} - 72 q^{61} - 24 q^{65} - 12 q^{77} + 48 q^{81} - 96 q^{85} + 120 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)