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Properties

Label 1232.2.db
Level $1232$
Weight $2$
Character orbit 1232.db
Rep. character $\chi_{1232}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $384$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.db (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

\( 384 q - 48 q^{9} + O(q^{10}) \) \( 384 q - 48 q^{9} + 24 q^{25} - 12 q^{33} + 120 q^{41} - 96 q^{49} - 24 q^{53} - 96 q^{69} - 120 q^{73} + 12 q^{77} + 48 q^{81} + 240 q^{85} - 48 q^{89} - 120 q^{93} - 48 q^{97} + O(q^{100}) \)

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

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