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Properties

Label 1232.2.bz
Level $1232$
Weight $2$
Character orbit 1232.bz
Rep. character $\chi_{1232}(127,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
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.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 816 144 672
Cusp forms 720 144 576
Eisenstein series 96 0 96

Trace form

\( 144 q + 12 q^{9} + O(q^{10}) \) \( 144 q + 12 q^{9} - 36 q^{25} + 36 q^{33} + 96 q^{45} - 36 q^{49} + 24 q^{53} + 60 q^{57} - 24 q^{69} - 120 q^{81} - 120 q^{85} - 72 q^{89} - 96 q^{93} - 132 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)