Properties

Label 1232.2.bi
Level $1232$
Weight $2$
Character orbit 1232.bi
Rep. character $\chi_{1232}(527,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $3$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 408 96 312
Cusp forms 360 96 264
Eisenstein series 48 0 48

Trace form

\( 96 q + 48 q^{9} + O(q^{10}) \) \( 96 q + 48 q^{9} - 24 q^{25} + 12 q^{33} - 24 q^{49} + 24 q^{53} + 96 q^{69} - 72 q^{77} - 48 q^{81} + 48 q^{89} + 48 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1232.2.bi.a 1232.bi 308.n $32$ $9.838$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1232.2.bi.b 1232.bi 308.n $32$ $9.838$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1232.2.bi.c 1232.bi 308.n $32$ $9.838$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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