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Properties

Label 232.2.q
Level $232$
Weight $2$
Character orbit 232.q
Rep. character $\chi_{232}(9,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $48$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 232.q (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(232, [\chi])\).

Total New Old
Modular forms 204 48 156
Cusp forms 156 48 108
Eisenstein series 48 0 48

Trace form

\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
232.2.q.a 232.q 29.e $48$ $1.853$ None 232.2.q.a \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{2}^{\mathrm{old}}(232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(232, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)