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Properties

Label 232.4.q
Level $232$
Weight $4$
Character orbit 232.q
Rep. character $\chi_{232}(9,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $132$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(232, [\chi])\).

Total New Old
Modular forms 564 132 432
Cusp forms 516 132 384
Eisenstein series 48 0 48

Trace form

\( 132 q - 18 q^{5} + 12 q^{7} + 152 q^{9} + O(q^{10}) \) \( 132 q - 18 q^{5} + 12 q^{7} + 152 q^{9} + 58 q^{13} + 294 q^{15} + 602 q^{21} - 76 q^{23} - 98 q^{25} - 38 q^{29} + 6 q^{33} - 200 q^{35} + 144 q^{45} - 742 q^{47} - 3164 q^{49} + 600 q^{51} + 666 q^{53} + 4116 q^{55} + 876 q^{57} + 6704 q^{59} + 1260 q^{61} - 446 q^{63} + 42 q^{65} - 268 q^{67} - 5068 q^{69} + 1722 q^{71} - 2814 q^{73} + 2506 q^{77} + 818 q^{81} - 3304 q^{83} - 3432 q^{87} + 2310 q^{89} + 692 q^{91} - 942 q^{93} + 420 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
232.4.q.a 232.q 29.e $132$ $13.688$ None \(0\) \(0\) \(-18\) \(12\) $\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{4}^{\mathrm{old}}(232, [\chi])\) into lower level spaces

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