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Properties

Label 232.4.e
Level $232$
Weight $4$
Character orbit 232.e
Rep. character $\chi_{232}(57,\cdot)$
Character field $\Q$
Dimension $22$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q\)
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 94 22 72
Cusp forms 86 22 64
Eisenstein series 8 0 8

Trace form

\( 22 q + 18 q^{5} - 12 q^{7} - 152 q^{9} + O(q^{10}) \) \( 22 q + 18 q^{5} - 12 q^{7} - 152 q^{9} - 58 q^{13} + 76 q^{23} + 980 q^{25} + 38 q^{29} - 6 q^{33} - 668 q^{35} - 1404 q^{45} + 1358 q^{49} - 180 q^{51} - 1002 q^{53} + 720 q^{57} + 1500 q^{59} + 3512 q^{63} - 1386 q^{65} - 656 q^{67} - 3472 q^{71} - 818 q^{81} + 1092 q^{83} - 1356 q^{87} - 692 q^{91} + 942 q^{93} + O(q^{100}) \)

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.e.a 232.e 29.b $22$ $13.688$ None \(0\) \(0\) \(18\) \(-12\) $\mathrm{SU}(2)[C_{2}]$

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

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