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Properties

Label 230.4.j
Level $230$
Weight $4$
Character orbit 230.j
Rep. character $\chi_{230}(9,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $360$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(230, [\chi])\).

Total New Old
Modular forms 1120 360 760
Cusp forms 1040 360 680
Eisenstein series 80 0 80

Trace form

\( 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9} + 96 q^{11} + 208 q^{14} - 752 q^{15} - 576 q^{16} + 48 q^{19} + 224 q^{20} - 272 q^{21} - 32 q^{24} + 904 q^{25} - 152 q^{26} - 20 q^{29} - 1272 q^{30}+ \cdots + 23448 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.4.j.a 230.j 115.j $360$ $13.570$ None 230.4.j.a \(0\) \(0\) \(32\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{4}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(230, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)