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Properties

Label 230.2.j
Level $230$
Weight $2$
Character orbit 230.j
Rep. character $\chi_{230}(9,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $120$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(230, [\chi])\).

Total New Old
Modular forms 400 120 280
Cusp forms 320 120 200
Eisenstein series 80 0 80

Trace form

\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + O(q^{10}) \) \( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.2.j.a 230.j 115.j $120$ $1.837$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

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