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 $0$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
230.2.j.a \(120\) \(1.837\) None \(0\) \(0\) \(0\) \(0\)

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

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