Properties

Label 230.2.l
Level $230$
Weight $2$
Character orbit 230.l
Rep. character $\chi_{230}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $240$
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.l (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
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 800 240 560
Cusp forms 640 240 400
Eisenstein series 160 0 160

Trace form

\( 240q - 8q^{3} - 8q^{6} + O(q^{10}) \) \( 240q - 8q^{3} - 8q^{6} - 8q^{12} + 16q^{13} + 24q^{16} - 72q^{18} - 80q^{23} - 8q^{26} + 16q^{27} - 44q^{28} + 24q^{31} - 44q^{33} - 8q^{35} - 32q^{36} - 88q^{37} - 24q^{41} - 8q^{46} - 80q^{47} + 8q^{48} + 8q^{50} + 16q^{52} - 44q^{56} - 88q^{57} - 176q^{61} - 32q^{62} - 176q^{66} + 24q^{70} - 336q^{71} + 16q^{72} - 88q^{73} - 36q^{75} - 24q^{77} + 40q^{78} - 136q^{81} + 40q^{82} - 100q^{85} - 44q^{86} + 40q^{87} + 8q^{92} + 56q^{93} + 52q^{95} + 8q^{96} + 132q^{97} + 24q^{98} + O(q^{100}) \)

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.l.a \(240\) \(1.837\) None \(0\) \(-8\) \(0\) \(0\)

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

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