Properties

Label 230.2.b
Level $230$
Weight $2$
Character orbit 230.b
Rep. character $\chi_{230}(139,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

Trace form

\( 12q - 12q^{4} + 4q^{6} - 8q^{9} + O(q^{10}) \) \( 12q - 12q^{4} + 4q^{6} - 8q^{9} - 8q^{11} - 16q^{15} + 12q^{16} + 16q^{19} - 4q^{24} + 8q^{25} + 4q^{26} + 8q^{29} - 12q^{31} - 16q^{35} + 8q^{36} - 8q^{39} + 28q^{41} + 8q^{44} - 16q^{45} + 4q^{46} - 8q^{49} - 12q^{50} + 24q^{51} - 16q^{54} - 8q^{55} - 8q^{59} + 16q^{60} + 16q^{61} - 12q^{64} - 16q^{65} + 8q^{66} - 8q^{69} + 20q^{70} + 44q^{71} - 32q^{75} - 16q^{76} + 16q^{79} + 28q^{81} - 24q^{85} - 40q^{86} - 48q^{89} - 24q^{90} - 32q^{91} - 24q^{94} + 48q^{95} + 4q^{96} + 32q^{99} + O(q^{100}) \)

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.b.a \(4\) \(1.837\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b \(8\) \(1.837\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)

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

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