Properties

Label 230.2.e
Level $230$
Weight $2$
Character orbit 230.e
Rep. character $\chi_{230}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $3$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24q + 8q^{3} + 8q^{6} + O(q^{10}) \) \( 24q + 8q^{3} + 8q^{6} + 8q^{12} - 16q^{13} - 24q^{16} - 16q^{18} - 8q^{23} + 8q^{26} - 16q^{27} - 24q^{31} + 8q^{35} + 32q^{36} + 24q^{41} + 8q^{46} - 8q^{47} - 8q^{48} - 8q^{50} - 16q^{52} + 32q^{62} - 24q^{70} - 104q^{71} - 16q^{72} + 88q^{73} - 8q^{75} + 24q^{77} - 40q^{78} - 40q^{81} - 40q^{82} + 56q^{85} - 40q^{87} - 8q^{92} - 56q^{93} - 96q^{95} - 8q^{96} + 64q^{98} + O(q^{100}) \)

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.e.a \(8\) \(1.837\) 8.0.110166016.2 None \(0\) \(-4\) \(-4\) \(0\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.b \(8\) \(1.837\) 8.0.110166016.2 None \(0\) \(-4\) \(4\) \(0\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.c \(8\) \(1.837\) \(\Q(\zeta_{16})\) None \(0\) \(16\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)

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

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