Properties

Label 460.2.c
Level $460$
Weight $2$
Character orbit 460.c
Rep. character $\chi_{460}(369,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(460, [\chi])\).

Total New Old
Modular forms 78 12 66
Cusp forms 66 12 54
Eisenstein series 12 0 12

Trace form

\( 12q - 20q^{9} + O(q^{10}) \) \( 12q - 20q^{9} + 4q^{11} + 2q^{15} - 8q^{19} + 8q^{25} - 10q^{29} + 18q^{31} - 10q^{35} + 16q^{39} - 2q^{41} + 2q^{45} - 38q^{49} - 24q^{51} + 16q^{55} + 22q^{59} - 8q^{61} + 38q^{65} - 8q^{69} - 34q^{71} + 16q^{75} - 20q^{79} + 28q^{81} + 6q^{85} + 48q^{89} - 8q^{91} + 12q^{95} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(460, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
460.2.c.a \(12\) \(3.673\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{6})q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)