Properties

Label 460.2.e
Level $460$
Weight $2$
Character orbit 460.e
Rep. character $\chi_{460}(91,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 76 48 28
Cusp forms 68 48 20
Eisenstein series 8 0 8

Trace form

\( 48q + 4q^{2} - 2q^{6} - 2q^{8} - 48q^{9} + O(q^{10}) \) \( 48q + 4q^{2} - 2q^{6} - 2q^{8} - 48q^{9} - 6q^{12} + 24q^{16} - 26q^{18} - 4q^{24} - 48q^{25} + 14q^{26} - 40q^{29} - 16q^{32} + 42q^{36} + 8q^{41} - 44q^{46} + 14q^{48} + 56q^{49} - 4q^{50} + 50q^{52} + 2q^{54} + 26q^{58} - 30q^{62} + 30q^{64} - 4q^{69} - 110q^{72} + 154q^{78} + 8q^{81} - 22q^{82} - 32q^{85} + 64q^{92} - 80q^{93} - 6q^{94} - 6q^{96} + 44q^{98} + O(q^{100}) \)

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.e.a \(16\) \(3.673\) 16.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots\)
460.2.e.b \(32\) \(3.673\) None \(4\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)