Properties

Label 460.2.g
Level $460$
Weight $2$
Character orbit 460.g
Rep. character $\chi_{460}(459,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $3$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68q - 8q^{4} - 16q^{6} + 52q^{9} + O(q^{10}) \) \( 68q - 8q^{4} - 16q^{6} + 52q^{9} - 8q^{16} - 20q^{24} - 4q^{25} + 24q^{26} - 16q^{29} - 48q^{36} - 16q^{41} + 12q^{46} - 44q^{49} - 32q^{50} - 12q^{54} + 4q^{64} - 28q^{69} - 4q^{70} + 12q^{81} + 16q^{85} + 52q^{94} + 56q^{96} + O(q^{100}) \)

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.g.a \(4\) \(3.673\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots\)
460.2.g.b \(8\) \(3.673\) 8.0.207360000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
460.2.g.c \(56\) \(3.673\) None \(0\) \(0\) \(0\) \(0\)