Properties

Label 460.2.o
Level $460$
Weight $2$
Character orbit 460.o
Rep. character $\chi_{460}(19,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $680$
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.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{22})\)
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 760 760 0
Cusp forms 680 680 0
Eisenstein series 80 80 0

Trace form

\( 680q - 14q^{4} - 22q^{5} - 6q^{6} - 96q^{9} + O(q^{10}) \) \( 680q - 14q^{4} - 22q^{5} - 6q^{6} - 96q^{9} - 11q^{10} - 22q^{14} - 14q^{16} - 11q^{20} - 44q^{21} - 24q^{24} - 18q^{25} - 46q^{26} - 28q^{29} - 11q^{30} - 44q^{34} + 26q^{36} - 11q^{40} - 28q^{41} - 154q^{44} - 34q^{46} + 21q^{50} - 98q^{54} - 22q^{56} - 11q^{60} - 44q^{61} - 26q^{64} - 22q^{65} + 44q^{66} - 16q^{69} - 18q^{70} - 22q^{74} + 88q^{76} - 110q^{80} - 232q^{81} - 22q^{84} + 94q^{85} + 198q^{86} - 44q^{89} - 242q^{90} - 118q^{94} + 340q^{96} + O(q^{100}) \)

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.o.a \(40\) \(3.673\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\)
460.2.o.b \(640\) \(3.673\) None \(0\) \(0\) \(-22\) \(0\)