Properties

Label 460.2.w
Level $460$
Weight $2$
Character orbit 460.w
Rep. character $\chi_{460}(3,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1360$
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.w (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{44})\)
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 1520 1520 0
Cusp forms 1360 1360 0
Eisenstein series 160 160 0

Trace form

\( 1360q - 18q^{2} - 36q^{5} - 44q^{6} - 18q^{8} + O(q^{10}) \) \( 1360q - 18q^{2} - 36q^{5} - 44q^{6} - 18q^{8} - 18q^{10} - 6q^{12} - 36q^{13} - 44q^{16} - 36q^{17} - 38q^{18} - 14q^{20} - 88q^{21} - 28q^{22} - 36q^{25} - 36q^{26} - 34q^{28} + 2q^{30} + 2q^{32} - 60q^{33} - 36q^{36} - 36q^{37} - 10q^{38} + 2q^{40} - 56q^{41} - 202q^{42} - 120q^{45} - 44q^{46} - 50q^{48} - 34q^{50} - 250q^{52} - 84q^{53} - 84q^{56} - 44q^{57} - 58q^{58} - 42q^{60} - 136q^{61} - 82q^{62} - 68q^{65} - 84q^{66} - 4q^{68} + 16q^{70} - 104q^{72} - 36q^{73} + 4q^{76} - 44q^{77} - 50q^{78} + 204q^{80} + 80q^{81} - 10q^{82} - 252q^{85} + 44q^{86} - 50q^{88} + 264q^{90} - 22q^{92} - 88q^{93} + 52q^{96} - 36q^{97} + 30q^{98} + O(q^{100}) \)

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.w.a \(1360\) \(3.673\) None \(-18\) \(0\) \(-36\) \(0\)