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 $1$

Related objects

Downloads

Learn more

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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.2.g.a 460.g 460.g $4$ $3.673$ \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots\)
460.2.g.b 460.g 460.g $8$ $3.673$ 8.0.207360000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
460.2.g.c 460.g 460.g $56$ $3.673$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$