Properties

Label 460.1.n
Level $460$
Weight $1$
Character orbit 460.n
Rep. character $\chi_{460}(39,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $20$
Newform subspaces $2$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 460.n (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(460, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 8 q^{21} - 4 q^{24} - 2 q^{25} - 4 q^{29} - 4 q^{30} - 6 q^{36} - 4 q^{41} + 16 q^{45} - 2 q^{46} + 16 q^{49} + 14 q^{54} + 18 q^{56} - 4 q^{61} - 2 q^{64} - 4 q^{69} - 4 q^{70} - 2 q^{80} - 10 q^{81} + 14 q^{84} + 18 q^{86} - 4 q^{89} - 4 q^{94} - 4 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(460, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.1.n.a 460.n 460.n $10$ $0.230$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-1\) \(9\) \(q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots\)
460.1.n.b 460.n 460.n $10$ $0.230$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-1\) \(-9\) \(q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots\)