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Properties

Label 460.2.e
Level $460$
Weight $2$
Character orbit 460.e
Rep. character $\chi_{460}(91,\cdot)$
Character field $\Q$
Dimension $48$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
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 76 48 28
Cusp forms 68 48 20
Eisenstein series 8 0 8

Trace form

\( 48 q + 4 q^{2} - 2 q^{6} - 2 q^{8} - 48 q^{9} - 6 q^{12} + 24 q^{16} - 26 q^{18} - 4 q^{24} - 48 q^{25} + 14 q^{26} - 40 q^{29} - 16 q^{32} + 42 q^{36} + 8 q^{41} - 44 q^{46} + 14 q^{48} + 56 q^{49} - 4 q^{50}+ \cdots + 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.2.e.a 460.e 92.b $16$ $3.673$ 16.0.\(\cdots\).3 None 460.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots\)
460.2.e.b 460.e 92.b $32$ $3.673$ None 460.2.e.b \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(460, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)