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Properties

Label 495.2.u
Level $495$
Weight $2$
Character orbit 495.u
Rep. character $\chi_{495}(34,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

Total New Old
Modular forms 152 120 32
Cusp forms 136 120 16
Eisenstein series 16 0 16

Trace form

\( 120 q + 60 q^{4} - q^{5} + 8 q^{6} + 2 q^{9} + 8 q^{11} - 20 q^{14} - 28 q^{15} - 60 q^{16} - 10 q^{20} - 40 q^{21} - 16 q^{24} + 3 q^{25} - 48 q^{26} - 12 q^{29} + 26 q^{30} - 6 q^{31} + 12 q^{34} + 48 q^{36}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.u.a 495.u 45.j $52$ $3.953$ None 495.2.u.a \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$
495.2.u.b 495.u 45.j $68$ $3.953$ None 495.2.u.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)