Properties

Label 495.2.z
Level $495$
Weight $2$
Character orbit 495.z
Rep. character $\chi_{495}(134,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 320 96 224
Cusp forms 256 96 160
Eisenstein series 64 0 64

Trace form

\( 96 q + 24 q^{4} + O(q^{10}) \) \( 96 q + 24 q^{4} + 24 q^{16} - 12 q^{25} + 40 q^{31} + 16 q^{34} - 60 q^{40} - 40 q^{46} - 112 q^{49} - 32 q^{55} - 40 q^{61} - 96 q^{64} - 28 q^{70} - 40 q^{79} + 100 q^{85} - 32 q^{91} - 40 q^{94} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.z.a 495.z 165.r $96$ $3.953$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)