Properties

Label 495.2.d
Level $495$
Weight $2$
Character orbit 495.d
Rep. character $\chi_{495}(494,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
Sturm bound $144$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(29\)

Dimensions

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

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q - 24 q^{4} + O(q^{10}) \) \( 24 q - 24 q^{4} + 56 q^{16} - 48 q^{25} - 16 q^{34} + 72 q^{49} - 8 q^{55} - 184 q^{64} + 8 q^{70} + 32 q^{91} + O(q^{100}) \)

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.d.a 495.d 165.d $4$ $3.953$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}+q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
495.2.d.b 495.d 165.d $4$ $3.953$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
495.2.d.c 495.d 165.d $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{13}q^{2}+(-2-\beta _{3})q^{4}+\beta _{7}q^{5}+\cdots\)

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

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