↑

Properties

Label 495.2.l
Level $495$
Weight $2$
Character orbit 495.l
Rep. character $\chi_{495}(188,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $2$
Sturm bound $144$
Trace bound $8$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 160 40 120
Cusp forms 128 40 88
Eisenstein series 32 0 32

Trace form

\( 40 q + O(q^{10}) \) \( 40 q + 8 q^{13} - 56 q^{16} - 64 q^{28} + 64 q^{31} + 24 q^{37} + 56 q^{40} - 104 q^{52} + 8 q^{58} - 96 q^{61} + 32 q^{67} - 64 q^{70} + 24 q^{73} - 96 q^{76} + 8 q^{82} + 64 q^{85} + 48 q^{88} + 96 q^{91} - 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 495.l 15.e $20$ $3.953$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}-\beta _{9}q^{5}+\cdots\)
495.2.l.b 495.l 15.e $20$ $3.953$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}+\beta _{9}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)