↑

Properties

Label 495.2.k
Level $495$
Weight $2$
Character orbit 495.k
Rep. character $\chi_{495}(208,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(5\)
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 64 96
Cusp forms 128 56 72
Eisenstein series 32 8 24

Trace form

\( 56 q + O(q^{10}) \) \( 56 q + 4 q^{11} - 60 q^{16} + 16 q^{20} + 4 q^{22} + 18 q^{23} - 18 q^{25} + 40 q^{26} - 24 q^{31} + 30 q^{37} + 16 q^{38} + 12 q^{47} - 8 q^{53} - 10 q^{55} - 160 q^{56} + 24 q^{58} - 90 q^{67} + 80 q^{70} + 76 q^{71} - 24 q^{77} + 128 q^{80} + 40 q^{82} - 80 q^{86} + 20 q^{88} - 128 q^{92} + 18 q^{97} + O(q^{100}) \)

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.k.a 495.k 55.e $4$ $3.953$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-2\beta _{2}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
495.2.k.b 495.k 55.e $4$ $3.953$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2+\beta _{2})q^{5}+\beta _{3}q^{8}+\cdots\)
495.2.k.c 495.k 55.e $24$ $3.953$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
495.2.k.d 495.k 55.e $24$ $3.953$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)