↑

Properties

Label 55.3.k
Level $55$
Weight $3$
Character orbit 55.k
Rep. character $\chi_{55}(3,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $80$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 55.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(55, [\chi])\).

Total New Old
Modular forms 112 112 0
Cusp forms 80 80 0
Eisenstein series 32 32 0

Trace form

\( 80 q - 6 q^{2} - 8 q^{3} - 2 q^{5} - 12 q^{6} - 40 q^{7} - 22 q^{8} - 32 q^{10} - 20 q^{11} + 76 q^{12} - 14 q^{13} - 110 q^{15} - 4 q^{16} + 36 q^{17} + 14 q^{18} - 52 q^{20} + 24 q^{21} - 10 q^{22} - 24 q^{23}+ \cdots + 1780 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.3.k.a 55.k 55.k $80$ $1.499$ None 55.3.k.a \(-6\) \(-8\) \(-2\) \(-40\) $\mathrm{SU}(2)[C_{20}]$