↑

Properties

Label 31.2.c
Level $31$
Weight $2$
Character orbit 31.c
Rep. character $\chi_{31}(5,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(31, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} - 4 q^{15} + 12 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21}+ \cdots + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(31, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
31.2.c.a 31.c 31.c $4$ $0.248$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 31.2.c.a \(-4\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)