Properties

Label 39.2.e
Level $39$
Weight $2$
Character orbit 39.e
Rep. character $\chi_{39}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $9$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(39, [\chi])\).

Total New Old
Modular forms 14 6 8
Cusp forms 6 6 0
Eisenstein series 8 0 8

Trace form

\( 6 q - 2 q^{2} - q^{3} - 4 q^{4} - 8 q^{5} + q^{7} + 12 q^{8} - 3 q^{9} - 6 q^{10} + 6 q^{11} + 12 q^{12} - 5 q^{13} - 16 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} - 10 q^{21} + 4 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.2.e.a 39.e 13.c $2$ $0.311$ \(\Q(\sqrt{-3}) \) None 39.2.e.a \(-1\) \(1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
39.2.e.b 39.e 13.c $4$ $0.311$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 39.2.e.b \(-1\) \(-2\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)