Properties

Label 13.4.e
Level $13$
Weight $4$
Character orbit 13.e
Rep. character $\chi_{13}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $4$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 13.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(13, [\chi])\).

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

Trace form

\( 4 q - 3 q^{2} + 5 q^{3} - q^{4} - 48 q^{6} + 15 q^{7} + q^{9} + 51 q^{10} - 15 q^{11} + 76 q^{12} + 65 q^{13} - 204 q^{14} + 174 q^{15} + 79 q^{16} - 144 q^{17} - 351 q^{19} - 111 q^{20} + 102 q^{22}+ \cdots - 1437 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(13, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
13.4.e.a 13.e 13.e $2$ $0.767$ \(\Q(\sqrt{-3}) \) None 13.4.e.a \(-6\) \(7\) \(0\) \(39\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
13.4.e.b 13.e 13.e $2$ $0.767$ \(\Q(\sqrt{-3}) \) None 13.4.e.b \(3\) \(-2\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)