Properties

Label 20.2.e
Level $20$
Weight $2$
Character orbit 20.e
Rep. character $\chi_{20}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(20, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

Trace form

\( 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + O(q^{10}) \) \( 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 6 q^{10} - 2 q^{13} - 8 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{25} + 4 q^{26} + 8 q^{32} + 12 q^{36} - 14 q^{37} - 4 q^{40} - 16 q^{41} + 6 q^{45} - 14 q^{50} - 4 q^{52} + 18 q^{53} + 8 q^{58} + 24 q^{61} + 2 q^{65} - 12 q^{68} - 12 q^{72} - 22 q^{73} + 16 q^{80} - 18 q^{81} + 16 q^{82} - 18 q^{85} + 6 q^{90} + 26 q^{97} + 14 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.2.e.a 20.e 20.e $2$ $0.160$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 20.2.e.a \(-2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)