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 $0$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.2.e.a \(2\) \(0.160\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)