Properties

Label 20.3.f
Level 20
Weight 3
Character orbit f
Rep. character \(\chi_{20}(13,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2q + 2q^{3} - 6q^{5} - 14q^{7} + O(q^{10}) \) \( 2q + 2q^{3} - 6q^{5} - 14q^{7} + 20q^{11} + 18q^{13} + 2q^{15} + 2q^{17} - 28q^{21} - 46q^{23} - 14q^{25} + 32q^{27} - 28q^{31} + 20q^{33} + 98q^{35} + 66q^{37} - 28q^{41} - 30q^{43} - 56q^{45} - 78q^{47} + 4q^{51} - 14q^{53} - 60q^{55} - 16q^{57} + 84q^{61} + 98q^{63} + 18q^{65} - 14q^{67} + 196q^{71} + 98q^{73} - 62q^{75} - 140q^{77} - 62q^{81} - 126q^{83} - 14q^{85} - 16q^{87} - 252q^{91} - 28q^{93} + 64q^{95} + 66q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.3.f.a \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)