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

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

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

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