Properties

Label 20.3.b
Level 20
Weight 3
Character orbit b
Rep. character \(\chi_{20}(11,\cdot)\)
Character field \(\Q\)
Dimension 4
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
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 8 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 24q^{17} \) \(\mathstrut +\mathstrut 22q^{18} \) \(\mathstrut +\mathstrut 20q^{20} \) \(\mathstrut +\mathstrut 40q^{21} \) \(\mathstrut -\mathstrut 80q^{22} \) \(\mathstrut -\mathstrut 80q^{24} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 40q^{30} \) \(\mathstrut +\mathstrut 128q^{32} \) \(\mathstrut +\mathstrut 80q^{33} \) \(\mathstrut +\mathstrut 92q^{34} \) \(\mathstrut -\mathstrut 36q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 80q^{38} \) \(\mathstrut +\mathstrut 40q^{40} \) \(\mathstrut -\mathstrut 112q^{41} \) \(\mathstrut -\mathstrut 120q^{42} \) \(\mathstrut -\mathstrut 80q^{44} \) \(\mathstrut -\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 10q^{50} \) \(\mathstrut +\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 176q^{53} \) \(\mathstrut +\mathstrut 80q^{54} \) \(\mathstrut +\mathstrut 80q^{56} \) \(\mathstrut -\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 40q^{60} \) \(\mathstrut +\mathstrut 128q^{61} \) \(\mathstrut -\mathstrut 80q^{62} \) \(\mathstrut -\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut +\mathstrut 80q^{66} \) \(\mathstrut -\mathstrut 136q^{68} \) \(\mathstrut +\mathstrut 120q^{69} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 264q^{73} \) \(\mathstrut -\mathstrut 108q^{74} \) \(\mathstrut +\mathstrut 240q^{77} \) \(\mathstrut -\mathstrut 80q^{78} \) \(\mathstrut -\mathstrut 80q^{80} \) \(\mathstrut -\mathstrut 276q^{81} \) \(\mathstrut +\mathstrut 116q^{82} \) \(\mathstrut +\mathstrut 160q^{84} \) \(\mathstrut -\mathstrut 160q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut +\mathstrut 160q^{88} \) \(\mathstrut -\mathstrut 88q^{89} \) \(\mathstrut +\mathstrut 30q^{90} \) \(\mathstrut -\mathstrut 120q^{92} \) \(\mathstrut -\mathstrut 400q^{93} \) \(\mathstrut -\mathstrut 120q^{94} \) \(\mathstrut -\mathstrut 264q^{97} \) \(\mathstrut +\mathstrut 102q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(4\) \(0.545\) \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)