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

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

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 \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)