Properties

Label 21.3.b
Level 21
Weight 3
Character orbit b
Rep. character \(\chi_{21}(8,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(21, [\chi])\).

Total New Old
Modular forms 8 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\( 4q - 2q^{3} - 12q^{4} + 14q^{6} - 20q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 12q^{4} + 14q^{6} - 20q^{9} + 28q^{10} - 22q^{12} - 36q^{13} + 28q^{15} + 36q^{16} + 56q^{18} + 12q^{19} + 14q^{21} - 56q^{22} - 126q^{24} - 12q^{25} + 10q^{27} - 56q^{28} - 28q^{30} + 136q^{31} + 28q^{33} + 116q^{36} + 16q^{37} + 4q^{39} + 84q^{40} + 70q^{42} - 160q^{43} - 140q^{45} - 168q^{46} + 38q^{48} + 28q^{49} - 84q^{51} + 164q^{52} - 154q^{54} + 56q^{55} + 64q^{57} + 112q^{58} + 140q^{60} - 156q^{61} - 28q^{63} + 4q^{64} - 28q^{66} - 24q^{67} + 168q^{69} - 28q^{70} - 32q^{73} + 146q^{75} - 316q^{76} - 196q^{78} + 128q^{79} - 68q^{81} + 392q^{82} - 14q^{84} + 168q^{85} + 28q^{87} + 168q^{88} - 112q^{90} - 28q^{91} - 96q^{93} - 336q^{94} - 98q^{96} - 8q^{97} + 112q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.3.b.a \(4\) \(0.572\) 4.0.65856.1 None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)