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

Related objects

Downloads

Learn more about

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

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

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 \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)