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Properties

Label 21.3.b
Level $21$
Weight $3$
Character orbit 21.b
Rep. character $\chi_{21}(8,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.3.b.a 21.b 3.b $4$ $0.572$ 4.0.65856.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)