Properties

Label 21.3.h
Level 21
Weight 3
Character orbit h
Rep. character \(\chi_{21}(2,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 6
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 14 14 0
Cusp forms 6 6 0
Eisenstein series 8 8 0

Trace form

\(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 38q^{13} \) \(\mathstrut +\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 22q^{16} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut -\mathstrut 100q^{22} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut -\mathstrut 65q^{25} \) \(\mathstrut -\mathstrut 142q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 50q^{33} \) \(\mathstrut +\mathstrut 240q^{34} \) \(\mathstrut +\mathstrut 76q^{36} \) \(\mathstrut +\mathstrut 49q^{37} \) \(\mathstrut +\mathstrut 77q^{39} \) \(\mathstrut -\mathstrut 30q^{40} \) \(\mathstrut -\mathstrut 70q^{42} \) \(\mathstrut +\mathstrut 54q^{43} \) \(\mathstrut -\mathstrut 40q^{45} \) \(\mathstrut -\mathstrut 60q^{46} \) \(\mathstrut -\mathstrut 248q^{48} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 120q^{51} \) \(\mathstrut -\mathstrut 96q^{52} \) \(\mathstrut +\mathstrut 70q^{54} \) \(\mathstrut +\mathstrut 100q^{55} \) \(\mathstrut +\mathstrut 62q^{57} \) \(\mathstrut -\mathstrut 70q^{58} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut +\mathstrut 127q^{63} \) \(\mathstrut -\mathstrut 36q^{64} \) \(\mathstrut +\mathstrut 100q^{66} \) \(\mathstrut -\mathstrut 91q^{67} \) \(\mathstrut +\mathstrut 120q^{69} \) \(\mathstrut +\mathstrut 70q^{70} \) \(\mathstrut +\mathstrut 120q^{72} \) \(\mathstrut +\mathstrut 61q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 24q^{76} \) \(\mathstrut +\mathstrut 40q^{78} \) \(\mathstrut +\mathstrut 147q^{79} \) \(\mathstrut +\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 140q^{82} \) \(\mathstrut -\mathstrut 76q^{84} \) \(\mathstrut -\mathstrut 240q^{85} \) \(\mathstrut -\mathstrut 70q^{87} \) \(\mathstrut +\mathstrut 150q^{88} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 327q^{91} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut -\mathstrut 70q^{96} \) \(\mathstrut -\mathstrut 368q^{97} \) \(\mathstrut -\mathstrut 400q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.h.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-13\) \(q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
21.3.h.b \(4\) \(0.572\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(14\) \(q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)