Properties

Label 21.3.f
Level 21
Weight 3
Character orbit f
Rep. character \(\chi_{21}(10,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 6
Newforms 3
Sturm bound 8
Trace bound 2

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(8\)
Trace bound: \(2\)
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 6 8
Cusp forms 6 6 0
Eisenstein series 8 0 8

Trace form

\(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut 24q^{12} \) \(\mathstrut +\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 22q^{16} \) \(\mathstrut +\mathstrut 48q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 36q^{21} \) \(\mathstrut +\mathstrut 28q^{22} \) \(\mathstrut -\mathstrut 68q^{23} \) \(\mathstrut -\mathstrut 54q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 126q^{26} \) \(\mathstrut -\mathstrut 34q^{28} \) \(\mathstrut +\mathstrut 64q^{29} \) \(\mathstrut +\mathstrut 48q^{30} \) \(\mathstrut -\mathstrut 69q^{31} \) \(\mathstrut +\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 108q^{33} \) \(\mathstrut +\mathstrut 114q^{35} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 43q^{37} \) \(\mathstrut +\mathstrut 174q^{38} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 48q^{42} \) \(\mathstrut -\mathstrut 134q^{43} \) \(\mathstrut -\mathstrut 108q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 52q^{46} \) \(\mathstrut -\mathstrut 222q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 68q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 84q^{52} \) \(\mathstrut -\mathstrut 32q^{53} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 90q^{57} \) \(\mathstrut +\mathstrut 34q^{58} \) \(\mathstrut +\mathstrut 84q^{59} \) \(\mathstrut +\mathstrut 18q^{60} \) \(\mathstrut +\mathstrut 216q^{61} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut -\mathstrut 28q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 108q^{66} \) \(\mathstrut +\mathstrut 69q^{67} \) \(\mathstrut +\mathstrut 36q^{68} \) \(\mathstrut -\mathstrut 198q^{70} \) \(\mathstrut +\mathstrut 244q^{71} \) \(\mathstrut +\mathstrut 12q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut +\mathstrut 39q^{75} \) \(\mathstrut +\mathstrut 52q^{77} \) \(\mathstrut +\mathstrut 204q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut -\mathstrut 144q^{82} \) \(\mathstrut +\mathstrut 120q^{84} \) \(\mathstrut -\mathstrut 96q^{85} \) \(\mathstrut +\mathstrut 158q^{86} \) \(\mathstrut +\mathstrut 54q^{87} \) \(\mathstrut -\mathstrut 202q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut +\mathstrut 303q^{91} \) \(\mathstrut -\mathstrut 168q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 150q^{95} \) \(\mathstrut -\mathstrut 234q^{96} \) \(\mathstrut -\mathstrut 176q^{98} \) \(\mathstrut -\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.f.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(9\) \(13\) \(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
21.3.f.b \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-9\) \(-7\) \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
21.3.f.c \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-7\) \(q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)