Properties

Label 21.2.e
Level 21
Weight 2
Character orbit e
Rep. character \(\chi_{21}(4,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 21.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(21, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 9q^{31} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 11q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 36q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut -\mathstrut 16q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 3q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut q^{79} \) \(\mathstrut -\mathstrut 8q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 5q^{91} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(21, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.2.e.a \(2\) \(0.168\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(2\) \(-5\) \(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)