Properties

Label 21.2.g
Level 21
Weight 2
Character orbit g
Rep. character \(\chi_{21}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
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.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 9q^{19} \) \(\mathstrut -\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 18q^{57} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 11q^{67} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut +\mathstrut 13q^{79} \) \(\mathstrut -\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut +\mathstrut 9q^{91} \) \(\mathstrut -\mathstrut 15q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.g.a \(2\) \(0.168\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(1\) \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)