Properties

Label 21.3.d
Level 21
Weight 3
Character orbit d
Rep. character \(\chi_{21}(13,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newforms: \( 1 \)
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 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 20q^{11} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 28q^{23} \) \(\mathstrut -\mathstrut 46q^{25} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 76q^{29} \) \(\mathstrut +\mathstrut 24q^{30} \) \(\mathstrut +\mathstrut 66q^{32} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 18q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 24q^{42} \) \(\mathstrut +\mathstrut 52q^{43} \) \(\mathstrut -\mathstrut 60q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 94q^{49} \) \(\mathstrut -\mathstrut 46q^{50} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 14q^{56} \) \(\mathstrut +\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 76q^{58} \) \(\mathstrut -\mathstrut 72q^{60} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 26q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 148q^{67} \) \(\mathstrut +\mathstrut 96q^{70} \) \(\mathstrut -\mathstrut 124q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 52q^{74} \) \(\mathstrut +\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 92q^{79} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 140q^{88} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut +\mathstrut 84q^{92} \) \(\mathstrut -\mathstrut 96q^{93} \) \(\mathstrut -\mathstrut 288q^{95} \) \(\mathstrut -\mathstrut 94q^{98} \) \(\mathstrut -\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)