Properties

Label 21.3.d
Level $21$
Weight $3$
Character orbit 21.d
Rep. character $\chi_{21}(13,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

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

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