Properties

Label 39.2.j
Level $39$
Weight $2$
Character orbit 39.j
Rep. character $\chi_{39}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(39, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 6 2 4
Eisenstein series 8 0 8

Trace form

\( 2q + q^{3} - 2q^{4} - 3q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 2q^{4} - 3q^{7} - q^{9} - 6q^{11} - 4q^{12} + 7q^{13} + 6q^{15} - 4q^{16} + 6q^{19} + 12q^{20} + 6q^{23} - 14q^{25} - 2q^{27} + 6q^{28} - 6q^{29} - 6q^{33} - 6q^{35} - 2q^{36} + 2q^{39} - 12q^{41} + q^{43} + 6q^{45} + 4q^{48} - 4q^{49} - 10q^{52} + 24q^{53} + 12q^{55} - 6q^{59} - q^{61} + 3q^{63} + 16q^{64} + 6q^{65} + 15q^{67} - 6q^{69} - 18q^{71} - 7q^{75} - 12q^{76} + 12q^{77} - 22q^{79} - 24q^{80} - q^{81} + 6q^{84} + 6q^{87} + 12q^{89} - 9q^{91} - 24q^{92} + 3q^{93} + 12q^{95} - 9q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
39.2.j.a \(2\) \(0.311\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-3\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(39, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(39, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)