Properties

Label 39.2.k
Level $39$
Weight $2$
Character orbit 39.k
Rep. character $\chi_{39}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $12$
Newform subspaces $2$
Sturm bound $9$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 28 28 0
Cusp forms 12 12 0
Eisenstein series 16 16 0

Trace form

\( 12q - 2q^{3} - 12q^{4} - 2q^{6} - 14q^{7} - 2q^{9} + O(q^{10}) \) \( 12q - 2q^{3} - 12q^{4} - 2q^{6} - 14q^{7} - 2q^{9} + 12q^{10} + 8q^{13} - 14q^{15} + 4q^{16} + 4q^{18} - 2q^{19} + 22q^{21} + 4q^{22} + 18q^{24} + 4q^{27} + 18q^{30} - 6q^{31} + 16q^{33} - 36q^{34} - 36q^{36} - 30q^{37} - 38q^{39} - 24q^{40} - 16q^{42} + 30q^{43} - 20q^{45} - 14q^{48} + 18q^{49} + 76q^{52} + 46q^{54} + 4q^{55} + 28q^{57} + 28q^{58} + 44q^{60} + 28q^{61} + 16q^{63} - 40q^{66} - 8q^{67} - 32q^{70} + 12q^{72} - 62q^{73} - 18q^{75} - 36q^{76} - 80q^{78} + 16q^{79} - 14q^{81} - 24q^{82} - 8q^{84} + 12q^{85} - 34q^{87} - 12q^{88} + 10q^{91} + 10q^{93} + 64q^{94} + 16q^{96} - 18q^{97} + 40q^{99} + O(q^{100}) \)

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.k.a \(4\) \(0.311\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-10\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(-2+\cdots)q^{7}+\cdots\)
39.2.k.b \(8\) \(0.311\) 8.0.56070144.2 None \(0\) \(-2\) \(0\) \(-4\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+2\beta _{5}+\beta _{7})q^{2}+\cdots\)