Properties

Label 39.1.d
Level $39$
Weight $1$
Character orbit 39.d
Rep. character $\chi_{39}(38,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 39.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(39, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{3} - q^{4} + q^{9} + O(q^{10}) \) \( q - q^{3} - q^{4} + q^{9} + q^{12} - q^{13} + q^{16} - q^{25} - q^{27} - q^{36} + q^{39} + 2 q^{43} - q^{48} + q^{49} + q^{52} - 2 q^{61} - q^{64} + q^{75} - 2 q^{79} + q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.1.d.a 39.d 39.d $1$ $0.019$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) 39.1.d.a \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)