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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
39.1.d.a \(1\) \(0.019\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 + T^{2} \)
$7$ \( ( 1 - T )( 1 + T ) \)
$11$ \( 1 + T^{2} \)
$13$ \( 1 + T \)
$17$ \( ( 1 - T )( 1 + T ) \)
$19$ \( ( 1 - T )( 1 + T ) \)
$23$ \( ( 1 - T )( 1 + T ) \)
$29$ \( ( 1 - T )( 1 + T ) \)
$31$ \( ( 1 - T )( 1 + T ) \)
$37$ \( ( 1 - T )( 1 + T ) \)
$41$ \( 1 + T^{2} \)
$43$ \( ( 1 - T )^{2} \)
$47$ \( 1 + T^{2} \)
$53$ \( ( 1 - T )( 1 + T ) \)
$59$ \( 1 + T^{2} \)
$61$ \( ( 1 + T )^{2} \)
$67$ \( ( 1 - T )( 1 + T ) \)
$71$ \( 1 + T^{2} \)
$73$ \( ( 1 - T )( 1 + T ) \)
$79$ \( ( 1 + T )^{2} \)
$83$ \( 1 + T^{2} \)
$89$ \( 1 + T^{2} \)
$97$ \( ( 1 - T )( 1 + T ) \)
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