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Properties

Label 1560.1.dk
Level $1560$
Weight $1$
Character orbit 1560.dk
Rep. character $\chi_{1560}(1109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $336$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1560.dk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1560, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{4} - 4 q^{9} - 4 q^{16} - 8 q^{25} - 4 q^{30} + 4 q^{36} + 4 q^{39} + 12 q^{46} + 4 q^{49} - 4 q^{55} - 8 q^{64} - 8 q^{66} - 8 q^{79} - 4 q^{81} - 4 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1560.1.dk.a 1560.dk 1560.ck $4$ $0.779$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-30}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
1560.1.dk.b 1560.dk 1560.ck $4$ $0.779$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-30}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)