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Properties

Label 1560.1.cs
Level $1560$
Weight $1$
Character orbit 1560.cs
Rep. character $\chi_{1560}(467,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $6$
Sturm bound $336$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1560.cs (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(10\)

Dimensions

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

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 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 40 0 0 0

Trace form

\( 40 q + O(q^{10}) \) \( 40 q + 8 q^{10} - 8 q^{12} - 24 q^{16} - 8 q^{22} + 12 q^{27} - 4 q^{30} + 8 q^{40} - 12 q^{42} - 16 q^{43} + 8 q^{52} + 12 q^{75} - 16 q^{81} - 8 q^{82} - 8 q^{88} + 12 q^{90} + O(q^{100}) \)

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.cs.a 1560.cs 1560.bs $4$ $0.779$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
1560.1.cs.b 1560.cs 1560.bs $4$ $0.779$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-26}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
1560.1.cs.c 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-26}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)
1560.1.cs.d 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1560.1.cs.e 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
1560.1.cs.f 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)