Properties

Label 1560.1.y
Level $1560$
Weight $1$
Character orbit 1560.y
Rep. character $\chi_{1560}(389,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
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.y (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
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 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 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

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} - 4 q^{10} + 8 q^{16} + 4 q^{30} - 8 q^{39} - 4 q^{40} - 8 q^{49} - 8 q^{55} + 8 q^{66} + 8 q^{81} - 4 q^{90} - 8 q^{94} + O(q^{100}) \)

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.y.a 1560.y 1560.y $1$ $0.779$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(-1\) \(-1\) \(1\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1560.1.y.b 1560.y 1560.y $1$ $0.779$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1560.1.y.c 1560.y 1560.y $1$ $0.779$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(1\) \(-1\) \(-1\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1560.1.y.d 1560.y 1560.y $1$ $0.779$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1560.1.y.e 1560.y 1560.y $2$ $0.779$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{130}) \) \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
1560.1.y.f 1560.y 1560.y $2$ $0.779$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{130}) \) \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+iq^{8}+\cdots\)