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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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Level Weight Analytic conductor \(Nk^2\) Dim.
Bad \(p\) Char. Primitive character Character order Coefficient field
Self-twists CM/RM discriminant Inner twist count Is self-dual Analytic rank
Coefficient ring index Coefficient ring gens. Projective image Projective image type
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Results (15 matches)

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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 13
1638.2.a.a 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.c 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.f 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
1638.2.a.g 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.i 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1638.2.a.j 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
1638.2.a.k 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
1638.2.a.p 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots\)
1638.2.a.q 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}-q^{13}+\cdots\)
1638.2.a.r 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1638.2.a.s 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
1638.2.a.t 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(3\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1638.2.a.w 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{41}) \) None \(-2\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1638.2.a.x 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.a.y 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{57}) \) None \(2\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
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