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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 (8 matches)

  displayed columns for results
Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11 13
4719.2.a.e 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.g 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.l 4719.a 1.a $1$ $37.681$ \(\Q\) None \(2\) \(-1\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
4719.2.a.n 4719.a 1.a $2$ $37.681$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
4719.2.a.r 4719.a 1.a $3$ $37.681$ 3.3.321.1 None \(-2\) \(-3\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots\)
4719.2.a.u 4719.a 1.a $3$ $37.681$ 3.3.564.1 None \(1\) \(-3\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4719.2.a.x 4719.a 1.a $4$ $37.681$ 4.4.2777.1 None \(-2\) \(-4\) \(-3\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.bi 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(-8\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
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