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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 (8 matches)

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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5
405.4.a.a 405.a 1.a $1$ $23.896$ \(\Q\) None \(-5\) \(0\) \(5\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+5q^{5}+9q^{7}-45q^{8}+\cdots\)
405.4.a.d 405.a 1.a $2$ $23.896$ \(\Q(\sqrt{33}) \) None \(-1\) \(0\) \(10\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+\beta q^{4}+5q^{5}+(5-\beta )q^{7}+(-8+\cdots)q^{8}+\cdots\)
405.4.a.e 405.a 1.a $2$ $23.896$ \(\Q(\sqrt{33}) \) None \(1\) \(0\) \(-10\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{4}-5q^{5}+(5-\beta )q^{7}+(8+\cdots)q^{8}+\cdots\)
405.4.a.f 405.a 1.a $2$ $23.896$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(10\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-4+2\beta )q^{4}+5q^{5}+\cdots\)
405.4.a.g 405.a 1.a $3$ $23.896$ 3.3.7032.1 None \(-1\) \(0\) \(15\) \(-25\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
405.4.a.h 405.a 1.a $3$ $23.896$ 3.3.2292.1 None \(-1\) \(0\) \(15\) \(-43\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(3-\beta _{1}-\beta _{2})q^{4}+5q^{5}+\cdots\)
405.4.a.j 405.a 1.a $3$ $23.896$ 3.3.2292.1 None \(1\) \(0\) \(-15\) \(-43\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3-\beta _{1}-\beta _{2})q^{4}-5q^{5}+\cdots\)
405.4.a.k 405.a 1.a $6$ $23.896$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-4\) \(0\) \(-30\) \(40\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{3})q^{4}+\cdots\)
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