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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 (17 matches)

  displayed columns for results
Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 23 29
4002.2.a.b 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
4002.2.a.d 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
4002.2.a.f 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.h 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
4002.2.a.i 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
4002.2.a.j 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(1\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
4002.2.a.k 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4002.2.a.m 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-3\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.o 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
4002.2.a.p 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4002.2.a.v 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4002.2.a.z 4002.a 1.a $3$ $31.956$ 3.3.316.1 None \(3\) \(-3\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.bb 4002.a 1.a $4$ $31.956$ 4.4.23252.1 None \(-4\) \(4\) \(-3\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
4002.2.a.bc 4002.a 1.a $4$ $31.956$ 4.4.11324.1 None \(4\) \(4\) \(-4\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4002.2.a.be 4002.a 1.a $5$ $31.956$ 5.5.2389280.1 None \(-5\) \(-5\) \(1\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bg 4002.a 1.a $7$ $31.956$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-5\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bi 4002.a 1.a $8$ $31.956$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(-3\) \(-6\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
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