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Level Weight Analytic conductor Analytic rank Dim.
Bad \(p\) Char. Primitive character Character order Is maximal/largest
Coefficient field Self-twists CM/RM discriminant Inner twist count Is self-dual
Coefficient ring index Coefficient ring gens. Is twist minimal Projective image
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Results (28 matches)

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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 23 41
5658.2.a.a 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.a \(-1\) \(-1\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
5658.2.a.b 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.b \(-1\) \(-1\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
5658.2.a.c 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.c \(-1\) \(-1\) \(0\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
5658.2.a.d 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.d \(1\) \(-1\) \(-4\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-2q^{7}+\cdots\)
5658.2.a.e 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.e \(1\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
5658.2.a.f 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.f \(1\) \(-1\) \(1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5658.2.a.g 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.g \(1\) \(1\) \(-3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
5658.2.a.h 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.h \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5658.2.a.i 5658.a 1.a $1$ $45.179$ \(\Q\) None 5658.2.a.i \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
5658.2.a.j 5658.a 1.a $2$ $45.179$ \(\Q(\sqrt{3}) \) None 5658.2.a.j \(2\) \(-2\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2\beta q^{5}-q^{6}+2q^{7}+\cdots\)
5658.2.a.k 5658.a 1.a $2$ $45.179$ \(\Q(\sqrt{17}) \) None 5658.2.a.k \(2\) \(-2\) \(3\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5658.2.a.l 5658.a 1.a $2$ $45.179$ \(\Q(\sqrt{2}) \) None 5658.2.a.l \(2\) \(2\) \(4\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
5658.2.a.m 5658.a 1.a $5$ $45.179$ 5.5.89417.1 None 5658.2.a.m \(5\) \(5\) \(-5\) \(-7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{3}-\beta _{4})q^{5}+\cdots\)
5658.2.a.n 5658.a 1.a $6$ $45.179$ 6.6.105029297.1 None 5658.2.a.n \(6\) \(-6\) \(-7\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots\)
5658.2.a.o 5658.a 1.a $6$ $45.179$ 6.6.51083225.1 None 5658.2.a.o \(6\) \(-6\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(\beta _{3}-\beta _{4})q^{5}-q^{6}+\cdots\)
5658.2.a.p 5658.a 1.a $7$ $45.179$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 5658.2.a.p \(7\) \(7\) \(7\) \(11\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots\)
5658.2.a.q 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.q \(-8\) \(-8\) \(-2\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
5658.2.a.r 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.r \(-8\) \(-8\) \(1\) \(9\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
5658.2.a.s 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.s \(-8\) \(-8\) \(3\) \(-9\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5658.2.a.t 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.t \(-8\) \(8\) \(-1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+(\beta _{3}+\cdots)q^{7}+\cdots\)
5658.2.a.u 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.u \(-8\) \(8\) \(1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
5658.2.a.v 5658.a 1.a $8$ $45.179$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5658.2.a.v \(8\) \(-8\) \(3\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
5658.2.a.w 5658.a 1.a $9$ $45.179$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 5658.2.a.w \(-9\) \(-9\) \(4\) \(-7\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5658.2.a.x 5658.a 1.a $9$ $45.179$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 5658.2.a.x \(9\) \(9\) \(-8\) \(-13\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
5658.2.a.y 5658.a 1.a $9$ $45.179$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 5658.2.a.y \(9\) \(9\) \(9\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{6})q^{5}+q^{6}+\cdots\)
5658.2.a.z 5658.a 1.a $10$ $45.179$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5658.2.a.z \(-10\) \(10\) \(-2\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+\beta _{5}q^{7}+\cdots\)
5658.2.a.ba 5658.a 1.a $10$ $45.179$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5658.2.a.ba \(-10\) \(10\) \(2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
5658.2.a.bb 5658.a 1.a $11$ $45.179$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 5658.2.a.bb \(11\) \(-11\) \(3\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+\beta _{7}q^{7}+\cdots\)
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