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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 (19 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 11 61
4026.2.a.a 4026.a 1.a $1$ $32.148$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
4026.2.a.c 4026.a 1.a $1$ $32.148$ \(\Q\) None \(-1\) \(1\) \(3\) \(-4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-4q^{7}+\cdots\)
4026.2.a.d 4026.a 1.a $1$ $32.148$ \(\Q\) None \(-1\) \(1\) \(4\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4026.2.a.e 4026.a 1.a $1$ $32.148$ \(\Q\) None \(-1\) \(1\) \(4\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots\)
4026.2.a.f 4026.a 1.a $1$ $32.148$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
4026.2.a.g 4026.a 1.a $1$ $32.148$ \(\Q\) None \(1\) \(-1\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4026.2.a.h 4026.a 1.a $1$ $32.148$ \(\Q\) None \(1\) \(-1\) \(3\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
4026.2.a.i 4026.a 1.a $1$ $32.148$ \(\Q\) None \(1\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
4026.2.a.j 4026.a 1.a $1$ $32.148$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4026.2.a.k 4026.a 1.a $2$ $32.148$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-6\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-3+\beta )q^{5}-q^{6}+\cdots\)
4026.2.a.l 4026.a 1.a $2$ $32.148$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4026.2.a.q 4026.a 1.a $4$ $32.148$ 4.4.6809.1 None \(-4\) \(-4\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4026.2.a.s 4026.a 1.a $4$ $32.148$ 4.4.26825.1 None \(4\) \(-4\) \(3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{3})q^{5}-q^{6}+\cdots\)
4026.2.a.u 4026.a 1.a $5$ $32.148$ 5.5.9176805.1 None \(-5\) \(5\) \(-1\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4026.2.a.v 4026.a 1.a $5$ $32.148$ 5.5.11492689.1 None \(5\) \(-5\) \(7\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.z 4026.a 1.a $7$ $32.148$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots\)
4026.2.a.ba 4026.a 1.a $7$ $32.148$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(7\) \(-5\) \(9\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.bb 4026.a 1.a $8$ $32.148$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(5\) \(13\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{5})q^{5}+q^{6}+\cdots\)
4026.2.a.bc 4026.a 1.a $9$ $32.148$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(9\) \(8\) \(9\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
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