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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 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 (15 matches)

  displayed columns for results
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 7 11
1232.4.a.b 1232.a 1.a $1$ $72.690$ \(\Q\) None 154.4.a.e \(0\) \(-7\) \(3\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-7q^{3}+3q^{5}-7q^{7}+22q^{9}+11q^{11}+\cdots\)
1232.4.a.e 1232.a 1.a $1$ $72.690$ \(\Q\) None 154.4.a.b \(0\) \(0\) \(2\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+7q^{7}-3^{3}q^{9}-11q^{11}+26q^{13}+\cdots\)
1232.4.a.f 1232.a 1.a $1$ $72.690$ \(\Q\) None 154.4.a.d \(0\) \(2\) \(18\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+18q^{5}-7q^{7}-23q^{9}+11q^{11}+\cdots\)
1232.4.a.i 1232.a 1.a $1$ $72.690$ \(\Q\) None 154.4.a.c \(0\) \(10\) \(-14\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+10q^{3}-14q^{5}-7q^{7}+73q^{9}+11q^{11}+\cdots\)
1232.4.a.l 1232.a 1.a $2$ $72.690$ \(\Q(\sqrt{5}) \) None 616.4.a.d \(0\) \(2\) \(6\) \(14\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+3\beta )q^{3}+(3+\beta )q^{5}+7q^{7}+(19+\cdots)q^{9}+\cdots\)
1232.4.a.m 1232.a 1.a $2$ $72.690$ \(\Q(\sqrt{2}) \) None 77.4.a.b \(0\) \(4\) \(-4\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+(-2-3\beta )q^{5}-7q^{7}-23q^{9}+\cdots\)
1232.4.a.p 1232.a 1.a $2$ $72.690$ \(\Q(\sqrt{137}) \) None 154.4.a.f \(0\) \(5\) \(-7\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{3}+(-3-\beta )q^{5}-7q^{7}+(2^{4}+\cdots)q^{9}+\cdots\)
1232.4.a.q 1232.a 1.a $3$ $72.690$ 3.3.7636.1 None 154.4.a.i \(0\) \(-6\) \(26\) \(21\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(9-\beta _{2})q^{5}+7q^{7}+\cdots\)
1232.4.a.u 1232.a 1.a $4$ $72.690$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 616.4.a.f \(0\) \(3\) \(-13\) \(-28\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-4+\beta _{1}-\beta _{2})q^{5}+\cdots\)
1232.4.a.v 1232.a 1.a $4$ $72.690$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 308.4.a.d \(0\) \(3\) \(1\) \(28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+7q^{7}+(-5+\cdots)q^{9}+\cdots\)
1232.4.a.w 1232.a 1.a $4$ $72.690$ 4.4.509800.1 None 77.4.a.c \(0\) \(12\) \(-18\) \(28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{2})q^{3}+(-5+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1232.4.a.x 1232.a 1.a $5$ $72.690$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 308.4.a.e \(0\) \(-5\) \(15\) \(-35\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(3+\beta _{2})q^{5}-7q^{7}+\cdots\)
1232.4.a.z 1232.a 1.a $5$ $72.690$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 616.4.a.g \(0\) \(-2\) \(-14\) \(35\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-2-\beta _{1}-\beta _{2})q^{5}+7q^{7}+\cdots\)
1232.4.a.bc 1232.a 1.a $7$ $72.690$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 616.4.a.k \(0\) \(-3\) \(11\) \(-49\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(2-\beta _{2})q^{5}-7q^{7}+(15+\beta _{3}+\cdots)q^{9}+\cdots\)
1232.4.a.bd 1232.a 1.a $7$ $72.690$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 616.4.a.j \(0\) \(0\) \(6\) \(49\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+7q^{7}+(15-\beta _{2}+\cdots)q^{9}+\cdots\)
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