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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 (1-50 of 208 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
26.2.a.a	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
26.2.a.b	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	$\Q$	None	✓	$1$	$0$	$1$	$-3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
26.2.b.a	$26$	$2$	26.b	13.b	$2$	$2$	$2$	$0.208$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots$
26.2.c.a	$26$	$2$	26.c	13.c	$3$	$2$	$1$	$0.208$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots$
26.3.d.a	$26$	$3$	26.d	13.d	$4$	$2$	$1$	$0.708$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$-6$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots$
26.3.f.a	$26$	$3$	26.f	13.f	$12$	$4$	$1$	$0.708$	$\Q(\zeta_{12})$	None		$2$	$0$	$2$	$0$	$0$	$-22$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
26.3.f.b	$26$	$3$	26.f	13.f	$12$	$8$	$2$	$0.708$	8.0.$\cdots$.1	None		$2$	$0$	$-4$	$0$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
26.4.a.a	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$11$	$19$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+11q^{5}-6q^{6}+\cdots$
26.4.a.b	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$17$	$-35$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+4q^{4}+17q^{5}-2q^{6}+\cdots$
26.4.a.c	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	$\Q$	None	✓	$1$	$0$	$2$	$4$	$-18$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{3}+4q^{4}-18q^{5}+8q^{6}+\cdots$
26.4.b.a	$26$	$4$	26.b	13.b	$2$	$4$	$4$	$1.534$	$\Q(i, \sqrt{217})$	None		$2$	$0$	$0$	$-6$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-2+\beta _{3})q^{3}-4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
26.4.c.a	$26$	$4$	26.c	13.c	$3$	$2$	$1$	$1.534$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$3$	$4$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
26.4.c.b	$26$	$4$	26.c	13.c	$3$	$4$	$2$	$1.534$	$\Q(\sqrt{-3}, \sqrt{217})$	None		$2$	$0$	$-4$	$3$	$-14$	$45$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots$
26.4.e.a	$26$	$4$	26.e	13.e	$6$	$8$	$4$	$1.534$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$-6$	$0$	$18$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(-2+2\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots$
26.5.d.a	$26$	$5$	26.d	13.d	$4$	$6$	$3$	$2.688$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-12$	$0$	$18$	$-42$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+\cdots$
26.5.d.b	$26$	$5$	26.d	13.d	$4$	$6$	$3$	$2.688$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$12$	$0$	$-30$	$-90$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2\beta _{2})q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+(-5+\cdots)q^{5}+\cdots$
26.5.f.a	$26$	$5$	26.f	13.f	$12$	$8$	$2$	$2.688$	8.0.$\cdots$.3	None		$2$	$0$	$-8$	$0$	$30$	$-92$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2\beta _{4}-2\beta _{5}-2\beta _{6})q^{2}+(-1-\beta _{1}+\cdots)q^{3}+\cdots$
26.5.f.b	$26$	$5$	26.f	13.f	$12$	$8$	$2$	$2.688$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$8$	$0$	$-18$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(2\beta _{3}-2\beta _{6})q^{2}+(\beta _{1}+3\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$
26.6.a.a	$26$	$6$	26.a	1.a	$1$	$1$	$1$	$4.170$	$\Q$	None	✓	$1$	$1$	$-4$	$0$	$-14$	$-170$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+2^{4}q^{4}-14q^{5}-170q^{7}+\cdots$
26.6.a.b	$26$	$6$	26.a	1.a	$1$	$2$	$2$	$4.170$	$\Q(\sqrt{2785}) $	None	✓	$1$	$0$	$-8$	$9$	$-37$	$327$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(-19+\cdots)q^{5}+\cdots$
26.6.a.c	$26$	$6$	26.a	1.a	$1$	$2$	$2$	$4.170$	$\Q(\sqrt{849}) $	None	✓	$1$	$0$	$8$	$9$	$73$	$155$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(35+3\beta )q^{5}+\cdots$
26.6.b.a	$26$	$6$	26.b	13.b	$2$	$2$	$2$	$4.170$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-26$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4iq^{2}-13q^{3}-2^{4}q^{4}-51iq^{5}+\cdots$
26.6.b.b	$26$	$6$	26.b	13.b	$2$	$2$	$2$	$4.170$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+4q^{3}-2^{4}q^{4}+34iq^{5}+\cdots$
26.6.c.a	$26$	$6$	26.c	13.c	$3$	$6$	$3$	$4.170$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-12$	$0$	$2$	$-202$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-4\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{4}+2^{4}\beta _{1}+\cdots)q^{4}+\cdots$
26.6.c.b	$26$	$6$	26.c	13.c	$3$	$8$	$4$	$4.170$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$16$	$0$	$-24$	$126$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(4+4\beta _{2})q^{2}-\beta _{1}q^{3}+2^{4}\beta _{2}q^{4}+\cdots$
26.6.e.a	$26$	$6$	26.e	13.e	$6$	$12$	$6$	$4.170$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$360$		$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}-\beta _{3}q^{3}+2^{4}\beta _{7}q^{4}+(5+\beta _{3}+\cdots)q^{5}+\cdots$
26.7.d.a	$26$	$7$	26.d	13.d	$4$	$6$	$3$	$5.981$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$24$	$0$	$-150$	$150$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(4+4\beta _{2})q^{2}+\beta _{3}q^{3}+2^{5}\beta _{2}q^{4}+\cdots$
26.7.d.b	$26$	$7$	26.d	13.d	$4$	$8$	$4$	$5.981$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-32$	$0$	$84$	$-230$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4+4\beta _{3})q^{2}-\beta _{2}q^{3}-2^{5}\beta _{3}q^{4}+\cdots$
26.7.f.a	$26$	$7$	26.f	13.f	$12$	$12$	$3$	$5.981$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-24$	$0$	$150$	$-1026$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-4+4\beta _{2}+4\beta _{3})q^{2}+(-\beta _{7}-\beta _{11})q^{3}+\cdots$
26.7.f.b	$26$	$7$	26.f	13.f	$12$	$16$	$4$	$5.981$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$32$	$0$	$-84$	$-334$		$2^{4}\cdot 3^{4}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(4-4\beta _{3}+4\beta _{4})q^{2}-\beta _{1}q^{3}+(2^{5}\beta _{4}+\cdots)q^{4}+\cdots$
26.8.a.a	$26$	$8$	26.a	1.a	$1$	$1$	$1$	$8.122$	$\Q$	None	✓	$1$	$1$	$-8$	$-39$	$385$	$-293$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-39q^{3}+2^{6}q^{4}+385q^{5}+\cdots$
26.8.a.b	$26$	$8$	26.a	1.a	$1$	$1$	$1$	$8.122$	$\Q$	None	✓	$1$	$0$	$8$	$-87$	$321$	$-181$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-87q^{3}+2^{6}q^{4}+321q^{5}+\cdots$
26.8.a.c	$26$	$8$	26.a	1.a	$1$	$1$	$1$	$8.122$	$\Q$	None	✓	$1$	$1$	$8$	$-27$	$-245$	$-587$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-245q^{5}+\cdots$
26.8.a.d	$26$	$8$	26.a	1.a	$1$	$2$	$2$	$8.122$	$\Q(\sqrt{105}) $	None	✓	$1$	$0$	$-16$	$-12$	$-146$	$-1780$	$+$	$2$	$\mathrm{SU}(2)$	$q-8q^{2}+(-6-7\beta )q^{3}+2^{6}q^{4}+(-73+\cdots)q^{5}+\cdots$
26.8.a.e	$26$	$8$	26.a	1.a	$1$	$2$	$2$	$8.122$	$\Q(\sqrt{2305}) $	None	✓	$1$	$0$	$16$	$87$	$215$	$705$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+(44-\beta )q^{3}+2^{6}q^{4}+(110+\cdots)q^{5}+\cdots$
26.8.b.a	$26$	$8$	26.b	13.b	$2$	$10$	$10$	$8.122$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$54$	$0$	$0$		$2^{19}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+(5-\beta _{2})q^{3}-2^{6}q^{4}+(2\beta _{6}+\cdots)q^{5}+\cdots$
26.8.c.a	$26$	$8$	26.c	13.c	$3$	$6$	$3$	$8.122$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-24$	$0$	$-666$	$1160$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-8-8\beta _{3})q^{2}-\beta _{1}q^{3}+2^{6}\beta _{3}q^{4}+\cdots$
26.8.c.b	$26$	$8$	26.c	13.c	$3$	$8$	$4$	$8.122$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$32$	$0$	$556$	$-548$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-8\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{6}-2^{6}\beta _{1}+\cdots)q^{4}+\cdots$
26.8.e.a	$26$	$8$	26.e	13.e	$6$	$16$	$8$	$8.122$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$2520$		$2^{34}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{7}-\beta _{9})q^{2}+\beta _{3}q^{3}+2^{6}\beta _{1}q^{4}+\cdots$
26.9.d.a	$26$	$9$	26.d	13.d	$4$	$8$	$4$	$10.592$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-64$	$0$	$420$	$-2702$		$2\cdot 3^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}+\beta _{5}q^{3}-2^{7}\beta _{1}q^{4}+\cdots$
26.9.d.b	$26$	$9$	26.d	13.d	$4$	$8$	$4$	$10.592$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$64$	$0$	$-252$	$-4910$		$2\cdot 13^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8+8\beta _{2})q^{2}-\beta _{1}q^{3}+2^{7}\beta _{2}q^{4}+\cdots$
26.9.f.a	$26$	$9$	26.f	13.f	$12$	$20$	$5$	$10.592$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-80$	$0$	$252$	$6844$		$2^{10}\cdot 3^{8}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-8-8\beta _{1}-8\beta _{5})q^{2}+(5\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots$
26.9.f.b	$26$	$9$	26.f	13.f	$12$	$20$	$5$	$10.592$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$80$	$0$	$-420$	$-4292$		$2^{10}\cdot 3^{4}\cdot 13^{3}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-8\beta _{1}+8\beta _{3})q^{2}+(5\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots$
26.10.a.a	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	$\Q$	None	✓	$1$	$1$	$-16$	$-273$	$1015$	$3955$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-273q^{3}+2^{8}q^{4}+1015q^{5}+\cdots$
26.10.a.b	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	$\Q$	None	✓	$1$	$1$	$-16$	$192$	$-1310$	$-5810$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+192q^{3}+2^{8}q^{4}-1310q^{5}+\cdots$
26.10.a.c	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	$\Q$	None	✓	$1$	$1$	$16$	$75$	$-1979$	$-10115$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+75q^{3}+2^{8}q^{4}-1979q^{5}+\cdots$
26.10.a.d	$26$	$10$	26.a	1.a	$1$	$3$	$3$	$13.391$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$-48$	$0$	$248$	$-2956$	$-$	$2$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-\beta _{2}q^{3}+2^{8}q^{4}+(79-11\beta _{1}+\cdots)q^{5}+\cdots$
26.10.a.e	$26$	$10$	26.a	1.a	$1$	$3$	$3$	$13.391$	3.3.2119705.1	None	✓	$1$	$0$	$48$	$156$	$-1272$	$17058$	$-$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(52-\beta _{1}-\beta _{2})q^{3}+2^{8}q^{4}+\cdots$
26.10.b.a	$26$	$10$	26.b	13.b	$2$	$10$	$10$	$13.391$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$162$	$0$	$0$		$2^{22}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(2^{4}-\beta _{1})q^{3}-2^{8}q^{4}+(-15\beta _{5}+\cdots)q^{5}+\cdots$
26.10.c.a	$26$	$10$	26.c	13.c	$3$	$10$	$5$	$13.391$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$80$	$-81$	$-1828$	$3323$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2^{4}-2^{4}\beta _{2})q^{2}+(-2^{4}-\beta _{1}+2^{4}\beta _{2}+\cdots)q^{3}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.