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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 (1-50 of 322 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
90.2.a.a	$90$	$2$	90.a	1.a	$1$	$1$	$1$	$0.719$	$\Q$	None	✓	✓	✓	✓	90.2.a.a	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
90.2.a.b	$90$	$2$	90.a	1.a	$1$	$1$	$1$	$0.719$	$\Q$	None	✓	✓	✓	✓	90.2.a.a	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
90.2.a.c	$90$	$2$	90.a	1.a	$1$	$1$	$1$	$0.719$	$\Q$	None	✓		✓	✓	30.2.a.a	$1$	$0$	$1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
90.2.c.a	$90$	$2$	90.c	5.b	$2$	$2$	$2$	$0.719$	$\Q(\sqrt{-1}) $	None			✓	✓	30.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i+2)q^{5}+2 i q^{7}+\cdots$
90.2.e.a	$90$	$2$	90.e	9.c	$3$	$2$	$1$	$0.719$	$\Q(\sqrt{-3}) $	None		✓			90.2.e.a	$2$	$0$	$-1$	$3$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
90.2.e.b	$90$	$2$	90.e	9.c	$3$	$2$	$1$	$0.719$	$\Q(\sqrt{-3}) $	None		✓			90.2.e.b	$2$	$0$	$1$	$-3$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
90.2.e.c	$90$	$2$	90.e	9.c	$3$	$4$	$2$	$0.719$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓	✓		90.2.e.c	$2$	$0$	$2$	$2$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
90.2.f.a	$90$	$2$	90.f	15.e	$4$	$4$	$2$	$0.719$	$\Q(\zeta_{8})$	None		✓	✓	✓	90.2.f.a	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
90.2.i.a	$90$	$2$	90.i	45.j	$6$	$4$	$2$	$0.719$	$\Q(\zeta_{12})$	None		✓			90.2.i.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
90.2.i.b	$90$	$2$	90.i	45.j	$6$	$8$	$4$	$0.719$	$\Q(\zeta_{24})$	None		✓	✓		90.2.i.b	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
90.2.l.a	$90$	$2$	90.l	45.l	$12$	$8$	$2$	$0.719$	$\Q(\zeta_{24})$	None		✓			90.2.l.a	$4$	$0$	$0$	$4$	$12$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
90.2.l.b	$90$	$2$	90.l	45.l	$12$	$16$	$4$	$0.719$	16.0.$\cdots$.9	None		✓	✓		90.2.l.b	$4$	$0$	$0$	$0$	$-12$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{11}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots$
90.3.b.a	$90$	$3$	90.b	15.d	$2$	$4$	$4$	$2.452$	$\Q(\zeta_{8})$	None		✓	✓	✓	90.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}-4\zeta_{8}^{2}q^{7}+\cdots$
90.3.g.a	$90$	$3$	90.g	5.c	$4$	$2$	$1$	$2.452$	$\Q(\sqrt{-1}) $	None		✓			90.3.g.a	$2$	$0$	$-2$	$0$	$-6$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(4 i-3)q^{5}+\cdots$
90.3.g.b	$90$	$3$	90.g	5.c	$4$	$2$	$1$	$2.452$	$\Q(\sqrt{-1}) $	None					10.3.c.a	$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+5 i q^{5}+(2 i+2)q^{7}+\cdots$
90.3.g.c	$90$	$3$	90.g	5.c	$4$	$2$	$1$	$2.452$	$\Q(\sqrt{-1}) $	None		✓			90.3.g.a	$2$	$0$	$2$	$0$	$6$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(-4 i+3)q^{5}+\cdots$
90.3.g.d	$90$	$3$	90.g	5.c	$4$	$4$	$2$	$2.452$	$\Q(i, \sqrt{6})$	None			✓		30.3.f.a	$2$	$0$	$-4$	$0$	$0$	$-16$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
90.3.h.a	$90$	$3$	90.h	9.d	$6$	$16$	$8$	$2.452$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	90.3.h.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{3}+\cdots$
90.3.j.a	$90$	$3$	90.j	45.h	$6$	$8$	$4$	$2.452$	$\Q(\zeta_{24})$	None		✓			90.3.j.a	$4$	$0$	$0$	$0$	$-12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta_{4} q^{2}+3\beta_1 q^{3}+(2\beta_{2}-2)q^{4}+\cdots$
90.3.j.b	$90$	$3$	90.j	45.h	$6$	$16$	$8$	$2.452$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		90.3.j.b	$4$	$0$	$0$	$0$	$30$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
90.3.k.a	$90$	$3$	90.k	45.k	$12$	$24$	$6$	$2.452$		None		✓			90.3.k.a	$4$	$0$	$-12$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{12}]$
90.3.k.b	$90$	$3$	90.k	45.k	$12$	$24$	$6$	$2.452$		None		✓			90.3.k.b	$4$	$0$	$12$	$4$	$0$	$6$			$\mathrm{SU}(2)[C_{12}]$
90.4.a.a	$90$	$4$	90.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	None	✓		✓	✓	10.4.a.a	$1$	$1$	$-2$	$0$	$-5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-5q^{5}-4q^{7}-8q^{8}+\cdots$
90.4.a.b	$90$	$4$	90.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	None	✓	✓	✓	✓	90.4.a.b	$1$	$0$	$-2$	$0$	$-5$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-5q^{5}+14q^{7}-8q^{8}+\cdots$
90.4.a.c	$90$	$4$	90.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	None	✓		✓	✓	30.4.a.b	$1$	$0$	$-2$	$0$	$5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots$
90.4.a.d	$90$	$4$	90.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	None	✓		✓	✓	30.4.a.a	$1$	$0$	$2$	$0$	$-5$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-5q^{5}+2^{5}q^{7}+8q^{8}+\cdots$
90.4.a.e	$90$	$4$	90.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	None	✓	✓	✓	✓	90.4.a.b	$1$	$0$	$2$	$0$	$5$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+5q^{5}+14q^{7}+8q^{8}+\cdots$
90.4.c.a	$90$	$4$	90.c	5.b	$2$	$2$	$2$	$5.310$	$\Q(\sqrt{-1}) $	None					30.4.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-4 q^{4}+(11 i-2)q^{5}+2 i q^{7}+\cdots$
90.4.c.b	$90$	$4$	90.c	5.b	$2$	$2$	$2$	$5.310$	$\Q(\sqrt{-1}) $	None					10.4.b.a	$2$	$0$	$0$	$0$	$10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-4 q^{4}+(-5\beta+5)q^{5}-13\beta q^{7}+\cdots$
90.4.c.c	$90$	$4$	90.c	5.b	$2$	$4$	$4$	$5.310$	$\Q(i, \sqrt{31})$	None		✓	✓		90.4.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{8}+\cdots$
90.4.e.a	$90$	$4$	90.e	9.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	None		✓			90.4.e.a	$2$	$0$	$-2$	$-9$	$5$	$16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-3-3\zeta_{6})q^{3}+\cdots$
90.4.e.b	$90$	$4$	90.e	9.c	$3$	$4$	$2$	$5.310$	$\Q(\sqrt{-3}, \sqrt{-5})$	None		✓			90.4.e.b	$2$	$0$	$-4$	$12$	$10$	$-16$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\beta _{1})q^{2}+(4-2\beta _{1}+\beta _{2})q^{3}+\cdots$
90.4.e.c	$90$	$4$	90.e	9.c	$3$	$4$	$2$	$5.310$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			90.4.e.c	$2$	$0$	$4$	$6$	$10$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{1}q^{2}+(3-3\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
90.4.e.d	$90$	$4$	90.e	9.c	$3$	$6$	$3$	$5.310$	6.0.41783472.1	None		✓			90.4.e.d	$2$	$0$	$6$	$-9$	$-15$	$-3$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+4\beta _{1}q^{4}+\cdots$
90.4.e.e	$90$	$4$	90.e	9.c	$3$	$8$	$4$	$5.310$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		90.4.e.e	$2$	$0$	$-8$	$2$	$-20$	$-23$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-2\beta _{3})q^{2}-\beta _{1}q^{3}+4\beta _{3}q^{4}+\cdots$
90.4.f.a	$90$	$4$	90.f	15.e	$4$	$4$	$2$	$5.310$	$\Q(\zeta_{8})$	None		✓			90.4.f.a	$4$	$0$	$0$	$0$	$0$	$-16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(5\zeta_{8}+10\zeta_{8}^{3})q^{5}+\cdots$
90.4.f.b	$90$	$4$	90.f	15.e	$4$	$8$	$4$	$5.310$	8.0.$\cdots$.8	None		✓	✓		90.4.f.b	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{2}-\beta _{3})q^{2}-4\beta _{1}q^{4}+(3\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
90.4.i.a	$90$	$4$	90.i	45.j	$6$	$36$	$18$	$5.310$		None		✓	✓	✓	90.4.i.a	$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{6}]$
90.4.l.a	$90$	$4$	90.l	45.l	$12$	$72$	$18$	$5.310$		None		✓	✓	✓	90.4.l.a	$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
90.5.b.a	$90$	$5$	90.b	15.d	$2$	$8$	$8$	$9.303$	8.0.$\cdots$.1	None		✓	✓	✓	90.5.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+8q^{4}+(2\beta _{2}-\beta _{3}+\beta _{4})q^{5}+\cdots$
90.5.d.a	$90$	$5$	90.d	3.b	$2$	$4$	$4$	$9.303$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			90.5.d.a	$2$	$0$	$0$	$0$	$0$	$32$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(8+3\beta _{3})q^{7}+\cdots$
90.5.d.b	$90$	$5$	90.d	3.b	$2$	$4$	$4$	$9.303$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			90.5.d.b	$2$	$0$	$0$	$0$	$0$	$128$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(2^{5}-3\beta _{3})q^{7}+\cdots$
90.5.g.a	$90$	$5$	90.g	5.c	$4$	$2$	$1$	$9.303$	$\Q(\sqrt{-1}) $	None					10.5.c.b	$2$	$0$	$-4$	$0$	$30$	$-38$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{2}+8 i q^{4}+(20 i+15)q^{5}+\cdots$
90.5.g.b	$90$	$5$	90.g	5.c	$4$	$2$	$1$	$9.303$	$\Q(\sqrt{-1}) $	None					10.5.c.a	$2$	$0$	$4$	$0$	$30$	$58$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i+2)q^{2}+8 i q^{4}+(-20 i+15)q^{5}+\cdots$
90.5.g.c	$90$	$5$	90.g	5.c	$4$	$4$	$2$	$9.303$	$\Q(i, \sqrt{6})$	None					30.5.f.b	$2$	$0$	$-8$	$0$	$-36$	$68$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-9-11\beta _{1}+\cdots)q^{5}+\cdots$
90.5.g.d	$90$	$5$	90.g	5.c	$4$	$4$	$2$	$9.303$	$\Q(i, \sqrt{26})$	None		✓			90.5.g.d	$2$	$0$	$-8$	$0$	$-24$	$-100$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{2})q^{2}+8\beta _{2}q^{4}+(-6-2\beta _{1}+\cdots)q^{5}+\cdots$
90.5.g.e	$90$	$5$	90.g	5.c	$4$	$4$	$2$	$9.303$	$\Q(i, \sqrt{6})$	None					30.5.f.a	$2$	$0$	$8$	$0$	$-84$	$-28$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2-2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-21+\beta _{1}+\cdots)q^{5}+\cdots$
90.5.g.f	$90$	$5$	90.g	5.c	$4$	$4$	$2$	$9.303$	$\Q(i, \sqrt{26})$	None		✓			90.5.g.d	$2$	$0$	$8$	$0$	$24$	$-100$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2\beta _{2})q^{2}+8\beta _{2}q^{4}+(6-2\beta _{1}+\cdots)q^{5}+\cdots$
90.5.h.a	$90$	$5$	90.h	9.d	$6$	$32$	$16$	$9.303$		None		✓	✓	✓	90.5.h.a	$2$	$0$	$0$	$8$	$0$	$52$			$\mathrm{SU}(2)[C_{6}]$
90.5.j.a	$90$	$5$	90.j	45.h	$6$	$48$	$24$	$9.303$		None		✓	✓	✓	90.5.j.a	$4$	$0$	$0$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.