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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 234 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
30.2.a.a	$30$	$2$	30.a	1.a	$1$	$1$	$1$	$0.240$	$\Q$	None	✓	✓	✓	✓	30.2.a.a	$1$	$0$	$-1$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
30.2.c.a	$30$	$2$	30.c	5.b	$2$	$2$	$2$	$0.240$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	30.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(i-2)q^{5}+\cdots$
30.2.e.a	$30$	$2$	30.e	15.e	$4$	$4$	$2$	$0.240$	$\Q(\zeta_{8})$	None		✓	✓	✓	30.2.e.a	$4$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
30.3.b.a	$30$	$3$	30.b	15.d	$2$	$4$	$4$	$0.817$	$\Q(\sqrt{2}, \sqrt{-17})$	None		✓	✓	✓	30.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$
30.3.d.a	$30$	$3$	30.d	3.b	$2$	$4$	$4$	$0.817$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓	✓	✓	30.3.d.a	$2$	$0$	$0$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots$
30.3.f.a	$30$	$3$	30.f	5.c	$4$	$4$	$2$	$0.817$	$\Q(i, \sqrt{6})$	None		✓	✓	✓	30.3.f.a	$2$	$0$	$4$	$0$	$0$	$-16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
30.4.a.a	$30$	$4$	30.a	1.a	$1$	$1$	$1$	$1.770$	$\Q$	None	✓	✓	✓	✓	30.4.a.a	$1$	$0$	$-2$	$3$	$5$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
30.4.a.b	$30$	$4$	30.a	1.a	$1$	$1$	$1$	$1.770$	$\Q$	None	✓	✓	✓	✓	30.4.a.b	$1$	$0$	$2$	$3$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
30.4.c.a	$30$	$4$	30.c	5.b	$2$	$2$	$2$	$1.770$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	30.4.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}+3 i q^{3}-4 q^{4}+(11 i+2)q^{5}+\cdots$
30.4.e.a	$30$	$4$	30.e	15.e	$4$	$12$	$6$	$1.770$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	30.4.e.a	$4$	$0$	$0$	$8$	$0$	$12$		$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(1-\beta _{3}-\beta _{9})q^{3}-4\beta _{3}q^{4}+\cdots$
30.5.b.a	$30$	$5$	30.b	15.d	$2$	$8$	$8$	$3.101$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	30.5.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+8q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
30.5.d.a	$30$	$5$	30.d	3.b	$2$	$4$	$4$	$3.101$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓	✓	✓	30.5.d.a	$2$	$0$	$0$	$-8$	$0$	$-184$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-2-2\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
30.5.f.a	$30$	$5$	30.f	5.c	$4$	$4$	$2$	$3.101$	$\Q(i, \sqrt{6})$	None		✓			30.5.f.a	$2$	$0$	$-8$	$0$	$84$	$-28$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots$
30.5.f.b	$30$	$5$	30.f	5.c	$4$	$4$	$2$	$3.101$	$\Q(i, \sqrt{6})$	None		✓			30.5.f.b	$2$	$0$	$8$	$0$	$36$	$68$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2-2\beta _{2})q^{2}+3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots$
30.6.a.a	$30$	$6$	30.a	1.a	$1$	$1$	$1$	$4.812$	$\Q$	None	✓	✓	✓	✓	30.6.a.a	$1$	$0$	$-4$	$9$	$-25$	$164$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots$
30.6.a.b	$30$	$6$	30.a	1.a	$1$	$1$	$1$	$4.812$	$\Q$	None	✓	✓	✓	✓	30.6.a.b	$1$	$0$	$4$	$9$	$25$	$32$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots$
30.6.c.a	$30$	$6$	30.c	5.b	$2$	$2$	$2$	$4.812$	$\Q(\sqrt{-1}) $	None		✓			30.6.c.a	$2$	$0$	$0$	$0$	$-110$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4 i q^{2}+9 i q^{3}-16 q^{4}+(10 i-55)q^{5}+\cdots$
30.6.c.b	$30$	$6$	30.c	5.b	$2$	$4$	$4$	$4.812$	$\Q(i, \sqrt{1249})$	None		✓	✓		30.6.c.b	$2$	$0$	$0$	$0$	$6$	$0$		$2\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-4\beta _{1}q^{2}+9\beta _{1}q^{3}-2^{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
30.6.e.a	$30$	$6$	30.e	15.e	$4$	$20$	$10$	$4.812$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	30.6.e.a	$4$	$0$	$0$	$-4$	$0$	$76$		$2^{25}\cdot 3^{14}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+2^{4}\beta _{5}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$
30.7.b.a	$30$	$7$	30.b	15.d	$2$	$12$	$12$	$6.902$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	30.7.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{20}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+2^{5}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
30.7.d.a	$30$	$7$	30.d	3.b	$2$	$8$	$8$	$6.902$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	30.7.d.a	$2$	$0$	$0$	$-20$	$0$	$400$		$2^{6}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-2-\beta _{2}-\beta _{3})q^{3}-2^{5}q^{4}+\cdots$
30.7.f.a	$30$	$7$	30.f	5.c	$4$	$4$	$2$	$6.902$	$\Q(i, \sqrt{6})$	None		✓			30.7.f.a	$2$	$0$	$16$	$0$	$-420$	$596$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(4-4\beta _{2})q^{2}+3\beta _{1}q^{3}-2^{5}\beta _{2}q^{4}+\cdots$
30.7.f.b	$30$	$7$	30.f	5.c	$4$	$8$	$4$	$6.902$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		30.7.f.b	$2$	$0$	$-32$	$0$	$60$	$388$		$2\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4-4\beta _{1})q^{2}-\beta _{3}q^{3}+2^{5}\beta _{1}q^{4}+\cdots$
30.8.a.a	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.a	$1$	$0$	$-8$	$-27$	$-125$	$-1084$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}+6^{3}q^{6}+\cdots$
30.8.a.b	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.b	$1$	$1$	$-8$	$-27$	$125$	$416$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}+6^{3}q^{6}+\cdots$
30.8.a.c	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.c	$1$	$0$	$-8$	$27$	$125$	$-232$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}-6^{3}q^{6}+\cdots$
30.8.a.d	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.d	$1$	$1$	$8$	$-27$	$-125$	$-988$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}-6^{3}q^{6}+\cdots$
30.8.a.e	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.e	$1$	$0$	$8$	$-27$	$125$	$512$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}-6^{3}q^{6}+\cdots$
30.8.a.f	$30$	$8$	30.a	1.a	$1$	$1$	$1$	$9.372$	$\Q$	None	✓	✓	✓	✓	30.8.a.f	$1$	$0$	$8$	$27$	$-125$	$1604$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}+6^{3}q^{6}+\cdots$
30.8.c.a	$30$	$8$	30.c	5.b	$2$	$2$	$2$	$9.372$	$\Q(\sqrt{-1}) $	None		✓			30.8.c.a	$2$	$0$	$0$	$0$	$-100$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8 i q^{2}-27 i q^{3}-64 q^{4}+(275 i-50)q^{5}+\cdots$
30.8.c.b	$30$	$8$	30.c	5.b	$2$	$4$	$4$	$9.372$	$\Q(i, \sqrt{2641})$	None		✓	✓		30.8.c.b	$2$	$0$	$0$	$0$	$264$	$0$		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-8\beta _{1}q^{2}-3^{3}\beta _{1}q^{3}-2^{6}q^{4}+(66+\cdots)q^{5}+\cdots$
30.8.e.a	$30$	$8$	30.e	15.e	$4$	$28$	$14$	$9.372$		None		✓	✓	✓	30.8.e.a	$4$	$0$	$0$	$-52$	$0$	$-1348$			$\mathrm{SU}(2)[C_{4}]$
30.9.b.a	$30$	$9$	30.b	15.d	$2$	$16$	$16$	$12.221$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	30.9.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{40}\cdot 3^{20}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+2^{7}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
30.9.d.a	$30$	$9$	30.d	3.b	$2$	$12$	$12$	$12.221$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	30.9.d.a	$2$	$0$	$0$	$112$	$0$	$-11304$		$2^{25}\cdot 3^{12}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(9-\beta _{1}-\beta _{2})q^{3}-2^{7}q^{4}+\cdots$
30.9.f.a	$30$	$9$	30.f	5.c	$4$	$8$	$4$	$12.221$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			30.9.f.a	$2$	$0$	$-64$	$0$	$636$	$-1484$		$2\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}-\beta _{5}q^{3}-2^{7}\beta _{1}q^{4}+\cdots$
30.9.f.b	$30$	$9$	30.f	5.c	$4$	$8$	$4$	$12.221$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			30.9.f.b	$2$	$0$	$64$	$0$	$924$	$-7436$		$2\cdot 3^{8}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8-8\beta _{1})q^{2}-\beta _{7}q^{3}-2^{7}\beta _{1}q^{4}+\cdots$
30.10.a.a	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.a	$1$	$1$	$-16$	$-81$	$-625$	$6332$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots$
30.10.a.b	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.b	$1$	$0$	$-16$	$-81$	$625$	$-7168$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
30.10.a.c	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.c	$1$	$0$	$-16$	$81$	$-625$	$7196$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots$
30.10.a.d	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.d	$1$	$0$	$16$	$-81$	$-625$	$3164$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots$
30.10.a.e	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.e	$1$	$1$	$16$	$-81$	$625$	$-10336$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
30.10.a.f	$30$	$10$	30.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	None	✓	✓	✓	✓	30.10.a.f	$1$	$0$	$16$	$81$	$625$	$2408$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
30.10.c.a	$30$	$10$	30.c	5.b	$2$	$4$	$4$	$15.451$	$\Q(i, \sqrt{889})$	None		✓			30.10.c.a	$2$	$0$	$0$	$0$	$1710$	$0$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+(421+\cdots)q^{5}+\cdots$
30.10.c.b	$30$	$10$	30.c	5.b	$2$	$6$	$6$	$15.451$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓		30.10.c.b	$2$	$0$	$0$	$0$	$266$	$0$		$2^{4}\cdot 3^{2}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+(44+\cdots)q^{5}+\cdots$
30.10.e.a	$30$	$10$	30.e	15.e	$4$	$36$	$18$	$15.451$		None		✓	✓	✓	30.10.e.a	$4$	$0$	$0$	$296$	$0$	$9756$			$\mathrm{SU}(2)[C_{4}]$
30.11.b.a	$30$	$11$	30.b	15.d	$2$	$20$	$20$	$19.061$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	30.11.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{68}\cdot 3^{32}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2^{9}q^{4}+\cdots$
30.11.d.a	$30$	$11$	30.d	3.b	$2$	$12$	$12$	$19.061$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	30.11.d.a	$2$	$0$	$0$	$-44$	$0$	$71832$		$2^{26}\cdot 3^{15}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-4+\beta _{2}+\beta _{3})q^{3}-2^{9}q^{4}+\cdots$
30.11.f.a	$30$	$11$	30.f	5.c	$4$	$8$	$4$	$19.061$	8.0.$\cdots$.1	None		✓			30.11.f.a	$2$	$0$	$-128$	$0$	$-9240$	$-14168$		$2^{10}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{4}+2^{4}\beta _{1})q^{2}+3\beta _{2}q^{3}-2^{9}\beta _{1}q^{4}+\cdots$
30.11.f.b	$30$	$11$	30.f	5.c	$4$	$12$	$6$	$19.061$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		30.11.f.b	$2$	$0$	$192$	$0$	$-5880$	$11352$		$2^{12}\cdot 3^{24}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{4}+2^{4}\beta _{1})q^{2}+\beta _{2}q^{3}+2^{9}\beta _{1}q^{4}+\cdots$
30.12.a.a	$30$	$12$	30.a	1.a	$1$	$1$	$1$	$23.050$	$\Q$	None	✓	✓	✓	✓	30.12.a.a	$1$	$0$	$-32$	$-243$	$-3125$	$-22876$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$

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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.