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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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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
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
15.3.c.a	$15$	$3$	15.c	3.b	$2$	$2$	$2$	$0.409$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$-4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots$
15.3.d.a	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-1$	$3$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots$
15.3.d.b	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$1$	$-3$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots$
15.3.f.a	$15$	$3$	15.f	5.c	$4$	$4$	$2$	$0.409$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
15.4.a.a	$15$	$4$	15.a	1.a	$1$	$1$	$1$	$0.885$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$5$	$-24$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots$
15.4.a.b	$15$	$4$	15.a	1.a	$1$	$1$	$1$	$0.885$	$\Q$	None	✓	$1$	$0$	$3$	$-3$	$-5$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots$
15.4.b.a	$15$	$4$	15.b	5.b	$2$	$4$	$4$	$0.885$	$\Q(i, \sqrt{41})$	None		$2$	$0$	$0$	$0$	$6$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
15.4.e.a	$15$	$4$	15.e	15.e	$4$	$8$	$4$	$0.885$	8.0.$\cdots$.8	None		$4$	$0$	$0$	$-6$	$0$	$-16$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
15.5.c.a	$15$	$5$	15.c	3.b	$2$	$6$	$6$	$1.551$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$8$	$0$	$76$		$3\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
15.5.d.a	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-7$	$9$	$25$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.b	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$7$	$-9$	$-25$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.c	$15$	$5$	15.d	15.d	$2$	$4$	$4$	$1.551$	$\Q(\sqrt{10}, \sqrt{-26})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
15.5.f.a	$15$	$5$	15.f	5.c	$4$	$8$	$4$	$1.551$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$-84$	$20$		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$
15.6.a.a	$15$	$6$	15.a	1.a	$1$	$1$	$1$	$2.406$	$\Q$	None	✓	$1$	$1$	$-2$	$-9$	$-25$	$-132$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots$
15.6.a.b	$15$	$6$	15.a	1.a	$1$	$1$	$1$	$2.406$	$\Q$	None	✓	$1$	$0$	$7$	$9$	$-25$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots$
15.6.a.c	$15$	$6$	15.a	1.a	$1$	$2$	$2$	$2.406$	$\Q(\sqrt{409}) $	None	✓	$1$	$0$	$-1$	$-18$	$50$	$-112$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots$
15.6.b.a	$15$	$6$	15.b	5.b	$2$	$4$	$4$	$2.406$	$\Q(i, \sqrt{89})$	None		$2$	$0$	$0$	$0$	$120$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-11+\beta _{3})q^{4}+\cdots$
15.6.e.a	$15$	$6$	15.e	15.e	$4$	$16$	$8$	$2.406$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-80$		$2^{9}\cdot 3^{10}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots$
15.7.c.a	$15$	$7$	15.c	3.b	$2$	$8$	$8$	$3.451$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$20$	$0$	$160$		$2\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(2-\beta _{5})q^{3}+(-41-\beta _{3}+\cdots)q^{4}+\cdots$
15.7.d.a	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-11$	$-27$	$125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots$
15.7.d.b	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$11$	$27$	$-125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots$
15.7.d.c	$15$	$7$	15.d	15.d	$2$	$8$	$8$	$3.451$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots$
15.7.f.a	$15$	$7$	15.f	5.c	$4$	$12$	$6$	$3.451$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$16$	$0$	$136$	$-696$		$2\cdot 3^{10}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots$
15.8.a.a	$15$	$8$	15.a	1.a	$1$	$1$	$1$	$4.686$	$\Q$	None	✓	$1$	$1$	$-22$	$27$	$-125$	$-420$	$-$	$1$	$\mathrm{SU}(2)$	$q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots$
15.8.a.b	$15$	$8$	15.a	1.a	$1$	$1$	$1$	$4.686$	$\Q$	None	✓	$1$	$0$	$-13$	$-27$	$-125$	$1380$	$+$	$1$	$\mathrm{SU}(2)$	$q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots$
15.8.a.c	$15$	$8$	15.a	1.a	$1$	$2$	$2$	$4.686$	$\Q(\sqrt{601}) $	None	✓	$1$	$0$	$7$	$54$	$250$	$1304$	$+$	$1$	$\mathrm{SU}(2)$	$q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots$
15.8.b.a	$15$	$8$	15.b	5.b	$2$	$8$	$8$	$4.686$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$-444$	$0$		$2^{4}\cdot 3^{12}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots$
15.8.e.a	$15$	$8$	15.e	15.e	$4$	$24$	$12$	$4.686$		None		$4$	$0$	$0$	$24$	$0$	$1344$			$\mathrm{SU}(2)[C_{4}]$
15.9.c.a	$15$	$9$	15.c	3.b	$2$	$10$	$10$	$6.111$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$-112$	$0$	$7156$		$2^{4}\cdot 3^{10}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots$
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-17$	$-81$	$-625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots$
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$17$	$81$	$625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots$
15.9.d.c	$15$	$9$	15.d	15.d	$2$	$12$	$12$	$6.111$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{13}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots$
15.9.f.a	$15$	$9$	15.f	5.c	$4$	$16$	$8$	$6.111$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-444$	$4540$		$2^{11}\cdot 3^{20}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots$
15.10.a.a	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	$\Q$	None	✓	$1$	$1$	$-4$	$81$	$625$	$-7680$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots$
15.10.a.b	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	$\Q$	None	✓	$1$	$1$	$22$	$-81$	$-625$	$-5988$	$+$	$1$	$\mathrm{SU}(2)$	$q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots$
15.10.a.c	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	$\Q(\sqrt{4729}) $	None	✓	$1$	$0$	$19$	$162$	$-1250$	$-11872$	$-$	$1$	$\mathrm{SU}(2)$	$q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots$
15.10.a.d	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	$\Q(\sqrt{241}) $	None	✓	$1$	$0$	$31$	$-162$	$1250$	$14112$	$-$	$3$	$\mathrm{SU}(2)$	$q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots$
15.10.b.a	$15$	$10$	15.b	5.b	$2$	$8$	$8$	$7.726$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$-690$	$0$		$2^{3}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots$
15.10.e.a	$15$	$10$	15.e	15.e	$4$	$32$	$16$	$7.726$		None		$4$	$0$	$0$	$-150$	$0$	$-9760$			$\mathrm{SU}(2)[C_{4}]$
15.11.c.a	$15$	$11$	15.c	3.b	$2$	$14$	$14$	$9.530$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$44$	$0$	$-50548$		$2^{9}\cdot 3^{20}\cdot 5^{21}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots$
15.11.d.a	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-61$	$243$	$-3125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots$
15.11.d.b	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$61$	$-243$	$3125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots$
15.11.d.c	$15$	$11$	15.d	15.d	$2$	$16$	$16$	$9.530$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}\cdot 3^{32}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots$
15.11.f.a	$15$	$11$	15.f	5.c	$4$	$20$	$10$	$9.530$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-64$	$0$	$10676$	$10604$		$2^{21}\cdot 3^{34}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots$
15.12.a.a	$15$	$12$	15.a	1.a	$1$	$1$	$1$	$11.525$	$\Q$	None	✓	$1$	$1$	$-56$	$-243$	$3125$	$27984$	$-$	$1$	$\mathrm{SU}(2)$	$q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots$
15.12.a.b	$15$	$12$	15.a	1.a	$1$	$2$	$2$	$11.525$	$\Q(\sqrt{1609}) $	None	✓	$1$	$1$	$-22$	$486$	$-6250$	$-10864$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots$
15.12.a.c	$15$	$12$	15.a	1.a	$1$	$2$	$2$	$11.525$	$\Q(\sqrt{1801}) $	None	✓	$1$	$0$	$-13$	$-486$	$-6250$	$7784$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots$
15.12.a.d	$15$	$12$	15.a	1.a	$1$	$3$	$3$	$11.525$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$-1$	$729$	$9375$	$-14608$	$+$	$2\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots$
15.12.b.a	$15$	$12$	15.b	5.b	$2$	$12$	$12$	$11.525$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$2556$	$0$		$2^{10}\cdot 3^{28}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots$

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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.