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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 93 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
750.2.a.a	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	750.2.a.a	$1$	$0$	$-2$	$-2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-2\beta )q^{7}+\cdots$
750.2.a.b	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	750.2.a.b	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots$
750.2.a.c	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓			750.2.a.c	$1$	$0$	$-2$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2\beta q^{7}-q^{8}+\cdots$
750.2.a.d	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓			750.2.a.d	$1$	$0$	$-2$	$2$	$0$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(4-\beta )q^{7}+\cdots$
750.2.a.e	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	750.2.a.d	$1$	$1$	$2$	$-2$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-3-\beta )q^{7}+\cdots$
750.2.a.f	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	750.2.a.c	$1$	$0$	$2$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2\beta q^{7}+q^{8}+\cdots$
750.2.a.g	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓			750.2.a.b	$1$	$0$	$2$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(1-\beta )q^{7}+\cdots$
750.2.a.h	$750$	$2$	750.a	1.a	$1$	$2$	$2$	$5.989$	$\Q(\sqrt{5}) $	None	✓	✓			750.2.a.a	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(4-2\beta )q^{7}+\cdots$
750.2.c.a	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	$\Q(i, \sqrt{5})$	None		✓			750.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(\beta _{1}+4\beta _{3})q^{7}+\cdots$
750.2.c.b	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	$\Q(i, \sqrt{5})$	None		✓			750.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}-q^{6}+2\beta _{1}q^{7}+\cdots$
750.2.c.c	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	$\Q(i, \sqrt{5})$	None		✓			750.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots$
750.2.c.d	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	$\Q(i, \sqrt{5})$	None		✓			750.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots$
750.2.e.a	$750$	$2$	750.e	15.e	$4$	$32$	$16$	$5.989$		None		✓			750.2.e.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
750.2.e.b	$750$	$2$	750.e	15.e	$4$	$32$	$16$	$5.989$		None		✓			750.2.e.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
750.2.g.a	$750$	$2$	750.g	25.d	$5$	$4$	$1$	$5.989$	$\Q(\zeta_{10})$	None					150.2.g.b	$2$	$0$	$-1$	$-1$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
750.2.g.b	$750$	$2$	750.g	25.d	$5$	$4$	$1$	$5.989$	$\Q(\zeta_{10})$	None					150.2.g.a	$2$	$0$	$1$	$-1$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+\cdots$
750.2.g.c	$750$	$2$	750.g	25.d	$5$	$8$	$2$	$5.989$	$\Q(\zeta_{20})$	None					150.2.h.a	$2$	$0$	$-2$	$2$	$0$	$-8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta_{4} q^{2}+\beta_1 q^{3}-\beta_1 q^{4}+(-\beta_{4}+\beta_{3}-\beta_1+1)q^{6}+\cdots$
750.2.g.d	$750$	$2$	750.g	25.d	$5$	$8$	$2$	$5.989$	8.0.1064390625.3	None					150.2.g.c	$2$	$0$	$-2$	$2$	$0$	$2$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$
750.2.g.e	$750$	$2$	750.g	25.d	$5$	$8$	$2$	$5.989$	$\Q(\zeta_{20})$	None					150.2.h.a	$2$	$0$	$2$	$-2$	$0$	$8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta_{3} q^{2}+(\beta_{4}-\beta_{3}+\beta_1-1)q^{3}+\cdots$
750.2.g.f	$750$	$2$	750.g	25.d	$5$	$16$	$4$	$5.989$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					150.2.h.b	$2$	$0$	$-4$	$-4$	$0$	$8$		$5^{6}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}-\beta _{3}q^{6}+\cdots$
750.2.g.g	$750$	$2$	750.g	25.d	$5$	$16$	$4$	$5.989$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					150.2.h.b	$2$	$0$	$4$	$4$	$0$	$-8$		$5^{6}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}-\beta _{1}q^{6}+\cdots$
750.2.h.a	$750$	$2$	750.h	25.e	$10$	$8$	$2$	$5.989$	$\Q(\zeta_{20})$	None					150.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
750.2.h.b	$750$	$2$	750.h	25.e	$10$	$8$	$2$	$5.989$	$\Q(\zeta_{20})$	None					150.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots$
750.2.h.c	$750$	$2$	750.h	25.e	$10$	$8$	$2$	$5.989$	$\Q(\zeta_{20})$	None					150.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots$
750.2.h.d	$750$	$2$	750.h	25.e	$10$	$16$	$4$	$5.989$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					150.2.h.b	$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{8}q^{4}+\beta _{2}q^{6}+\cdots$
750.2.h.e	$750$	$2$	750.h	25.e	$10$	$16$	$4$	$5.989$	16.0.$\cdots$.12	None					150.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{11}q^{2}+\beta _{7}q^{3}+\beta _{9}q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
750.2.l.a	$750$	$2$	750.l	75.l	$20$	$80$	$10$	$5.989$		None					150.2.l.a	$4$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{20}]$
750.2.l.b	$750$	$2$	750.l	75.l	$20$	$80$	$10$	$5.989$		None					150.2.l.a	$4$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{20}]$
750.2.l.c	$750$	$2$	750.l	75.l	$20$	$80$	$10$	$5.989$		None					150.2.l.a	$4$	$0$	$0$	$4$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
750.2.m.a	$750$	$2$	750.m	125.g	$25$	$100$	$5$	$5.989$		None		✓			750.2.m.a	$2$	$0$	$0$	$0$	$-20$	$5$			$\mathrm{SU}(2)[C_{25}]$
750.2.m.b	$750$	$2$	750.m	125.g	$25$	$120$	$6$	$5.989$		None		✓			750.2.m.b	$2$	$0$	$0$	$0$	$20$	$-5$			$\mathrm{SU}(2)[C_{25}]$
750.2.m.c	$750$	$2$	750.m	125.g	$25$	$120$	$6$	$5.989$		None		✓			750.2.m.c	$2$	$0$	$0$	$0$	$20$	$-5$			$\mathrm{SU}(2)[C_{25}]$
750.2.m.d	$750$	$2$	750.m	125.g	$25$	$140$	$7$	$5.989$		None		✓	✓		750.2.m.d	$2$	$0$	$0$	$0$	$-20$	$5$			$\mathrm{SU}(2)[C_{25}]$
750.2.o.a	$750$	$2$	750.o	125.h	$50$	$240$	$12$	$5.989$		None		✓			750.2.o.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{50}]$
750.2.o.b	$750$	$2$	750.o	125.h	$50$	$280$	$14$	$5.989$		None		✓	✓		750.2.o.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{50}]$
750.2.r.a	$750$	$2$	750.r	375.r	$100$	$2000$	$50$	$5.989$		None		✓	✓	✓	750.2.r.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{100}]$
750.3.b.a	$750$	$3$	750.b	15.d	$2$	$16$	$16$	$20.436$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			750.3.d.b	$2$	$0$	$0$	$-10$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+2q^{4}+(\beta _{4}+\cdots)q^{6}+\cdots$
750.3.b.b	$750$	$3$	750.b	15.d	$2$	$16$	$16$	$20.436$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			750.3.d.b	$2$	$0$	$0$	$10$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(1+\beta _{2})q^{3}+2q^{4}+(\beta _{5}+\beta _{14}+\cdots)q^{6}+\cdots$
750.3.b.c	$750$	$3$	750.b	15.d	$2$	$32$	$32$	$20.436$		None		✓	✓		750.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
750.3.d.a	$750$	$3$	750.d	3.b	$2$	$32$	$32$	$20.436$		None		✓			750.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
750.3.d.b	$750$	$3$	750.d	3.b	$2$	$32$	$32$	$20.436$		None		✓			750.3.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
750.3.f.a	$750$	$3$	750.f	5.c	$4$	$16$	$8$	$20.436$	16.0.$\cdots$.9	None		✓			750.3.f.a	$2$	$0$	$-16$	$0$	$0$	$-16$		$2^{8}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
750.3.f.b	$750$	$3$	750.f	5.c	$4$	$16$	$8$	$20.436$	16.0.$\cdots$.2	None		✓			750.3.f.b	$2$	$0$	$-16$	$0$	$0$	$24$		$2^{8}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}-\beta _{2}q^{3}+2\beta _{1}q^{4}+\cdots$
750.3.f.c	$750$	$3$	750.f	5.c	$4$	$16$	$8$	$20.436$	16.0.$\cdots$.2	None		✓			750.3.f.b	$2$	$0$	$16$	$0$	$0$	$-24$		$2^{8}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1})q^{2}-\beta _{7}q^{3}-2\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
750.3.f.d	$750$	$3$	750.f	5.c	$4$	$16$	$8$	$20.436$	16.0.$\cdots$.9	None		✓			750.3.f.a	$2$	$0$	$16$	$0$	$0$	$16$		$2^{8}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
750.4.a.a	$750$	$4$	750.a	1.a	$1$	$2$	$2$	$44.251$	$\Q(\sqrt{5}) $	None	✓	✓			750.4.a.a	$1$	$0$	$-4$	$-6$	$0$	$28$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(10+8\beta )q^{7}+\cdots$
750.4.a.b	$750$	$4$	750.a	1.a	$1$	$2$	$2$	$44.251$	$\Q(\sqrt{5}) $	None	✓	✓			750.4.a.b	$1$	$1$	$-4$	$-6$	$0$	$43$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(26-9\beta )q^{7}+\cdots$
750.4.a.c	$750$	$4$	750.a	1.a	$1$	$2$	$2$	$44.251$	$\Q(\sqrt{5}) $	None	✓	✓			750.4.a.c	$1$	$1$	$-4$	$6$	$0$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots$
750.4.a.d	$750$	$4$	750.a	1.a	$1$	$2$	$2$	$44.251$	$\Q(\sqrt{5}) $	None	✓	✓			750.4.a.d	$1$	$1$	$-4$	$6$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(4-9\beta )q^{7}+\cdots$
750.4.a.e	$750$	$4$	750.a	1.a	$1$	$2$	$2$	$44.251$	$\Q(\sqrt{5}) $	None	✓	✓			750.4.a.d	$1$	$1$	$4$	$-6$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots$

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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.