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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 52 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
2370.2.a.a	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.a	$1$	$1$	$-1$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
2370.2.a.b	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓	✓	✓	2370.2.a.b	$1$	$1$	$-1$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
2370.2.a.c	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.c	$1$	$0$	$-1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
2370.2.a.d	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.d	$1$	$0$	$-1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
2370.2.a.e	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.e	$1$	$0$	$-1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2370.2.a.f	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.f	$1$	$0$	$1$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
2370.2.a.g	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.g	$1$	$0$	$1$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
2370.2.a.h	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.h	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
2370.2.a.i	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.i	$1$	$1$	$1$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
2370.2.a.j	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.j	$1$	$1$	$1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
2370.2.a.k	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.k	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
2370.2.a.l	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓	✓	✓	2370.2.a.l	$1$	$1$	$1$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-5q^{7}+\cdots$
2370.2.a.m	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.m	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
2370.2.a.n	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.n	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
2370.2.a.o	$2370$	$2$	2370.a	1.a	$1$	$1$	$1$	$18.925$	$\Q$	None	✓	✓			2370.2.a.o	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
2370.2.a.p	$2370$	$2$	2370.a	1.a	$1$	$2$	$2$	$18.925$	$\Q(\sqrt{17}) $	None	✓	✓	✓		2370.2.a.p	$1$	$1$	$-2$	$-2$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
2370.2.a.q	$2370$	$2$	2370.a	1.a	$1$	$2$	$2$	$18.925$	$\Q(\sqrt{2}) $	None	✓	✓			2370.2.a.q	$1$	$1$	$-2$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+2\beta )q^{7}+\cdots$
2370.2.a.r	$2370$	$2$	2370.a	1.a	$1$	$2$	$2$	$18.925$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	2370.2.a.r	$1$	$0$	$-2$	$-2$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
2370.2.a.s	$2370$	$2$	2370.a	1.a	$1$	$2$	$2$	$18.925$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	2370.2.a.s	$1$	$1$	$2$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
2370.2.a.t	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.316.1	None	✓	✓	✓	✓	2370.2.a.t	$1$	$0$	$-3$	$-3$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{2}q^{7}+\cdots$
2370.2.a.u	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.892.1	None	✓	✓	✓		2370.2.a.u	$1$	$1$	$-3$	$-3$	$3$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
2370.2.a.v	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.1384.1	None	✓	✓	✓		2370.2.a.v	$1$	$0$	$-3$	$3$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
2370.2.a.w	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.316.1	None	✓	✓	✓	✓	2370.2.a.w	$1$	$1$	$-3$	$3$	$3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
2370.2.a.x	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.316.1	None	✓	✓	✓		2370.2.a.x	$1$	$0$	$-3$	$3$	$3$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots$
2370.2.a.y	$2370$	$2$	2370.a	1.a	$1$	$3$	$3$	$18.925$	3.3.940.1	None	✓	✓	✓		2370.2.a.y	$1$	$0$	$3$	$3$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
2370.2.a.z	$2370$	$2$	2370.a	1.a	$1$	$4$	$4$	$18.925$	$\Q(\sqrt{17 +8 \sqrt{3}})$	None	✓	✓	✓	✓	2370.2.a.z	$1$	$1$	$4$	$-4$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
2370.2.a.ba	$2370$	$2$	2370.a	1.a	$1$	$4$	$4$	$18.925$	4.4.85688.1	None	✓	✓	✓	✓	2370.2.a.ba	$1$	$0$	$4$	$-4$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta _{3}q^{7}+\cdots$
2370.2.a.bb	$2370$	$2$	2370.a	1.a	$1$	$4$	$4$	$18.925$	4.4.191468.1	None	✓	✓	✓		2370.2.a.bb	$1$	$0$	$4$	$4$	$-4$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots$
2370.2.d.a	$2370$	$2$	2370.d	5.b	$2$	$2$	$2$	$18.925$	$\Q(\sqrt{-1}) $	None		✓			2370.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(i-2)q^{5}+\cdots$
2370.2.d.b	$2370$	$2$	2370.d	5.b	$2$	$2$	$2$	$18.925$	$\Q(\sqrt{-1}) $	None		✓			2370.2.d.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(2 i+1)q^{5}+\cdots$
2370.2.d.c	$2370$	$2$	2370.d	5.b	$2$	$2$	$2$	$18.925$	$\Q(\sqrt{-1}) $	None		✓			2370.2.d.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
2370.2.d.d	$2370$	$2$	2370.d	5.b	$2$	$8$	$8$	$18.925$	8.0.2058981376.2	None		✓			2370.2.d.d	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{4}q^{3}-q^{4}+(1+\beta _{1}-\beta _{7})q^{5}+\cdots$
2370.2.d.e	$2370$	$2$	2370.d	5.b	$2$	$14$	$14$	$18.925$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			2370.2.d.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
2370.2.d.f	$2370$	$2$	2370.d	5.b	$2$	$24$	$24$	$18.925$		None		✓			2370.2.d.f	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2370.2.d.g	$2370$	$2$	2370.d	5.b	$2$	$24$	$24$	$18.925$		None		✓			2370.2.d.g	$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
2370.4.a.a	$2370$	$4$	2370.a	1.a	$1$	$1$	$1$	$139.835$	$\Q$	None	✓	✓			2370.4.a.a	$1$	$0$	$-2$	$-3$	$5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
2370.4.a.b	$2370$	$4$	2370.a	1.a	$1$	$7$	$7$	$139.835$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		2370.4.a.b	$1$	$0$	$-14$	$-21$	$35$	$17$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
2370.4.a.c	$2370$	$4$	2370.a	1.a	$1$	$7$	$7$	$139.835$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.c	$1$	$1$	$14$	$21$	$35$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
2370.4.a.d	$2370$	$4$	2370.a	1.a	$1$	$8$	$8$	$139.835$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.d	$1$	$1$	$-16$	$24$	$-40$	$-35$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
2370.4.a.e	$2370$	$4$	2370.a	1.a	$1$	$8$	$8$	$139.835$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.e	$1$	$1$	$16$	$24$	$-40$	$-12$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
2370.4.a.f	$2370$	$4$	2370.a	1.a	$1$	$9$	$9$	$139.835$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.f	$1$	$1$	$-18$	$27$	$45$	$-58$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
2370.4.a.g	$2370$	$4$	2370.a	1.a	$1$	$9$	$9$	$139.835$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.g	$1$	$0$	$18$	$-27$	$-45$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
2370.4.a.h	$2370$	$4$	2370.a	1.a	$1$	$9$	$9$	$139.835$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.h	$1$	$1$	$18$	$-27$	$45$	$-21$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
2370.4.a.i	$2370$	$4$	2370.a	1.a	$1$	$10$	$10$	$139.835$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.i	$1$	$0$	$-20$	$-30$	$-50$	$-14$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
2370.4.a.j	$2370$	$4$	2370.a	1.a	$1$	$10$	$10$	$139.835$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.j	$1$	$1$	$-20$	$-30$	$-50$	$21$	$-$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
2370.4.a.k	$2370$	$4$	2370.a	1.a	$1$	$10$	$10$	$139.835$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.k	$1$	$0$	$-20$	$30$	$50$	$33$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
2370.4.a.l	$2370$	$4$	2370.a	1.a	$1$	$10$	$10$	$139.835$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.l	$1$	$1$	$20$	$-30$	$-50$	$16$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
2370.4.a.m	$2370$	$4$	2370.a	1.a	$1$	$11$	$11$	$139.835$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.m	$1$	$1$	$-22$	$-33$	$55$	$-30$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
2370.4.a.n	$2370$	$4$	2370.a	1.a	$1$	$11$	$11$	$139.835$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.n	$1$	$0$	$22$	$-33$	$55$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
2370.4.a.o	$2370$	$4$	2370.a	1.a	$1$	$11$	$11$	$139.835$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2370.4.a.o	$1$	$0$	$22$	$33$	$-55$	$23$	$+$	$2^{2}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$

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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.