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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 51 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
2442.2.a.a	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.a	$1$	$1$	$-1$	$-1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
2442.2.a.b	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.b	$1$	$1$	$-1$	$-1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots$
2442.2.a.c	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.c	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
2442.2.a.d	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.d	$1$	$1$	$-1$	$-1$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-4q^{7}+\cdots$
2442.2.a.e	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.e	$1$	$1$	$-1$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
2442.2.a.f	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.f	$1$	$1$	$-1$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
2442.2.a.g	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.g	$1$	$1$	$1$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots$
2442.2.a.h	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓	✓	✓	2442.2.a.h	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
2442.2.a.i	$2442$	$2$	2442.a	1.a	$1$	$1$	$1$	$19.499$	$\Q$	None	✓	✓			2442.2.a.i	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
2442.2.a.j	$2442$	$2$	2442.a	1.a	$1$	$2$	$2$	$19.499$	$\Q(\sqrt{6}) $	None	✓	✓			2442.2.a.j	$1$	$1$	$-2$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
2442.2.a.k	$2442$	$2$	2442.a	1.a	$1$	$2$	$2$	$19.499$	$\Q(\sqrt{17}) $	None	✓	✓			2442.2.a.k	$1$	$0$	$-2$	$2$	$-1$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+4q^{7}+\cdots$
2442.2.a.l	$2442$	$2$	2442.a	1.a	$1$	$2$	$2$	$19.499$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	2442.2.a.l	$1$	$1$	$2$	$-2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
2442.2.a.m	$2442$	$2$	2442.a	1.a	$1$	$2$	$2$	$19.499$	$\Q(\sqrt{3}) $	None	✓	✓	✓		2442.2.a.m	$1$	$1$	$2$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-3+\beta )q^{7}+\cdots$
2442.2.a.n	$2442$	$2$	2442.a	1.a	$1$	$2$	$2$	$19.499$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	2442.2.a.n	$1$	$1$	$2$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
2442.2.a.o	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.1304.1	None	✓	✓	✓		2442.2.a.o	$1$	$1$	$-3$	$-3$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots$
2442.2.a.p	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.148.1	None	✓	✓	✓	✓	2442.2.a.p	$1$	$0$	$-3$	$-3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
2442.2.a.q	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.148.1	None	✓	✓	✓	✓	2442.2.a.q	$1$	$0$	$-3$	$-3$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots$
2442.2.a.r	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.756.1	None	✓	✓	✓		2442.2.a.r	$1$	$0$	$-3$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
2442.2.a.s	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.1016.1	None	✓	✓			2442.2.a.s	$1$	$0$	$3$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+\beta _{2}q^{7}+\cdots$
2442.2.a.t	$2442$	$2$	2442.a	1.a	$1$	$3$	$3$	$19.499$	3.3.148.1	None	✓	✓			2442.2.a.t	$1$	$0$	$3$	$3$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$
2442.2.a.u	$2442$	$2$	2442.a	1.a	$1$	$4$	$4$	$19.499$	4.4.9248.1	None	✓	✓	✓	✓	2442.2.a.u	$1$	$1$	$-4$	$4$	$0$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
2442.2.a.v	$2442$	$2$	2442.a	1.a	$1$	$4$	$4$	$19.499$	4.4.134036.1	None	✓	✓	✓	✓	2442.2.a.v	$1$	$0$	$-4$	$4$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
2442.2.a.w	$2442$	$2$	2442.a	1.a	$1$	$5$	$5$	$19.499$	5.5.2171488.1	None	✓	✓	✓	✓	2442.2.a.w	$1$	$0$	$5$	$-5$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
2442.2.a.x	$2442$	$2$	2442.a	1.a	$1$	$5$	$5$	$19.499$	5.5.522052.1	None	✓	✓	✓	✓	2442.2.a.x	$1$	$0$	$5$	$-5$	$4$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
2442.2.a.y	$2442$	$2$	2442.a	1.a	$1$	$6$	$6$	$19.499$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		2442.2.a.y	$1$	$0$	$6$	$6$	$5$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{4})q^{5}+q^{6}+\cdots$
2442.2.d.a	$2442$	$2$	2442.d	37.b	$2$	$2$	$2$	$19.499$	$\Q(\sqrt{-1}) $	None		✓			2442.2.d.a	$2$	$1$	$0$	$2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+q^{3}-q^{4}+4 i q^{5}-i q^{6}+\cdots$
2442.2.d.b	$2442$	$2$	2442.d	37.b	$2$	$2$	$2$	$19.499$	$\Q(\sqrt{-1}) $	None		✓			2442.2.d.b	$2$	$0$	$0$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}+2 i q^{5}+i q^{6}+\cdots$
2442.2.d.c	$2442$	$2$	2442.d	37.b	$2$	$2$	$2$	$19.499$	$\Q(\sqrt{-1}) $	None		✓			2442.2.d.c	$2$	$0$	$0$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+q^{3}-q^{4}+3 i q^{5}-i q^{6}+\cdots$
2442.2.d.d	$2442$	$2$	2442.d	37.b	$2$	$12$	$12$	$19.499$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			2442.2.d.d	$2$	$0$	$0$	$12$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+q^{3}-q^{4}+\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots$
2442.2.d.e	$2442$	$2$	2442.d	37.b	$2$	$14$	$14$	$19.499$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			2442.2.d.e	$2$	$0$	$0$	$-14$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-q^{3}-q^{4}-\beta _{8}q^{5}-\beta _{6}q^{6}+\cdots$
2442.2.d.f	$2442$	$2$	2442.d	37.b	$2$	$16$	$16$	$19.499$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			2442.2.d.f	$2$	$0$	$0$	$-16$	$0$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{8}q^{6}+\cdots$
2442.2.d.g	$2442$	$2$	2442.d	37.b	$2$	$16$	$16$	$19.499$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			2442.2.d.g	$2$	$0$	$0$	$16$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{5}q^{6}+\cdots$
2442.4.a.a	$2442$	$4$	2442.a	1.a	$1$	$1$	$1$	$144.083$	$\Q$	None	✓	✓			2442.4.a.a	$1$	$1$	$-2$	$-3$	$-18$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots$
2442.4.a.b	$2442$	$4$	2442.a	1.a	$1$	$1$	$1$	$144.083$	$\Q$	None	✓	✓			2442.4.a.b	$1$	$1$	$2$	$3$	$12$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+12q^{5}+6q^{6}+\cdots$
2442.4.a.c	$2442$	$4$	2442.a	1.a	$1$	$2$	$2$	$144.083$	$\Q(\sqrt{249}) $	None	✓	✓			2442.4.a.c	$1$	$1$	$4$	$-6$	$0$	$-14$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-7+\cdots)q^{7}+\cdots$
2442.4.a.d	$2442$	$4$	2442.a	1.a	$1$	$7$	$7$	$144.083$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		2442.4.a.d	$1$	$1$	$14$	$21$	$-37$	$-35$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-5-\beta _{5})q^{5}+\cdots$
2442.4.a.e	$2442$	$4$	2442.a	1.a	$1$	$8$	$8$	$144.083$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		2442.4.a.e	$1$	$1$	$16$	$-24$	$-20$	$-25$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-3+\beta _{4})q^{5}+\cdots$
2442.4.a.f	$2442$	$4$	2442.a	1.a	$1$	$9$	$9$	$144.083$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.f	$1$	$1$	$18$	$27$	$-25$	$-53$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-3+\beta _{5})q^{5}+\cdots$
2442.4.a.g	$2442$	$4$	2442.a	1.a	$1$	$10$	$10$	$144.083$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.g	$1$	$0$	$-20$	$-30$	$15$	$11$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1})q^{5}+\cdots$
2442.4.a.h	$2442$	$4$	2442.a	1.a	$1$	$10$	$10$	$144.083$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.h	$1$	$1$	$-20$	$30$	$5$	$-67$	$-$	$2^{10}\cdot 3$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots$
2442.4.a.i	$2442$	$4$	2442.a	1.a	$1$	$10$	$10$	$144.083$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.i	$1$	$1$	$20$	$-30$	$-10$	$-17$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-1-\beta _{1})q^{5}+\cdots$
2442.4.a.j	$2442$	$4$	2442.a	1.a	$1$	$11$	$11$	$144.083$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.j	$1$	$0$	$-22$	$-33$	$5$	$17$	$+$	$2^{6}\cdot 37$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+\beta _{1}q^{5}+6q^{6}+\cdots$
2442.4.a.k	$2442$	$4$	2442.a	1.a	$1$	$11$	$11$	$144.083$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓		2442.4.a.k	$1$	$1$	$-22$	$-33$	$8$	$-5$	$-$	$2^{13}\cdot 3$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(1-\beta _{1})q^{5}+\cdots$
2442.4.a.l	$2442$	$4$	2442.a	1.a	$1$	$11$	$11$	$144.083$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.l	$1$	$1$	$-22$	$33$	$-5$	$-17$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-\beta _{1}q^{5}-6q^{6}+\cdots$
2442.4.a.m	$2442$	$4$	2442.a	1.a	$1$	$11$	$11$	$144.083$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.m	$1$	$0$	$-22$	$33$	$0$	$31$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots$
2442.4.a.n	$2442$	$4$	2442.a	1.a	$1$	$12$	$12$	$144.083$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.n	$1$	$1$	$-24$	$-36$	$-10$	$-25$	$-$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(-1+\beta _{1})q^{5}+\cdots$
2442.4.a.o	$2442$	$4$	2442.a	1.a	$1$	$12$	$12$	$144.083$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.o	$1$	$0$	$24$	$-36$	$15$	$31$	$+$	$2^{4}\cdot 11$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(1+\beta _{1})q^{5}+\cdots$
2442.4.a.p	$2442$	$4$	2442.a	1.a	$1$	$13$	$13$	$144.083$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.p	$1$	$0$	$-26$	$39$	$0$	$39$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots$
2442.4.a.q	$2442$	$4$	2442.a	1.a	$1$	$13$	$13$	$144.083$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.q	$1$	$0$	$26$	$-39$	$15$	$11$	$+$	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(1+\beta _{1})q^{5}+\cdots$
2442.4.a.r	$2442$	$4$	2442.a	1.a	$1$	$13$	$13$	$144.083$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	2442.4.a.r	$1$	$0$	$26$	$39$	$20$	$39$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(2-\beta _{1})q^{5}+\cdots$

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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.