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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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Results (1-50 of 53 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	13	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7514.2.a.a	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$2$	$-1$	$-2$	$-4$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-2q^{7}+\cdots$
7514.2.a.b	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-2q^{7}+\cdots$
7514.2.a.c	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$3$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
7514.2.a.d	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+4q^{5}-2q^{6}+2q^{7}+\cdots$
7514.2.a.e	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$-4$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}+4q^{7}+\cdots$
7514.2.a.f	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}-2q^{7}+\cdots$
7514.2.a.g	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots$
7514.2.a.h	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+2q^{7}+q^{8}-3q^{9}+\cdots$
7514.2.a.i	$7514$	$2$	7514.a	1.a	$1$	$1$	$1$	$60.000$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\cdots$
7514.2.a.j	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-4$	$2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}-2q^{5}+(1+\cdots)q^{6}+\cdots$
7514.2.a.k	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+3\beta q^{7}-q^{8}+\cdots$
7514.2.a.l	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-q^{8}-3q^{9}+\beta q^{10}+\cdots$
7514.2.a.m	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-3\beta q^{5}-\beta q^{6}+\cdots$
7514.2.a.n	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}-3\beta q^{5}-2\beta q^{6}+\cdots$
7514.2.a.o	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}-\beta q^{5}-2\beta q^{6}+\cdots$
7514.2.a.p	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$4$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(2+\beta )q^{3}+q^{4}-\beta q^{5}+(-2+\cdots)q^{6}+\cdots$
7514.2.a.q	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}+q^{8}-3q^{9}+\cdots$
7514.2.a.r	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-3\beta q^{5}+\beta q^{6}+\cdots$
7514.2.a.s	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{8}+\cdots$
7514.2.a.t	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots$
7514.2.a.u	$7514$	$2$	7514.a	1.a	$1$	$2$	$2$	$60.000$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+3\beta q^{7}+\cdots$
7514.2.a.v	$7514$	$2$	7514.a	1.a	$1$	$3$	$3$	$60.000$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$-3$	$0$	$-9$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+2\beta _{2}q^{5}+\cdots$
7514.2.a.w	$7514$	$2$	7514.a	1.a	$1$	$3$	$3$	$60.000$	3.3.148.1	None	✓	$1$	$1$	$-3$	$2$	$4$	$0$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{2})q^{5}+\cdots$
7514.2.a.x	$7514$	$2$	7514.a	1.a	$1$	$3$	$3$	$60.000$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$3$	$0$	$9$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{1})q^{3}+q^{4}-2\beta _{2}q^{5}+\cdots$
7514.2.a.y	$7514$	$2$	7514.a	1.a	$1$	$3$	$3$	$60.000$	3.3.316.1	None	✓	$1$	$1$	$3$	$-2$	$-4$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
7514.2.a.z	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.8725.1	None	✓	$1$	$1$	$-4$	$-2$	$1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
7514.2.a.ba	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.25717.1	None	✓	$1$	$1$	$-4$	$0$	$-1$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{3}q^{6}+\cdots$
7514.2.a.bb	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
7514.2.a.bc	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.170528.1	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
7514.2.a.bd	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.25717.1	None	✓	$1$	$0$	$-4$	$0$	$1$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{6}+\cdots$
7514.2.a.be	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.8725.1	None	✓	$1$	$0$	$-4$	$2$	$-1$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
7514.2.a.bf	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.19773.1	None	✓	$1$	$1$	$4$	$-2$	$-3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots$
7514.2.a.bg	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.1957.1	None	✓	$1$	$1$	$4$	$0$	$-1$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
7514.2.a.bh	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+\cdots$
7514.2.a.bi	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
7514.2.a.bj	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	$\Q(\sqrt{2}, \sqrt{13})$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
7514.2.a.bk	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.1957.1	None	✓	$1$	$0$	$4$	$0$	$1$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
7514.2.a.bl	$7514$	$2$	7514.a	1.a	$1$	$4$	$4$	$60.000$	4.4.19773.1	None	✓	$1$	$0$	$4$	$2$	$3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1+\beta _{2})q^{5}+\cdots$
7514.2.a.bm	$7514$	$2$	7514.a	1.a	$1$	$6$	$6$	$60.000$	6.6.118210688.1	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{4}q^{6}+\cdots$
7514.2.a.bn	$7514$	$2$	7514.a	1.a	$1$	$8$	$8$	$60.000$	8.8.7050625024.1	None	✓	$2$	$1$	$8$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
7514.2.a.bo	$7514$	$2$	7514.a	1.a	$1$	$9$	$9$	$60.000$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$-3$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{4})q^{5}+\cdots$
7514.2.a.bp	$7514$	$2$	7514.a	1.a	$1$	$9$	$9$	$60.000$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$3$	$0$	$6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{2}+\beta _{4})q^{5}+\cdots$
7514.2.a.bq	$7514$	$2$	7514.a	1.a	$1$	$10$	$10$	$60.000$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$-10$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots$
7514.2.a.br	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-12$	$-6$	$6$	$-9$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{7}q^{3}+q^{4}-\beta _{8}q^{5}-\beta _{7}q^{6}+\cdots$
7514.2.a.bs	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$-12$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots$
7514.2.a.bt	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-12$	$6$	$-6$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{7}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{7}q^{6}+\cdots$
7514.2.a.bu	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$12$	$-6$	$-12$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$
7514.2.a.bv	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$12$	$0$	$-6$	$-15$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{4}+\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots$
7514.2.a.bw	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$12$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{10}+\beta _{11})q^{5}+\cdots$
7514.2.a.bx	$7514$	$2$	7514.a	1.a	$1$	$12$	$12$	$60.000$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$12$	$0$	$6$	$15$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{4}-\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots$

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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.