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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 59 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1075.1.c.a	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-q^{11}-q^{13}+q^{16}+2q^{17}+\cdots$
1075.1.c.b	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-q^{11}+q^{13}+q^{16}-2q^{17}+\cdots$
1075.1.c.c	$1075$	$1$	1075.c	43.b	$2$	$6$	$6$	$0.536$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
1075.1.d.a	$1075$	$1$	1075.d	215.d	$2$	$2$	$2$	$0.536$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-q^{9}-q^{11}-iq^{13}+q^{16}+\cdots$
1075.2.a.a	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}-4q^{6}-2q^{7}+\cdots$
1075.2.a.b	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{6}+4q^{7}+3q^{8}+\cdots$
1075.2.a.c	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+4q^{7}+q^{9}+q^{11}+\cdots$
1075.2.a.d	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-3q^{9}-q^{11}+q^{13}+\cdots$
1075.2.a.e	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-4q^{7}+q^{9}+q^{11}+\cdots$
1075.2.a.f	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-2q^{6}-4q^{7}-3q^{8}+\cdots$
1075.2.a.g	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}-4q^{6}+2q^{7}+\cdots$
1075.2.a.h	$1075$	$2$	1075.a	1.a	$1$	$1$	$1$	$8.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+4q^{6}+q^{9}+\cdots$
1075.2.a.i	$1075$	$2$	1075.a	1.a	$1$	$2$	$2$	$8.584$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}-2q^{6}+(2+\beta )q^{7}-2\beta q^{8}+\cdots$
1075.2.a.j	$1075$	$2$	1075.a	1.a	$1$	$3$	$3$	$8.584$	3.3.169.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1075.2.a.k	$1075$	$2$	1075.a	1.a	$1$	$3$	$3$	$8.584$	3.3.169.1	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots$
1075.2.a.l	$1075$	$2$	1075.a	1.a	$1$	$3$	$3$	$8.584$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1075.2.a.m	$1075$	$2$	1075.a	1.a	$1$	$5$	$5$	$8.584$	5.5.1933097.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$1$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots$
1075.2.a.n	$1075$	$2$	1075.a	1.a	$1$	$5$	$5$	$8.584$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
1075.2.a.o	$1075$	$2$	1075.a	1.a	$1$	$5$	$5$	$8.584$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
1075.2.a.p	$1075$	$2$	1075.a	1.a	$1$	$6$	$6$	$8.584$	6.6.32503921.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-4$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots$
1075.2.a.q	$1075$	$2$	1075.a	1.a	$1$	$6$	$6$	$8.584$	6.6.282109865.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots$
1075.2.a.r	$1075$	$2$	1075.a	1.a	$1$	$6$	$6$	$8.584$	6.6.282109865.1	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots$
1075.2.a.s	$1075$	$2$	1075.a	1.a	$1$	$7$	$7$	$8.584$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-5$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots$
1075.2.a.t	$1075$	$2$	1075.a	1.a	$1$	$7$	$7$	$8.584$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$5$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
1075.2.b.a	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+2iq^{3}-2q^{4}-4q^{6}+2iq^{7}+\cdots$
1075.2.b.b	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2iq^{3}-2q^{4}+4q^{6}-q^{9}+\cdots$
1075.2.b.c	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots$
1075.2.b.d	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}+2q^{4}+4iq^{7}-q^{9}+q^{11}+\cdots$
1075.2.b.e	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+2iq^{7}+3q^{9}-q^{11}-iq^{13}+\cdots$
1075.2.b.f	$1075$	$2$	1075.b	5.b	$2$	$4$	$4$	$8.584$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{2}q^{3}-2q^{6}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
1075.2.b.g	$1075$	$2$	1075.b	5.b	$2$	$6$	$6$	$8.584$	6.0.6594624.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
1075.2.b.h	$1075$	$2$	1075.b	5.b	$2$	$10$	$10$	$8.584$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
1075.2.b.i	$1075$	$2$	1075.b	5.b	$2$	$10$	$10$	$8.584$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{4}q^{3}+(\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots$
1075.2.b.j	$1075$	$2$	1075.b	5.b	$2$	$12$	$12$	$8.584$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-2+\beta _{2})q^{4}+(2+\cdots)q^{6}+\cdots$
1075.2.b.k	$1075$	$2$	1075.b	5.b	$2$	$12$	$12$	$8.584$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{7})q^{2}+(-\beta _{7}-\beta _{10})q^{3}+(-2+\cdots)q^{4}+\cdots$
1075.4.a.a	$1075$	$4$	1075.a	1.a	$1$	$4$	$4$	$63.427$	4.4.45868.1	$_{}$	None	None	✓	$1$	$0$	$4$	$11$	$0$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$
1075.4.a.b	$1075$	$4$	1075.a	1.a	$1$	$6$	$6$	$63.427$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-7$	$0$	$-8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots$
1075.4.a.c	$1075$	$4$	1075.a	1.a	$1$	$6$	$6$	$63.427$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$5$	$5$	$0$	$34$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{5})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1075.4.a.d	$1075$	$4$	1075.a	1.a	$1$	$8$	$8$	$63.427$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$7$	$0$	$36$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(3+\beta _{2})q^{4}+\cdots$
1075.4.a.e	$1075$	$4$	1075.a	1.a	$1$	$13$	$13$	$63.427$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-5$	$0$	$-34$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(5+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
1075.4.a.f	$1075$	$4$	1075.a	1.a	$1$	$15$	$15$	$63.427$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-7$	$0$	$-36$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(6+\beta _{2})q^{4}+(3+\beta _{5}+\cdots)q^{6}+\cdots$
1075.4.a.g	$1075$	$4$	1075.a	1.a	$1$	$19$	$19$	$63.427$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots$
1075.4.a.h	$1075$	$4$	1075.a	1.a	$1$	$19$	$19$	$63.427$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots$
1075.4.a.i	$1075$	$4$	1075.a	1.a	$1$	$23$	$23$	$63.427$		$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
1075.4.a.j	$1075$	$4$	1075.a	1.a	$1$	$23$	$23$	$63.427$		$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
1075.4.a.k	$1075$	$4$	1075.a	1.a	$1$	$32$	$32$	$63.427$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-18$	$0$	$-28$	$-$		$\mathrm{SU}(2)$
1075.4.a.l	$1075$	$4$	1075.a	1.a	$1$	$32$	$32$	$63.427$		$_{}$	None	None	✓	$1$	$0$	$10$	$18$	$0$	$28$	$+$		$\mathrm{SU}(2)$
1075.6.a.a	$1075$	$6$	1075.a	1.a	$1$	$8$	$8$	$172.413$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$12$	$26$	$0$	$136$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+(2+\beta _{1}-\beta _{4}+\beta _{7})q^{3}+\cdots$
1075.6.a.b	$1075$	$6$	1075.a	1.a	$1$	$10$	$10$	$172.413$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-8$	$-28$	$0$	$-60$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-3-\beta _{6})q^{3}+(21+\cdots)q^{4}+\cdots$
1075.6.a.c	$1075$	$6$	1075.a	1.a	$1$	$13$	$13$	$172.413$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$7$	$16$	$0$	$372$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots$

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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.