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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 89 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
1035.1.d.a	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-115}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+q^{4}-q^{5}+q^{16}+2q^{17}-q^{20}+\cdots$
1035.1.d.b	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-115}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{4}+q^{5}+q^{16}-2q^{17}+q^{20}+\cdots$
1035.1.bd.a	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{22}^{2}-\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1035.1.bd.b	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(-\zeta_{22}^{2}+\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1035.2.a.a	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots$
1035.2.a.b	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}+q^{7}-2q^{10}+\cdots$
1035.2.a.c	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots$
1035.2.a.d	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-3q^{7}+4q^{11}+4q^{16}+\cdots$
1035.2.a.e	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}-4q^{11}+4q^{16}+\cdots$
1035.2.a.f	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots$
1035.2.a.g	$1035$	$2$	1035.a	1.a	$1$	$1$	$1$	$8.265$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots$
1035.2.a.h	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{5}+(-1+\beta )q^{7}-2\beta q^{8}+\cdots$
1035.2.a.i	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}+(-1-\beta )q^{7}-2\beta q^{8}+\cdots$
1035.2.a.j	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}+(-1+2\beta )q^{7}-2\beta q^{8}+\cdots$
1035.2.a.k	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}+q^{5}-q^{7}+2\beta q^{8}+\cdots$
1035.2.a.l	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}-3q^{7}+\cdots$
1035.2.a.m	$1035$	$2$	1035.a	1.a	$1$	$2$	$2$	$8.265$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots$
1035.2.a.n	$1035$	$2$	1035.a	1.a	$1$	$3$	$3$	$8.265$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(2+\beta _{2})q^{7}+\cdots$
1035.2.a.o	$1035$	$2$	1035.a	1.a	$1$	$4$	$4$	$8.265$	4.4.15317.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
1035.2.a.p	$1035$	$2$	1035.a	1.a	$1$	$6$	$6$	$8.265$	6.6.98838128.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-6$	$6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(2+\beta _{4})q^{4}-q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
1035.2.a.q	$1035$	$2$	1035.a	1.a	$1$	$6$	$6$	$8.265$	6.6.98838128.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$6$	$6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(2+\beta _{4})q^{4}+q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
1035.2.b.a	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2q^{4}+(-2+i)q^{5}-iq^{7}+\cdots$
1035.2.b.b	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots$
1035.2.b.c	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+(-1+2i)q^{5}+3iq^{8}+\cdots$
1035.2.b.d	$1035$	$2$	1035.b	5.b	$2$	$6$	$6$	$8.265$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1035.2.b.e	$1035$	$2$	1035.b	5.b	$2$	$8$	$8$	$8.265$	8.0.527896576.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-1-\beta _{2}+\beta _{4}-\beta _{6})q^{4}+\cdots$
1035.2.b.f	$1035$	$2$	1035.b	5.b	$2$	$14$	$14$	$8.265$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-2-\beta _{8}+\beta _{9})q^{4}-\beta _{10}q^{5}+\cdots$
1035.2.b.g	$1035$	$2$	1035.b	5.b	$2$	$20$	$20$	$8.265$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{16}q^{2}+(-\beta _{2}-\beta _{5})q^{4}+\beta _{10}q^{5}+\cdots$
1035.2.c.a	$1035$	$2$	1035.c	69.c	$2$	$4$	$4$	$8.265$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-2\beta _{2}q^{8}+\cdots$
1035.2.c.b	$1035$	$2$	1035.c	69.c	$2$	$4$	$4$	$8.265$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{5}+\beta _{1}q^{7}-2\beta _{2}q^{8}-\beta _{2}q^{10}+\cdots$
1035.2.c.c	$1035$	$2$	1035.c	69.c	$2$	$12$	$12$	$8.265$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots$
1035.2.c.d	$1035$	$2$	1035.c	69.c	$2$	$12$	$12$	$8.265$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+q^{5}-\beta _{9}q^{7}+\cdots$
1035.2.h.a	$1035$	$2$	1035.h	345.h	$2$	$8$	$8$	$8.265$	8.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{1}q^{5}+\beta _{4}q^{7}+4q^{16}-\beta _{5}q^{17}+\cdots$
1035.2.h.b	$1035$	$2$	1035.h	345.h	$2$	$40$	$40$	$8.265$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1035.2.i.a	$1035$	$2$	1035.i	9.c	$3$	$4$	$2$	$8.265$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-2\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
1035.2.i.b	$1035$	$2$	1035.i	9.c	$3$	$4$	$2$	$8.265$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$3$	$0$	$2$	$-7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(1+2\beta _{3})q^{3}+(3\beta _{1}+\cdots)q^{4}+\cdots$
1035.2.i.c	$1035$	$2$	1035.i	9.c	$3$	$34$	$17$	$8.265$		$_{}$	None	None		$2$	$0$	$-5$	$3$	$17$	$-6$			$\mathrm{SU}(2)[C_{3}]$
1035.2.i.d	$1035$	$2$	1035.i	9.c	$3$	$38$	$19$	$8.265$		$_{}$	None	None		$2$	$0$	$6$	$-1$	$-19$	$5$			$\mathrm{SU}(2)[C_{3}]$
1035.2.i.e	$1035$	$2$	1035.i	9.c	$3$	$46$	$23$	$8.265$		$_{}$	None	None		$2$	$0$	$3$	$3$	$23$	$4$			$\mathrm{SU}(2)[C_{3}]$
1035.2.i.f	$1035$	$2$	1035.i	9.c	$3$	$50$	$25$	$8.265$		$_{}$	None	None		$2$	$0$	$-4$	$-1$	$-25$	$5$			$\mathrm{SU}(2)[C_{3}]$
1035.2.j.a	$1035$	$2$	1035.j	15.e	$4$	$44$	$22$	$8.265$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
1035.2.j.b	$1035$	$2$	1035.j	15.e	$4$	$44$	$22$	$8.265$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{4}]$
1035.3.e.a	$1035$	$3$	1035.e	3.b	$2$	$56$	$56$	$28.202$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-32$			$\mathrm{SU}(2)[C_{2}]$
1035.3.f.a	$1035$	$3$	1035.f	15.d	$2$	$88$	$88$	$28.202$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1035.3.g.a	$1035$	$3$	1035.g	23.b	$2$	$6$	$6$	$28.202$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-3q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}-7q^{8}+\cdots$
1035.3.g.b	$1035$	$3$	1035.g	23.b	$2$	$10$	$10$	$28.202$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(3+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
1035.3.g.c	$1035$	$3$	1035.g	23.b	$2$	$32$	$32$	$28.202$		$_{}$	None	None		$2$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1035.3.g.d	$1035$	$3$	1035.g	23.b	$2$	$32$	$32$	$28.202$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1035.4.a.a	$1035$	$4$	1035.a	1.a	$1$	$1$	$1$	$61.067$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-4q^{4}-5q^{5}-2q^{7}+24q^{8}+\cdots$
1035.4.a.b	$1035$	$4$	1035.a	1.a	$1$	$1$	$1$	$61.067$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-1$	$0$	$5$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}+5q^{5}-2^{5}q^{7}+15q^{8}+\cdots$

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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.