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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 (35 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
3703.1.b.a	$3703$	$1$	3703.b	7.b	$2$	$4$	$4$	$1.848$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
3703.1.b.b	$3703$	$1$	3703.b	7.b	$2$	$5$	$5$	$1.848$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-5$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
3703.1.b.c	$3703$	$1$	3703.b	7.b	$2$	$5$	$5$	$1.848$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$5$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
3703.1.l.a	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{22}^{9}+\zeta_{22}^{10})q^{2}+(-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
3703.1.l.b	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{22}^{2}+\zeta_{22}^{6})q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
3703.1.l.c	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{22}^{3}-\zeta_{22}^{5})q^{2}+(\zeta_{22}^{6}+\zeta_{22}^{8}+\cdots)q^{4}+\cdots$
3703.1.l.d	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$		$1$		$q+(\zeta_{22}^{2}+\zeta_{22}^{6})q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
3703.1.l.e	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{22}^{9}+\zeta_{22}^{10})q^{2}+(-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
3703.1.l.f	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{22}-\zeta_{22}^{7})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{3}+\cdots)q^{4}+\cdots$
3703.1.l.g	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{22}^{3}-\zeta_{22}^{5})q^{2}+(\zeta_{22}^{6}+\zeta_{22}^{8}+\cdots)q^{4}+\cdots$
3703.1.l.h	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$9$	$0$	$0$	$-1$		$1$		$q+(1+\zeta_{22}^{8})q^{2}+(1-\zeta_{22}^{5}+\zeta_{22}^{8}+\cdots)q^{4}+\cdots$
3703.1.l.i	$3703$	$1$	3703.l	161.l	$22$	$10$	$1$	$1.848$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$9$	$0$	$0$	$1$		$1$		$q+(1+\zeta_{22}^{8})q^{2}+(1-\zeta_{22}^{5}+\zeta_{22}^{8}+\cdots)q^{4}+\cdots$
3703.1.l.j	$3703$	$1$	3703.l	161.l	$22$	$40$	$4$	$1.848$	$\Q(\zeta_{88})$	$S_{4}$	None	None		$40$	$0$	$4$	$0$	$0$	$0$		$1$		$q+\zeta_{88}^{28}q^{2}+\zeta_{88}^{26}q^{3}+(\zeta_{88}^{3}+\zeta_{88}^{25}+\cdots)q^{5}+\cdots$
3703.1.q.a	$3703$	$1$	3703.q	3703.q	$46$	$22$	$1$	$1.848$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{46}^{10}+\zeta_{46}^{22})q^{2}+(-\zeta_{46}^{9}+\zeta_{46}^{20}+\cdots)q^{4}+\cdots$
3703.1.z.a	$3703$	$1$	3703.z	3703.z	$506$	$220$	$1$	$1.848$	$\Q(\zeta_{253})$	$D_{253}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(\zeta_{506}^{126}+\zeta_{506}^{222})q^{2}+(-\zeta_{506}^{95}+\cdots)q^{4}+\cdots$
3703.2.a.a	$3703$	$2$	3703.a	1.a	$1$	$1$	$1$	$29.569$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots$
3703.2.a.b	$3703$	$2$	3703.a	1.a	$1$	$2$	$2$	$29.569$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
3703.2.a.c	$3703$	$2$	3703.a	1.a	$1$	$3$	$3$	$29.569$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
3703.2.a.d	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.70601.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-6$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
3703.2.a.e	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.70601.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$6$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
3703.2.a.f	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.1090433.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$-2$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
3703.2.a.g	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.1090433.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots$
3703.2.a.h	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.220036.1	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
3703.2.a.i	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.220036.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
3703.2.a.j	$3703$	$2$	3703.a	1.a	$1$	$5$	$5$	$29.569$	5.5.2147108.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
3703.2.a.k	$3703$	$2$	3703.a	1.a	$1$	$10$	$10$	$29.569$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-8$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}+\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots$
3703.2.a.l	$3703$	$2$	3703.a	1.a	$1$	$10$	$10$	$29.569$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$8$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}+\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots$
3703.2.a.m	$3703$	$2$	3703.a	1.a	$1$	$12$	$12$	$29.569$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-8$	$-12$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2}+\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots$
3703.2.a.n	$3703$	$2$	3703.a	1.a	$1$	$12$	$12$	$29.569$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$8$	$12$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2}+\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots$
3703.2.a.o	$3703$	$2$	3703.a	1.a	$1$	$24$	$24$	$29.569$		$_{}$	None	None	✓	$1$	$1$	$4$	$0$	$-16$	$-24$	$+$		$\mathrm{SU}(2)$
3703.2.a.p	$3703$	$2$	3703.a	1.a	$1$	$24$	$24$	$29.569$		$_{}$	None	None	✓	$1$	$0$	$4$	$0$	$16$	$24$	$-$		$\mathrm{SU}(2)$
3703.2.a.q	$3703$	$2$	3703.a	1.a	$1$	$25$	$25$	$29.569$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-11$	$0$	$-25$	$+$		$\mathrm{SU}(2)$
3703.2.a.r	$3703$	$2$	3703.a	1.a	$1$	$25$	$25$	$29.569$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-11$	$0$	$25$	$+$		$\mathrm{SU}(2)$
3703.2.a.s	$3703$	$2$	3703.a	1.a	$1$	$35$	$35$	$29.569$		$_{}$	None	None	✓	$1$	$0$	$9$	$9$	$-2$	$35$	$-$		$\mathrm{SU}(2)$
3703.2.a.t	$3703$	$2$	3703.a	1.a	$1$	$35$	$35$	$29.569$		$_{}$	None	None	✓	$1$	$0$	$9$	$9$	$2$	$-35$	$-$		$\mathrm{SU}(2)$

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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.