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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 168 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
396.1.d.a	$396$	$1$	396.d	132.d	$2$	$4$	$4$	$0.198$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{11}) $		✓	✓	✓	396.1.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
396.1.f.a	$396$	$1$	396.f	11.b	$2$	$1$	$1$	$0.198$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓		✓	✓	44.1.d.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{11}+q^{23}-q^{31}-q^{37}+\cdots$
396.1.m.a	$396$	$1$	396.m	99.h	$6$	$2$	$1$	$0.198$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		✓			396.1.m.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
396.1.m.b	$396$	$1$	396.m	99.h	$6$	$2$	$1$	$0.198$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		✓			396.1.m.b	$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q+q^{3}+\zeta_{6}^{2}q^{5}+q^{9}-\zeta_{6}q^{11}+2\zeta_{6}^{2}q^{15}+\cdots$
396.2.a.a	$396$	$2$	396.a	1.a	$1$	$1$	$1$	$3.162$	$\Q$	$_{}$	None	None	✓		✓	✓	132.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-q^{11}-2q^{13}-4q^{17}+\cdots$
396.2.a.b	$396$	$2$	396.a	1.a	$1$	$1$	$1$	$3.162$	$\Q$	$_{}$	None	None	✓				132.2.a.a	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+q^{11}+6q^{13}+4q^{17}+\cdots$
396.2.a.c	$396$	$2$	396.a	1.a	$1$	$1$	$1$	$3.162$	$\Q$	$_{}$	None	None	✓				44.2.a.a	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots$
396.2.b.a	$396$	$2$	396.b	33.d	$2$	$2$	$2$	$3.162$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			396.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+3\beta q^{7}+(-3-\beta )q^{11}-6q^{17}+\cdots$
396.2.b.b	$396$	$2$	396.b	33.d	$2$	$2$	$2$	$3.162$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			396.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-3\beta q^{7}+(3-\beta )q^{11}+6q^{17}+\cdots$
396.2.c.a	$396$	$2$	396.c	12.b	$2$	$10$	$10$	$3.162$	10.0.$\cdots$.1	$_{}$	None	None		✓			396.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}+\beta _{7}-\beta _{8})q^{5}+\cdots$
396.2.c.b	$396$	$2$	396.c	12.b	$2$	$10$	$10$	$3.162$	10.0.$\cdots$.1	$_{}$	None	None		✓			396.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$
396.2.h.a	$396$	$2$	396.h	44.c	$2$	$4$	$4$	$3.162$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-33}) $	None		✓			396.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots$
396.2.h.b	$396$	$2$	396.h	44.c	$2$	$4$	$4$	$3.162$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					44.2.c.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
396.2.h.c	$396$	$2$	396.h	44.c	$2$	$8$	$8$	$3.162$	8.0.207360000.1	$_{}$	None	None		✓			396.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{4}+\beta _{7})q^{5}+\cdots$
396.2.h.d	$396$	$2$	396.h	44.c	$2$	$12$	$12$	$3.162$	12.0.$\cdots$.2	$_{}$	None	None			✓		132.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{5}+\cdots$
396.2.i.a	$396$	$2$	396.i	9.c	$3$	$2$	$1$	$3.162$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			396.2.i.a	$2$	$1$	$0$	$-3$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
396.2.i.b	$396$	$2$	396.i	9.c	$3$	$2$	$1$	$3.162$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			396.2.i.b	$2$	$0$	$0$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots$
396.2.i.c	$396$	$2$	396.i	9.c	$3$	$2$	$1$	$3.162$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			396.2.i.c	$2$	$0$	$0$	$3$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
396.2.i.d	$396$	$2$	396.i	9.c	$3$	$6$	$3$	$3.162$	6.0.309123.1	$_{}$	None	None		✓			396.2.i.d	$2$	$0$	$0$	$2$	$5$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(-\beta _{1}-2\beta _{4}+\cdots)q^{5}+\cdots$
396.2.i.e	$396$	$2$	396.i	9.c	$3$	$8$	$4$	$3.162$	8.0.5206055409.1	$_{}$	None	None		✓	✓		396.2.i.e	$2$	$0$	$0$	$-3$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(\beta _{2}-\beta _{3}+\beta _{6})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$
396.2.j.a	$396$	$2$	396.j	11.c	$5$	$4$	$1$	$3.162$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$0$	$-3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{5}+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{7}+\cdots$
396.2.j.b	$396$	$2$	396.j	11.c	$5$	$4$	$1$	$3.162$	$\Q(\zeta_{10})$	$_{}$	None	None					132.2.i.a	$2$	$0$	$0$	$0$	$-3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{5}+(2-2\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots$
396.2.j.c	$396$	$2$	396.j	11.c	$5$	$4$	$1$	$3.162$	$\Q(\zeta_{10})$	$_{}$	None	None					132.2.i.b	$2$	$0$	$0$	$0$	$7$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(3-2\zeta_{10}+3\zeta_{10}^{2})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots$
396.2.j.d	$396$	$2$	396.j	11.c	$5$	$8$	$2$	$3.162$	8.0.484000000.6	$_{}$	None	None		✓	✓		396.2.j.d	$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\beta _{1}+\beta _{6}-\beta _{7})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
396.2.k.a	$396$	$2$	396.k	396.k	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			396.2.k.a	$4$	$0$	$0$	$-6$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
396.2.k.b	$396$	$2$	396.k	396.k	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			396.2.k.b	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(1+2\beta _{2})q^{3}+(-2+\cdots)q^{4}+\cdots$
396.2.k.c	$396$	$2$	396.k	396.k	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			396.2.k.b	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(-1-2\beta _{2})q^{3}+2q^{4}-2\beta _{2}q^{5}+\cdots$
396.2.k.d	$396$	$2$	396.k	396.k	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			396.2.k.a	$4$	$0$	$0$	$6$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots$
396.2.k.e	$396$	$2$	396.k	396.k	$6$	$120$	$60$	$3.162$		$_{}$	None	None		✓	✓		396.2.k.e	$8$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{6}]$
396.2.p.a	$396$	$2$	396.p	36.h	$6$	$60$	$30$	$3.162$		$_{}$	None	None		✓			396.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
396.2.p.b	$396$	$2$	396.p	36.h	$6$	$60$	$30$	$3.162$		$_{}$	None	None		✓			396.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
396.2.q.a	$396$	$2$	396.q	99.g	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			396.2.q.a	$4$	$0$	$0$	$-1$	$9$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{1}q^{3}+(3-\beta _{2}+\beta _{3})q^{5}+(3\beta _{2}+\beta _{3})q^{9}+\cdots$
396.2.q.b	$396$	$2$	396.q	99.g	$6$	$4$	$2$	$3.162$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			396.2.q.b	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1-\beta _{1}+\beta _{3})q^{3}+(\beta _{2}+2\beta _{3})q^{5}+\cdots$
396.2.q.c	$396$	$2$	396.q	99.g	$6$	$16$	$8$	$3.162$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		396.2.q.c	$4$	$0$	$0$	$0$	$-12$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{1}-\beta _{3}+\beta _{9}+\beta _{11})q^{3}+\cdots$
396.2.r.a	$396$	$2$	396.r	44.g	$10$	$16$	$4$	$3.162$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					44.2.g.a	$4$	$0$	$5$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{6}+\beta _{10}+\cdots)q^{4}+\cdots$
396.2.r.b	$396$	$2$	396.r	44.g	$10$	$48$	$12$	$3.162$		$_{}$	None	None					132.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
396.2.r.c	$396$	$2$	396.r	44.g	$10$	$48$	$12$	$3.162$		$_{}$	None	None		✓			396.2.r.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
396.2.w.a	$396$	$2$	396.w	132.o	$10$	$96$	$24$	$3.162$		$_{}$	None	None		✓	✓	✓	396.2.w.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
396.2.x.a	$396$	$2$	396.x	33.f	$10$	$16$	$4$	$3.162$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	396.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{4}+2\beta _{5}+\beta _{13}-\beta _{15})q^{5}+(-1+\cdots)q^{7}+\cdots$
396.2.y.a	$396$	$2$	396.y	99.m	$15$	$96$	$12$	$3.162$		$_{}$	None	None		✓	✓	✓	396.2.y.a	$4$	$0$	$0$	$1$	$1$	$0$			$\mathrm{SU}(2)[C_{15}]$
396.2.z.a	$396$	$2$	396.z	99.p	$30$	$96$	$12$	$3.162$		$_{}$	None	None		✓	✓	✓	396.2.z.a	$4$	$0$	$0$	$-1$	$3$	$0$			$\mathrm{SU}(2)[C_{30}]$
396.2.ba.a	$396$	$2$	396.ba	396.aa	$30$	$544$	$68$	$3.162$		$_{}$	None	None		✓	✓	✓	396.2.ba.a	$8$	$0$	$-9$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{30}]$
396.2.bf.a	$396$	$2$	396.bf	396.af	$30$	$544$	$68$	$3.162$		$_{}$	None	None		✓	✓	✓	396.2.bf.a	$8$	$0$	$-5$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{30}]$
396.3.d.a	$396$	$3$	396.d	132.d	$2$	$48$	$48$	$10.790$		$_{}$	None	None		✓	✓	✓	396.3.d.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
396.3.e.a	$396$	$3$	396.e	3.b	$2$	$8$	$8$	$10.790$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓	✓	✓	396.3.e.a	$2$	$0$	$0$	$0$	$0$	$-16$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}+(-2-\beta _{5})q^{7}-\beta _{3}q^{11}+\cdots$
396.3.f.a	$396$	$3$	396.f	11.b	$2$	$2$	$2$	$10.790$	$\Q(\sqrt{33}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓				44.3.d.a	$2$	$0$	$0$	$0$	$-1$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta )q^{5}+11q^{11}+(19+3\beta )q^{23}+\cdots$
396.3.f.b	$396$	$3$	396.f	11.b	$2$	$4$	$4$	$10.790$	4.0.131904.1	$_{}$	None	None					132.3.f.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-5+3\beta _{1}+\cdots)q^{11}+\cdots$
396.3.f.c	$396$	$3$	396.f	11.b	$2$	$4$	$4$	$10.790$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	None	None		✓			396.3.f.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{3})q^{11}-3\beta _{2}q^{13}+\cdots$
396.3.g.a	$396$	$3$	396.g	4.b	$2$	$4$	$4$	$10.790$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					132.3.g.a	$2$	$0$	$4$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+(-2+2\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
396.3.g.b	$396$	$3$	396.g	4.b	$2$	$10$	$10$	$10.790$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			396.3.g.b	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$

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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.