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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 134 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
444.1.h.a	$444$	$1$	444.h	111.d	$2$	$2$	$2$	$0.222$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $		✓	✓	✓	444.1.h.a	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{11}+\cdots$
444.1.bc.a	$444$	$1$	444.bc	111.n	$18$	$6$	$1$	$0.222$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	444.1.bc.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\zeta_{18}^{7}q^{3}+(\zeta_{18}^{5}-\zeta_{18}^{6})q^{7}-\zeta_{18}^{5}q^{9}+\cdots$
444.1.bf.a	$444$	$1$	444.bf	111.p	$18$	$6$	$1$	$0.222$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	444.1.bf.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{3}-\zeta_{18}^{7})q^{7}+\cdots$
444.2.a.a	$444$	$2$	444.a	1.a	$1$	$1$	$1$	$3.545$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	444.2.a.a	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+4q^{11}-2q^{13}+6q^{19}+\cdots$
444.2.a.b	$444$	$2$	444.a	1.a	$1$	$1$	$1$	$3.545$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	444.2.a.b	$1$	$1$	$0$	$1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
444.2.a.c	$444$	$2$	444.a	1.a	$1$	$2$	$2$	$3.545$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	444.2.a.c	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots$
444.2.a.d	$444$	$2$	444.a	1.a	$1$	$2$	$2$	$3.545$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓	✓	✓	444.2.a.d	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+2q^{7}+q^{9}+(2-2\beta )q^{13}+\cdots$
444.2.c.a	$444$	$2$	444.c	12.b	$2$	$8$	$8$	$3.545$	8.0.386672896.3	$_{}$	None	None		✓			444.2.c.a	$2$	$0$	$-2$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
444.2.c.b	$444$	$2$	444.c	12.b	$2$	$8$	$8$	$3.545$	8.0.386672896.3	$_{}$	None	None		✓			444.2.c.a	$2$	$0$	$2$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(-1-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$
444.2.c.c	$444$	$2$	444.c	12.b	$2$	$20$	$20$	$3.545$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			444.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{13}+\cdots)q^{5}+\cdots$
444.2.c.d	$444$	$2$	444.c	12.b	$2$	$36$	$36$	$3.545$		$_{}$	None	None		✓	✓		444.2.c.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
444.2.e.a	$444$	$2$	444.e	37.b	$2$	$4$	$4$	$3.545$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			444.2.e.a	$2$	$0$	$0$	$-4$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
444.2.e.b	$444$	$2$	444.e	37.b	$2$	$4$	$4$	$3.545$	$\Q(\sqrt{-5 + \sqrt{13}})$	$_{}$	None	None		✓			444.2.e.b	$2$	$0$	$0$	$4$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots$
444.2.g.a	$444$	$2$	444.g	444.g	$2$	$4$	$4$	$3.545$	$\Q(\sqrt{3}, \sqrt{-7})$	$_{}$	None	None		✓			444.2.g.a	$4$	$0$	$-2$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
444.2.g.b	$444$	$2$	444.g	444.g	$2$	$4$	$4$	$3.545$	$\Q(\sqrt{3}, \sqrt{-7})$	$_{}$	None	None		✓			444.2.g.a	$4$	$0$	$2$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{2}+\beta _{3}q^{3}+(-1-\beta _{2})q^{4}+\cdots$
444.2.g.c	$444$	$2$	444.g	444.g	$2$	$16$	$16$	$3.545$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-111}) $	None		✓			444.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{12}q^{5}+\cdots$
444.2.g.d	$444$	$2$	444.g	444.g	$2$	$48$	$48$	$3.545$		$_{}$	None	None		✓	✓		444.2.g.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
444.2.i.a	$444$	$2$	444.i	37.c	$3$	$2$	$1$	$3.545$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			444.2.i.a	$2$	$0$	$0$	$1$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}-2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$
444.2.i.b	$444$	$2$	444.i	37.c	$3$	$4$	$2$	$3.545$	$\Q(\sqrt{-3}, \sqrt{37})$	$_{}$	None	None		✓			444.2.i.b	$2$	$0$	$0$	$2$	$1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}-3\beta _{2}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
444.2.i.c	$444$	$2$	444.i	37.c	$3$	$6$	$3$	$3.545$	6.0.27379323.1	$_{}$	None	None		✓	✓		444.2.i.c	$2$	$0$	$0$	$-3$	$-1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots$
444.2.k.a	$444$	$2$	444.k	148.g	$4$	$2$	$1$	$3.545$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			444.2.k.a	$2$	$1$	$-2$	$2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+q^{3}-2 i q^{4}+(2 i-2)q^{5}+\cdots$
444.2.k.b	$444$	$2$	444.k	148.g	$4$	$2$	$1$	$3.545$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			444.2.k.a	$2$	$0$	$2$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}-q^{3}-2 i q^{4}+(2 i-2)q^{5}+\cdots$
444.2.k.c	$444$	$2$	444.k	148.g	$4$	$36$	$18$	$3.545$		$_{}$	None	None		✓			444.2.k.c	$2$	$0$	$-4$	$-36$	$2$	$0$			$\mathrm{SU}(2)[C_{4}]$
444.2.k.d	$444$	$2$	444.k	148.g	$4$	$36$	$18$	$3.545$		$_{}$	None	None		✓			444.2.k.c	$2$	$0$	$0$	$36$	$2$	$0$			$\mathrm{SU}(2)[C_{4}]$
444.2.m.a	$444$	$2$	444.m	111.g	$4$	$4$	$2$	$3.545$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			444.2.m.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}-q^{7}+(3+\beta _{3})q^{9}+(2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
444.2.m.b	$444$	$2$	444.m	111.g	$4$	$4$	$2$	$3.545$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			444.2.m.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta_{2} q^{3}+2\beta_{3} q^{7}-3 q^{9}+(2\beta_{3}-2\beta_{2}-\beta_1+1)q^{13}+\cdots$
444.2.m.c	$444$	$2$	444.m	111.g	$4$	$4$	$2$	$3.545$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			444.2.m.c	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1-2\zeta_{12}+\cdots)q^{5}+\cdots$
444.2.m.d	$444$	$2$	444.m	111.g	$4$	$12$	$6$	$3.545$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		444.2.m.d	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}-\beta _{7})q^{3}-\beta _{11}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
444.2.p.a	$444$	$2$	444.p	444.p	$6$	$4$	$2$	$3.545$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			444.2.p.a	$4$	$0$	$0$	$-6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
444.2.p.b	$444$	$2$	444.p	444.p	$6$	$4$	$2$	$3.545$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			444.2.p.a	$4$	$0$	$0$	$6$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
444.2.p.c	$444$	$2$	444.p	444.p	$6$	$136$	$68$	$3.545$		$_{}$	None	None		✓	✓		444.2.p.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
444.2.r.a	$444$	$2$	444.r	37.e	$6$	$2$	$1$	$3.545$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			444.2.r.a	$2$	$0$	$0$	$-1$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{3}+(-4+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$
444.2.r.b	$444$	$2$	444.r	37.e	$6$	$2$	$1$	$3.545$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			444.2.r.b	$2$	$0$	$0$	$-1$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}+2\zeta_{6}q^{7}+\cdots$
444.2.r.c	$444$	$2$	444.r	37.e	$6$	$4$	$2$	$3.545$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			444.2.r.c	$2$	$0$	$0$	$-2$	$9$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{3}+(3-2\beta _{2}+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots$
444.2.r.d	$444$	$2$	444.r	37.e	$6$	$8$	$4$	$3.545$	8.0.$\cdots$.1	$_{}$	None	None		✓	✓		444.2.r.d	$2$	$0$	$0$	$4$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{3})q^{3}+\beta _{5}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+\cdots$
444.2.t.a	$444$	$2$	444.t	444.t	$6$	$144$	$72$	$3.545$		$_{}$	None	None		✓	✓	✓	444.2.t.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
444.2.u.a	$444$	$2$	444.u	37.f	$9$	$12$	$2$	$3.545$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			444.2.u.a	$2$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{3}-\beta _{4})q^{3}+(1-\beta _{9}+\beta _{11})q^{5}+\cdots$
444.2.u.b	$444$	$2$	444.u	37.f	$9$	$18$	$3$	$3.545$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓		444.2.u.b	$2$	$0$	$0$	$0$	$3$	$3$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{8}q^{3}-\beta _{11}q^{5}+(-\beta _{5}+\beta _{6})q^{7}+\cdots$
444.2.w.a	$444$	$2$	444.w	111.m	$12$	$4$	$1$	$3.545$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			444.2.w.a	$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-1-\zeta_{12}^{2})q^{3}+(-\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots$
444.2.w.b	$444$	$2$	444.w	111.m	$12$	$4$	$1$	$3.545$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			444.2.w.b	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(1+\zeta_{12}^{2})q^{3}+(-3\zeta_{12}+6\zeta_{12}^{3})q^{7}+\cdots$
444.2.w.c	$444$	$2$	444.w	111.m	$12$	$40$	$10$	$3.545$		$_{}$	None	None		✓	✓		444.2.w.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
444.2.y.a	$444$	$2$	444.y	148.l	$12$	$8$	$2$	$3.545$	8.0.3468738816.6	$_{}$	None	None		✓			444.2.y.a	$2$	$0$	$-4$	$-4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\beta _{4}-\beta _{6})q^{2}+\beta _{6}q^{3}+(2\beta _{2}+\cdots)q^{4}+\cdots$
444.2.y.b	$444$	$2$	444.y	148.l	$12$	$8$	$2$	$3.545$	8.0.3468738816.6	$_{}$	None	None		✓			444.2.y.a	$2$	$0$	$-4$	$4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{2}+\beta _{4}+\beta _{6})q^{2}+(1+\beta _{6})q^{3}+\cdots$
444.2.y.c	$444$	$2$	444.y	148.l	$12$	$68$	$17$	$3.545$		$_{}$	None	None		✓			444.2.y.c	$2$	$0$	$6$	$-34$	$-4$	$-12$			$\mathrm{SU}(2)[C_{12}]$
444.2.y.d	$444$	$2$	444.y	148.l	$12$	$68$	$17$	$3.545$		$_{}$	None	None		✓			444.2.y.c	$2$	$0$	$6$	$34$	$-4$	$12$			$\mathrm{SU}(2)[C_{12}]$
444.2.z.a	$444$	$2$	444.z	444.z	$18$	$432$	$72$	$3.545$		$_{}$	None	None		✓	✓	✓	444.2.z.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
444.2.ba.a	$444$	$2$	444.ba	444.aa	$18$	$432$	$72$	$3.545$		$_{}$	None	None		✓	✓	✓	444.2.ba.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
444.2.bb.a	$444$	$2$	444.bb	37.h	$18$	$18$	$3$	$3.545$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			444.2.bb.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\beta _{1}-\beta _{5})q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$
444.2.bb.b	$444$	$2$	444.bb	37.h	$18$	$24$	$4$	$3.545$		$_{}$	None	None		✓	✓		444.2.bb.b	$2$	$0$	$0$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{18}]$
444.2.bg.a	$444$	$2$	444.bg	111.q	$36$	$12$	$1$	$3.545$	$\Q(\zeta_{36})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			444.2.bg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{36}]$	$q+(-\zeta_{36}^{4}+2\zeta_{36}^{10})q^{3}+(-\zeta_{36}^{3}+\cdots)q^{7}+\cdots$

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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.