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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 98 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
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		✓	✓	✓	148.1.f.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+i q^{3}-q^{7}-i q^{11}+(-i-1)q^{17}+\cdots$
148.1.i.a	$148$	$1$	148.i	148.i	$6$	$2$	$1$	$0.074$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	148.1.i.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
148.1.p.a	$148$	$1$	148.p	148.p	$18$	$6$	$1$	$0.074$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	148.1.p.a	$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
148.2.a.a	$148$	$2$	148.a	1.a	$1$	$1$	$1$	$1.182$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	148.2.a.a	$1$	$1$	$0$	$-1$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots$
148.2.a.b	$148$	$2$	148.a	1.a	$1$	$2$	$2$	$1.182$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	148.2.a.b	$1$	$0$	$0$	$-1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{5}+\beta q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots$
148.2.d.a	$148$	$2$	148.d	37.b	$2$	$2$	$2$	$1.182$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	148.2.d.a	$2$	$0$	$0$	$2$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+q^{7}-2 q^{9}+3 q^{11}+\cdots$
148.2.e.a	$148$	$2$	148.e	37.c	$3$	$6$	$3$	$1.182$	6.0.27870912.1	$_{}$	None	None		✓	✓	✓	148.2.e.a	$2$	$0$	$0$	$-1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{5})q^{7}+\cdots$
148.2.g.a	$148$	$2$	148.g	148.g	$4$	$2$	$1$	$1.182$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.2.g.a	$4$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(-3 i+3)q^{5}+\cdots$
148.2.g.b	$148$	$2$	148.g	148.g	$4$	$4$	$2$	$1.182$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			148.2.g.b	$4$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots$
148.2.g.c	$148$	$2$	148.g	148.g	$4$	$28$	$14$	$1.182$		$_{}$	None	None		✓	✓		148.2.g.c	$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
148.2.h.a	$148$	$2$	148.h	37.e	$6$	$2$	$1$	$1.182$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			148.2.h.a	$2$	$0$	$0$	$-1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{3}+(2-\zeta_{6})q^{5}-\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots$
148.2.h.b	$148$	$2$	148.h	37.e	$6$	$2$	$1$	$1.182$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			148.2.h.b	$2$	$0$	$0$	$2$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}+2\zeta_{6}q^{7}+\cdots$
148.2.k.a	$148$	$2$	148.k	37.f	$9$	$24$	$4$	$1.182$		$_{}$	None	None		✓	✓	✓	148.2.k.a	$2$	$0$	$0$	$3$	$-3$	$-9$			$\mathrm{SU}(2)[C_{9}]$
148.2.l.a	$148$	$2$	148.l	148.l	$12$	$4$	$1$	$1.182$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.2.l.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
148.2.l.b	$148$	$2$	148.l	148.l	$12$	$64$	$16$	$1.182$		$_{}$	None	None		✓	✓		148.2.l.b	$4$	$0$	$-4$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{12}]$
148.2.n.a	$148$	$2$	148.n	37.h	$18$	$6$	$1$	$1.182$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			148.2.n.a	$2$	$0$	$0$	$9$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots$
148.2.n.b	$148$	$2$	148.n	37.h	$18$	$12$	$2$	$1.182$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		148.2.n.b	$2$	$0$	$0$	$-12$	$0$	$6$		$3^{2}$	$\mathrm{SU}(2)[C_{18}]$	$q+(-1-\beta _{9})q^{3}+(-\beta _{5}-\beta _{8})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
148.2.q.a	$148$	$2$	148.q	148.q	$36$	$12$	$1$	$1.182$	$\Q(\zeta_{36})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.2.q.a	$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{36}]$	$q+(\zeta_{36}^{2}+\zeta_{36}^{5}-\zeta_{36}^{8})q^{2}+2\zeta_{36}q^{4}+\cdots$
148.2.q.b	$148$	$2$	148.q	148.q	$36$	$192$	$16$	$1.182$		$_{}$	None	None		✓	✓		148.2.q.b	$4$	$0$	$-12$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{36}]$
148.3.b.a	$148$	$3$	148.b	148.b	$2$	$1$	$1$	$4.033$	$\Q$	$_{}$	$\Q(\sqrt{-37}) $	None	✓	✓			148.3.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+2^{4}q^{16}+\cdots$
148.3.b.b	$148$	$3$	148.b	148.b	$2$	$1$	$1$	$4.033$	$\Q$	$_{}$	$\Q(\sqrt{-37}) $	None	✓	✓			148.3.b.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+8q^{8}+9q^{9}+2^{4}q^{16}+\cdots$
148.3.b.c	$148$	$3$	148.b	148.b	$2$	$2$	$2$	$4.033$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-4 q^{4}-4\beta q^{5}-4\beta q^{8}+\cdots$
148.3.b.d	$148$	$3$	148.b	148.b	$2$	$32$	$32$	$4.033$		$_{}$	None	None		✓	✓		148.3.b.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
148.3.c.a	$148$	$3$	148.c	4.b	$2$	$36$	$36$	$4.033$		$_{}$	None	None		✓	✓	✓	148.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
148.3.f.a	$148$	$3$	148.f	37.d	$4$	$14$	$7$	$4.033$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓	✓	148.3.f.a	$2$	$0$	$0$	$0$	$12$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(1-\beta _{4}-\beta _{8})q^{5}-\beta _{5}q^{7}+\cdots$
148.3.i.a	$148$	$3$	148.i	148.i	$6$	$72$	$36$	$4.033$		$_{}$	None	None		✓	✓	✓	148.3.i.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
148.3.j.a	$148$	$3$	148.j	148.j	$6$	$4$	$2$	$4.033$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.3.j.a	$4$	$0$	$0$	$0$	$-18$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+\beta_1 q^{2}+4\beta_{2} q^{4}+(2\beta_{3}+3\beta_{2}-2\beta_1-6)q^{5}+\cdots$
148.3.j.b	$148$	$3$	148.j	148.j	$6$	$68$	$34$	$4.033$		$_{}$	None	None		✓	✓		148.3.j.b	$4$	$0$	$-6$	$0$	$18$	$0$			$\mathrm{SU}(2)[C_{6}]$
148.3.m.a	$148$	$3$	148.m	37.g	$12$	$28$	$7$	$4.033$		$_{}$	None	None		✓	✓	✓	148.3.m.a	$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{12}]$
148.3.o.a	$148$	$3$	148.o	148.o	$18$	$12$	$2$	$4.033$	$\Q(\zeta_{36})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.3.o.a	$4$	$0$	$0$	$0$	$18$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{18}]$	$q+\beta_1 q^{2}+4\beta_{2} q^{4}+(2\beta_{9}-2\beta_{7}+\cdots+2\beta_1)q^{5}+\cdots$
148.3.o.b	$148$	$3$	148.o	148.o	$18$	$204$	$34$	$4.033$		$_{}$	None	None		✓	✓		148.3.o.b	$4$	$0$	$-3$	$0$	$-36$	$0$			$\mathrm{SU}(2)[C_{18}]$
148.3.p.a	$148$	$3$	148.p	148.p	$18$	$216$	$36$	$4.033$		$_{}$	None	None		✓	✓	✓	148.3.p.a	$4$	$0$	$-9$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{18}]$
148.3.r.a	$148$	$3$	148.r	37.i	$36$	$72$	$6$	$4.033$		$_{}$	None	None		✓	✓	✓	148.3.r.a	$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{36}]$
148.4.a.a	$148$	$4$	148.a	1.a	$1$	$4$	$4$	$8.732$	4.4.1264493.1	$_{}$	None	None	✓	✓	✓	✓	148.4.a.a	$1$	$1$	$0$	$-1$	$-19$	$-6$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-5-\beta _{1}+2\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
148.4.a.b	$148$	$4$	148.a	1.a	$1$	$5$	$5$	$8.732$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	148.4.a.b	$1$	$0$	$0$	$-1$	$21$	$22$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(4-\beta _{1}+\beta _{3})q^{5}+(5-2\beta _{1}+\cdots)q^{7}+\cdots$
148.4.d.a	$148$	$4$	148.d	37.b	$2$	$2$	$2$	$8.732$	$\Q(\sqrt{-7}) $	$_{}$	None	None		✓			148.4.d.a	$2$	$0$	$0$	$-10$	$0$	$-18$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-5q^{3}-\beta q^{5}-9q^{7}-2q^{9}+57q^{11}+\cdots$
148.4.d.b	$148$	$4$	148.d	37.b	$2$	$8$	$8$	$8.732$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		148.4.d.b	$2$	$0$	$0$	$0$	$0$	$2$		$2^{3}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{5}q^{5}+(\beta _{2}-\beta _{3}+\beta _{4})q^{7}+\cdots$
148.4.e.a	$148$	$4$	148.e	37.c	$3$	$18$	$9$	$8.732$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	148.4.e.a	$2$	$0$	$0$	$8$	$13$	$8$		$2^{22}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{4})q^{3}+(\beta _{4}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
148.4.g.a	$148$	$4$	148.g	148.g	$4$	$2$	$1$	$8.732$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.4.g.a	$4$	$0$	$-4$	$0$	$-18$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2 i-2)q^{2}+8 i q^{4}+(9 i-9)q^{5}+\cdots$
148.4.g.b	$148$	$4$	148.g	148.g	$4$	$108$	$54$	$8.732$		$_{}$	None	None		✓	✓		148.4.g.b	$4$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{4}]$
148.4.h.a	$148$	$4$	148.h	37.e	$6$	$20$	$10$	$8.732$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	148.4.h.a	$2$	$0$	$0$	$4$	$-18$	$-8$		$2^{24}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{8}q^{3}+(\beta _{3}+\beta _{7})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots$
148.4.k.a	$148$	$4$	148.k	37.f	$9$	$54$	$9$	$8.732$		$_{}$	None	None		✓	✓	✓	148.4.k.a	$2$	$0$	$0$	$-6$	$-15$	$48$			$\mathrm{SU}(2)[C_{9}]$
148.4.l.a	$148$	$4$	148.l	148.l	$12$	$4$	$1$	$8.732$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.4.l.a	$4$	$0$	$4$	$0$	$-48$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+8\zeta_{12}q^{4}+\cdots$
148.4.l.b	$148$	$4$	148.l	148.l	$12$	$216$	$54$	$8.732$		$_{}$	None	None		✓	✓		148.4.l.b	$4$	$0$	$-6$	$0$	$36$	$0$			$\mathrm{SU}(2)[C_{12}]$
148.4.n.a	$148$	$4$	148.n	37.h	$18$	$60$	$10$	$8.732$		$_{}$	None	None		✓	✓	✓	148.4.n.a	$2$	$0$	$0$	$6$	$18$	$-48$			$\mathrm{SU}(2)[C_{18}]$
148.4.q.a	$148$	$4$	148.q	148.q	$36$	$12$	$1$	$8.732$	$\Q(\zeta_{36})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			148.4.q.a	$4$	$0$	$0$	$0$	$66$	$0$		$1$	$\mathrm{U}(1)[D_{36}]$	$q+(-2\zeta_{36}^{2}-2\zeta_{36}^{5}+2\zeta_{36}^{8})q^{2}+\cdots$
148.4.q.b	$148$	$4$	148.q	148.q	$36$	$648$	$54$	$8.732$		$_{}$	None	None		✓	✓		148.4.q.b	$4$	$0$	$-12$	$0$	$-84$	$0$			$\mathrm{SU}(2)[C_{36}]$
148.5.b.a	$148$	$5$	148.b	148.b	$2$	$1$	$1$	$15.299$	$\Q$	$_{}$	$\Q(\sqrt{-37}) $	None	✓	✓			148.5.b.a	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+3^{4}q^{9}+2^{8}q^{16}+\cdots$
148.5.b.b	$148$	$5$	148.b	148.b	$2$	$1$	$1$	$15.299$	$\Q$	$_{}$	$\Q(\sqrt{-37}) $	None	✓	✓			148.5.b.a	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+2^{8}q^{16}+\cdots$
148.5.b.c	$148$	$5$	148.b	148.b	$2$	$72$	$72$	$15.299$		$_{}$	None	None		✓	✓		148.5.b.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.