LMFDB - Newform search results

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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 135 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
190.2.a.a	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	$\Q$	None	✓	✓	✓	✓	190.2.a.a	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
190.2.a.b	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	$\Q$	None	✓	✓	✓	✓	190.2.a.b	$1$	$1$	$1$	$-3$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots$
190.2.a.c	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	$\Q$	None	✓	✓	✓	✓	190.2.a.c	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
190.2.a.d	$190$	$2$	190.a	1.a	$1$	$2$	$2$	$1.517$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	190.2.a.d	$1$	$0$	$-2$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots$
190.2.b.a	$190$	$2$	190.b	5.b	$2$	$4$	$4$	$1.517$	$\Q(\zeta_{8})$	None		✓			190.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
190.2.b.b	$190$	$2$	190.b	5.b	$2$	$6$	$6$	$1.517$	6.0.5161984.1	None		✓	✓		190.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
190.2.e.a	$190$	$2$	190.e	19.c	$3$	$2$	$1$	$1.517$	$\Q(\sqrt{-3}) $	None		✓			190.2.e.a	$2$	$0$	$-1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
190.2.e.b	$190$	$2$	190.e	19.c	$3$	$2$	$1$	$1.517$	$\Q(\sqrt{-3}) $	None		✓			190.2.e.b	$2$	$0$	$1$	$1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
190.2.e.c	$190$	$2$	190.e	19.c	$3$	$4$	$2$	$1.517$	$\Q(\sqrt{-3}, \sqrt{17})$	None		✓	✓		190.2.e.c	$2$	$0$	$2$	$1$	$-2$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
190.2.f.a	$190$	$2$	190.f	95.g	$4$	$4$	$2$	$1.517$	$\Q(\zeta_{8})$	None		✓			190.2.f.a	$4$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots$
190.2.f.b	$190$	$2$	190.f	95.g	$4$	$16$	$8$	$1.517$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		190.2.f.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots$
190.2.i.a	$190$	$2$	190.i	95.i	$6$	$20$	$10$	$1.517$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	190.2.i.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
190.2.k.a	$190$	$2$	190.k	19.e	$9$	$6$	$1$	$1.517$	$\Q(\zeta_{18})$	None		✓			190.2.k.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
190.2.k.b	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			190.2.k.b	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
190.2.k.c	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			190.2.k.c	$2$	$0$	$0$	$3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots$
190.2.k.d	$190$	$2$	190.k	19.e	$9$	$18$	$3$	$1.517$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		190.2.k.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots$
190.2.m.a	$190$	$2$	190.m	95.l	$12$	$8$	$2$	$1.517$	$\Q(\zeta_{24})$	None		✓			190.2.m.a	$4$	$0$	$0$	$12$	$4$	$-16$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
190.2.m.b	$190$	$2$	190.m	95.l	$12$	$32$	$8$	$1.517$		None		✓	✓		190.2.m.b	$4$	$0$	$0$	$-12$	$0$	$24$			$\mathrm{SU}(2)[C_{12}]$
190.2.p.a	$190$	$2$	190.p	95.p	$18$	$60$	$10$	$1.517$		None		✓	✓	✓	190.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
190.2.r.a	$190$	$2$	190.r	95.r	$36$	$120$	$10$	$1.517$		None		✓	✓	✓	190.2.r.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{36}]$
190.3.c.a	$190$	$3$	190.c	19.b	$2$	$16$	$16$	$5.177$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	190.3.c.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots$
190.3.d.a	$190$	$3$	190.d	95.d	$2$	$20$	$20$	$5.177$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	190.3.d.a	$4$	$0$	$0$	$0$	$-2$	$0$		$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots$
190.3.g.a	$190$	$3$	190.g	5.c	$4$	$16$	$8$	$5.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			190.3.g.a	$2$	$0$	$-16$	$8$	$2$	$-10$		$2^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots$
190.3.g.b	$190$	$3$	190.g	5.c	$4$	$20$	$10$	$5.177$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		190.3.g.b	$2$	$0$	$20$	$0$	$2$	$14$		$2^{14}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots$
190.3.h.a	$190$	$3$	190.h	95.h	$6$	$4$	$2$	$5.177$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			190.3.h.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
190.3.h.b	$190$	$3$	190.h	95.h	$6$	$36$	$18$	$5.177$		None		✓	✓		190.3.h.b	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
190.3.j.a	$190$	$3$	190.j	19.d	$6$	$32$	$16$	$5.177$		None		✓	✓	✓	190.3.j.a	$2$	$0$	$0$	$-12$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$
190.3.l.a	$190$	$3$	190.l	95.m	$12$	$4$	$1$	$5.177$	$\Q(\zeta_{12})$	None		✓			190.3.l.a	$4$	$0$	$-2$	$-6$	$8$	$32$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots$
190.3.l.b	$190$	$3$	190.l	95.m	$12$	$4$	$1$	$5.177$	$\Q(\zeta_{12})$	None		✓			190.3.l.b	$4$	$0$	$2$	$6$	$10$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots$
190.3.l.c	$190$	$3$	190.l	95.m	$12$	$36$	$9$	$5.177$		None		✓			190.3.l.c	$4$	$0$	$-18$	$6$	$-10$	$-28$			$\mathrm{SU}(2)[C_{12}]$
190.3.l.d	$190$	$3$	190.l	95.m	$12$	$36$	$9$	$5.177$		None		✓			190.3.l.d	$4$	$0$	$18$	$-6$	$-12$	$12$			$\mathrm{SU}(2)[C_{12}]$
190.3.n.a	$190$	$3$	190.n	19.f	$18$	$72$	$12$	$5.177$		None		✓	✓	✓	190.3.n.a	$2$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
190.3.o.a	$190$	$3$	190.o	95.o	$18$	$120$	$20$	$5.177$		None		✓	✓	✓	190.3.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
190.3.q.a	$190$	$3$	190.q	95.q	$36$	$120$	$10$	$5.177$		None		✓			190.3.q.a	$4$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{36}]$
190.3.q.b	$190$	$3$	190.q	95.q	$36$	$120$	$10$	$5.177$		None		✓			190.3.q.b	$4$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{36}]$
190.4.a.a	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	$\Q$	None	✓	✓			190.4.a.a	$1$	$0$	$-2$	$-2$	$5$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots$
190.4.a.b	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	$\Q$	None	✓	✓	✓	✓	190.4.a.b	$1$	$1$	$-2$	$2$	$5$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots$
190.4.a.c	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	$\Q$	None	✓	✓	✓	✓	190.4.a.c	$1$	$1$	$2$	$-4$	$5$	$-20$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots$
190.4.a.d	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	$\Q(\sqrt{313}) $	None	✓	✓	✓		190.4.a.d	$1$	$0$	$-4$	$1$	$10$	$-27$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots$
190.4.a.e	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	190.4.a.e	$1$	$0$	$-4$	$2$	$-10$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots$
190.4.a.f	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	$\Q(\sqrt{34}) $	None	✓	✓	✓	✓	190.4.a.f	$1$	$0$	$4$	$0$	$-10$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots$
190.4.a.g	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.126168.1	None	✓	✓	✓	✓	190.4.a.g	$1$	$1$	$-6$	$-1$	$-15$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots$
190.4.a.h	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.5468.1	None	✓	✓	✓	✓	190.4.a.h	$1$	$1$	$6$	$-9$	$-15$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
190.4.a.i	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.15357.1	None	✓	✓	✓	✓	190.4.a.i	$1$	$0$	$6$	$11$	$15$	$29$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$
190.4.b.a	$190$	$4$	190.b	5.b	$2$	$12$	$12$	$11.210$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			190.4.b.a	$2$	$0$	$0$	$0$	$20$	$0$		$2^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots$
190.4.b.b	$190$	$4$	190.b	5.b	$2$	$14$	$14$	$11.210$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓		190.4.b.b	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{8}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
190.4.e.a	$190$	$4$	190.e	19.c	$3$	$2$	$1$	$11.210$	$\Q(\sqrt{-3}) $	None		✓			190.4.e.a	$2$	$0$	$2$	$2$	$-5$	$-56$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
190.4.e.b	$190$	$4$	190.e	19.c	$3$	$2$	$1$	$11.210$	$\Q(\sqrt{-3}) $	None		✓			190.4.e.b	$2$	$0$	$2$	$2$	$5$	$64$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
190.4.e.c	$190$	$4$	190.e	19.c	$3$	$6$	$3$	$11.210$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓			190.4.e.c	$2$	$0$	$6$	$3$	$-15$	$36$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots$
190.4.e.d	$190$	$4$	190.e	19.c	$3$	$8$	$4$	$11.210$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			190.4.e.d	$2$	$0$	$8$	$3$	$20$	$-82$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$

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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.