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 55 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
1449.1.c.a	$1449$	$1$	1449.c	483.c	$2$	$4$	$4$	$0.723$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1449.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+\zeta_{8}^{2}q^{7}+\cdots$
1449.1.bq.a	$1449$	$1$	1449.bq	161.l	$22$	$10$	$1$	$0.723$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None					161.1.l.a	$4$	$0$	$2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{22}^{3}-\zeta_{22}^{10})q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{6}+\cdots)q^{4}+\cdots$
1449.1.bq.b	$1449$	$1$	1449.bq	161.l	$22$	$20$	$2$	$0.723$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		✓	✓		1449.1.bq.b	$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(-\zeta_{44}^{5}-\zeta_{44}^{7})q^{2}+(\zeta_{44}^{10}+\zeta_{44}^{12}+\cdots)q^{4}+\cdots$
1449.1.bu.a	$1449$	$1$	1449.bu	483.w	$22$	$40$	$4$	$0.723$	$\Q(\zeta_{88})$	$D_{44}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1449.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{88}^{5}-\zeta_{88}^{7})q^{2}+(\zeta_{88}^{10}+\zeta_{88}^{12}+\cdots)q^{4}+\cdots$
1449.2.a.a	$1449$	$2$	1449.a	1.a	$1$	$1$	$1$	$11.570$	$\Q$	$_{}$	None	None	✓				483.2.a.b	$1$	$1$	$-2$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots$
1449.2.a.b	$1449$	$2$	1449.a	1.a	$1$	$1$	$1$	$11.570$	$\Q$	$_{}$	None	None	✓	✓			1449.2.a.b	$1$	$1$	$-2$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots$
1449.2.a.c	$1449$	$2$	1449.a	1.a	$1$	$1$	$1$	$11.570$	$\Q$	$_{}$	None	None	✓				483.2.a.a	$1$	$1$	$-2$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}-q^{11}+2q^{13}+\cdots$
1449.2.a.d	$1449$	$2$	1449.a	1.a	$1$	$1$	$1$	$11.570$	$\Q$	$_{}$	None	None	✓				161.2.a.a	$1$	$0$	$1$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots$
1449.2.a.e	$1449$	$2$	1449.a	1.a	$1$	$1$	$1$	$11.570$	$\Q$	$_{}$	None	None	✓	✓			1449.2.a.b	$1$	$0$	$2$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots$
1449.2.a.f	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				483.2.a.g	$1$	$1$	$-1$	$0$	$3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots$
1449.2.a.g	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				483.2.a.e	$1$	$1$	$1$	$0$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots$
1449.2.a.h	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				483.2.a.d	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
1449.2.a.i	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				161.2.a.b	$1$	$1$	$1$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
1449.2.a.j	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				483.2.a.f	$1$	$0$	$1$	$0$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}-q^{7}+\cdots$
1449.2.a.k	$1449$	$2$	1449.a	1.a	$1$	$2$	$2$	$11.570$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				483.2.a.c	$1$	$0$	$3$	$0$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(2+\beta )q^{5}+q^{7}+\cdots$
1449.2.a.l	$1449$	$2$	1449.a	1.a	$1$	$3$	$3$	$11.570$	3.3.837.1	$_{}$	None	None	✓		✓		483.2.a.h	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots$
1449.2.a.m	$1449$	$2$	1449.a	1.a	$1$	$3$	$3$	$11.570$	3.3.148.1	$_{}$	None	None	✓				161.2.a.c	$1$	$0$	$1$	$0$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(1+2\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
1449.2.a.n	$1449$	$2$	1449.a	1.a	$1$	$4$	$4$	$11.570$	4.4.2624.1	$_{}$	None	None	✓	✓	✓		1449.2.a.n	$1$	$1$	$-2$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1449.2.a.o	$1449$	$2$	1449.a	1.a	$1$	$4$	$4$	$11.570$	4.4.15317.1	$_{}$	None	None	✓		✓		483.2.a.j	$1$	$0$	$-2$	$0$	$-5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$
1449.2.a.p	$1449$	$2$	1449.a	1.a	$1$	$4$	$4$	$11.570$	4.4.24197.1	$_{}$	None	None	✓				483.2.a.i	$1$	$0$	$0$	$0$	$-5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
1449.2.a.q	$1449$	$2$	1449.a	1.a	$1$	$4$	$4$	$11.570$	4.4.2624.1	$_{}$	None	None	✓	✓	✓		1449.2.a.n	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1449.2.a.r	$1449$	$2$	1449.a	1.a	$1$	$5$	$5$	$11.570$	5.5.2147108.1	$_{}$	None	None	✓		✓		161.2.a.d	$1$	$0$	$-2$	$0$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
1449.2.a.s	$1449$	$2$	1449.a	1.a	$1$	$5$	$5$	$11.570$	5.5.1337792.1	$_{}$	None	None	✓	✓	✓	✓	1449.2.a.s	$1$	$1$	$0$	$0$	$-4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
1449.2.a.t	$1449$	$2$	1449.a	1.a	$1$	$5$	$5$	$11.570$	5.5.1337792.1	$_{}$	None	None	✓	✓	✓	✓	1449.2.a.s	$1$	$0$	$0$	$0$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
1449.2.d.a	$1449$	$2$	1449.d	21.c	$2$	$56$	$56$	$11.570$		$_{}$	None	None		✓	✓	✓	1449.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1449.2.e.a	$1449$	$2$	1449.e	69.c	$2$	$48$	$48$	$11.570$		$_{}$	None	None		✓	✓	✓	1449.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1449.2.h.a	$1449$	$2$	1449.h	161.c	$2$	$2$	$2$	$11.570$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None					161.2.c.a	$4$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+q^{2}-q^{4}+\beta q^{7}-3q^{8}-2\beta q^{11}+\cdots$
1449.2.h.b	$1449$	$2$	1449.h	161.c	$2$	$4$	$4$	$11.570$	$\Q(\sqrt{7}, \sqrt{-23})$	$_{}$	$\Q(\sqrt{-483}) $	None		✓			1449.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{1}q^{7}-\beta _{3}q^{11}+4q^{16}+\cdots$
1449.2.h.c	$1449$	$2$	1449.h	161.c	$2$	$4$	$4$	$11.570$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			1449.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+5q^{4}+\beta _{3}q^{7}-3\beta _{2}q^{8}+\cdots$
1449.2.h.d	$1449$	$2$	1449.h	161.c	$2$	$8$	$8$	$11.570$	8.0.342102016.5	$_{}$	None	None					483.2.h.a	$4$	$0$	$8$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
1449.2.h.e	$1449$	$2$	1449.h	161.c	$2$	$12$	$12$	$11.570$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					483.2.h.c	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1449.2.h.f	$1449$	$2$	1449.h	161.c	$2$	$12$	$12$	$11.570$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1449.2.h.f	$4$	$0$	$0$	$0$	$-20$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1-\beta _{2})q^{4}+(-2+\beta _{7})q^{5}+\cdots$
1449.2.h.g	$1449$	$2$	1449.h	161.c	$2$	$12$	$12$	$11.570$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					161.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\cdots$
1449.2.h.h	$1449$	$2$	1449.h	161.c	$2$	$12$	$12$	$11.570$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					483.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(1-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1449.2.h.i	$1449$	$2$	1449.h	161.c	$2$	$12$	$12$	$11.570$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1449.2.h.f	$4$	$0$	$0$	$0$	$20$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1-\beta _{2})q^{4}+(2-\beta _{7})q^{5}+\cdots$
1449.3.b.a	$1449$	$3$	1449.b	3.b	$2$	$88$	$88$	$39.482$		$_{}$	None	None		✓	✓	✓	1449.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1449.4.a.a	$1449$	$4$	1449.a	1.a	$1$	$1$	$1$	$85.494$	$\Q$	$_{}$	None	None	✓	✓			1449.4.a.a	$1$	$1$	$-3$	$0$	$-3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+q^{4}-3q^{5}+7q^{7}+21q^{8}+\cdots$
1449.4.a.b	$1449$	$4$	1449.a	1.a	$1$	$1$	$1$	$85.494$	$\Q$	$_{}$	None	None	✓	✓			1449.4.a.a	$1$	$0$	$3$	$0$	$3$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}+3q^{5}+7q^{7}-21q^{8}+\cdots$
1449.4.a.c	$1449$	$4$	1449.a	1.a	$1$	$3$	$3$	$85.494$	3.3.3877.1	$_{}$	None	None	✓				483.4.a.a	$1$	$0$	$4$	$0$	$-2$	$-21$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(1+4\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1449.4.a.d	$1449$	$4$	1449.a	1.a	$1$	$4$	$4$	$85.494$	4.4.8184789.1	$_{}$	None	None	✓				483.4.a.b	$1$	$0$	$-2$	$0$	$23$	$-28$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(3+\beta _{1})q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots$
1449.4.a.e	$1449$	$4$	1449.a	1.a	$1$	$5$	$5$	$85.494$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				161.4.a.a	$1$	$1$	$4$	$0$	$4$	$35$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(1+\beta _{2}-\beta _{4})q^{5}+\cdots$
1449.4.a.f	$1449$	$4$	1449.a	1.a	$1$	$7$	$7$	$85.494$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				483.4.a.e	$1$	$1$	$-2$	$0$	$11$	$49$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(1+2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$
1449.4.a.g	$1449$	$4$	1449.a	1.a	$1$	$7$	$7$	$85.494$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				483.4.a.d	$1$	$1$	$2$	$0$	$11$	$-49$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{4}+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots$
1449.4.a.h	$1449$	$4$	1449.a	1.a	$1$	$7$	$7$	$85.494$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				483.4.a.c	$1$	$0$	$6$	$0$	$41$	$49$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+(6+\cdots)q^{5}+\cdots$
1449.4.a.i	$1449$	$4$	1449.a	1.a	$1$	$8$	$8$	$85.494$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				161.4.a.b	$1$	$1$	$0$	$0$	$24$	$-56$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{3}-\beta _{4})q^{4}+(3+\cdots)q^{5}+\cdots$
1449.4.a.j	$1449$	$4$	1449.a	1.a	$1$	$9$	$9$	$85.494$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓		✓		483.4.a.i	$1$	$1$	$-8$	$0$	$-39$	$63$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(4-2\beta _{1}+\beta _{2})q^{4}+\cdots$
1449.4.a.k	$1449$	$4$	1449.a	1.a	$1$	$9$	$9$	$85.494$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓		✓		483.4.a.h	$1$	$1$	$-4$	$0$	$-39$	$-63$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(-4-\beta _{4})q^{5}+\cdots$
1449.4.a.l	$1449$	$4$	1449.a	1.a	$1$	$9$	$9$	$85.494$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓				483.4.a.g	$1$	$0$	$-4$	$0$	$-9$	$-63$	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$
1449.4.a.m	$1449$	$4$	1449.a	1.a	$1$	$9$	$9$	$85.494$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓				483.4.a.f	$1$	$0$	$0$	$0$	$-29$	$63$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-3-\beta _{7})q^{5}+\cdots$
1449.4.a.n	$1449$	$4$	1449.a	1.a	$1$	$9$	$9$	$85.494$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓				161.4.a.c	$1$	$0$	$0$	$0$	$4$	$-63$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(5+\beta _{1}+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$

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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.