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 96 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
680.1.k.a	$680$	$1$	680.k	680.k	$2$	$1$	$1$	$0.339$	$\Q$	$D_{3}$	$\Q(\sqrt{-170}) $	None	✓	✓			680.1.k.a	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
680.1.k.b	$680$	$1$	680.k	680.k	$2$	$1$	$1$	$0.339$	$\Q$	$D_{3}$	$\Q(\sqrt{-170}) $	None	✓	✓			680.1.k.a	$2$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
680.1.k.c	$680$	$1$	680.k	680.k	$2$	$1$	$1$	$0.339$	$\Q$	$D_{3}$	$\Q(\sqrt{-170}) $	None	✓	✓			680.1.k.a	$2$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
680.1.k.d	$680$	$1$	680.k	680.k	$2$	$1$	$1$	$0.339$	$\Q$	$D_{3}$	$\Q(\sqrt{-170}) $	None	✓	✓			680.1.k.a	$2$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
680.1.k.e	$680$	$1$	680.k	680.k	$2$	$4$	$4$	$0.339$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-34}) $	None		✓	✓		680.1.k.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
680.2.a.a	$680$	$2$	680.a	1.a	$1$	$1$	$1$	$5.430$	$\Q$	$_{}$	None	None	✓	✓			680.2.a.a	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
680.2.a.b	$680$	$2$	680.a	1.a	$1$	$1$	$1$	$5.430$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	680.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-2q^{13}+q^{17}-4q^{19}+\cdots$
680.2.a.c	$680$	$2$	680.a	1.a	$1$	$1$	$1$	$5.430$	$\Q$	$_{}$	None	None	✓	✓			680.2.a.c	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
680.2.a.d	$680$	$2$	680.a	1.a	$1$	$2$	$2$	$5.430$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	680.2.a.d	$1$	$1$	$0$	$-2$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(-3-\beta )q^{7}+\cdots$
680.2.a.e	$680$	$2$	680.a	1.a	$1$	$2$	$2$	$5.430$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	680.2.a.e	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}+(-2-3\beta )q^{11}+\cdots$
680.2.a.f	$680$	$2$	680.a	1.a	$1$	$3$	$3$	$5.430$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	680.2.a.f	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
680.2.a.g	$680$	$2$	680.a	1.a	$1$	$3$	$3$	$5.430$	3.3.1016.1	$_{}$	None	None	✓	✓	✓	✓	680.2.a.g	$1$	$0$	$0$	$1$	$-3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
680.2.a.h	$680$	$2$	680.a	1.a	$1$	$3$	$3$	$5.430$	3.3.940.1	$_{}$	None	None	✓	✓	✓	✓	680.2.a.h	$1$	$0$	$0$	$3$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
680.2.c.a	$680$	$2$	680.c	17.b	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-i q^{5}+4 i q^{7}+2 q^{9}-2 i q^{11}+\cdots$
680.2.c.b	$680$	$2$	680.c	17.b	$2$	$8$	$8$	$5.430$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			680.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
680.2.c.c	$680$	$2$	680.c	17.b	$2$	$8$	$8$	$5.430$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			680.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
680.2.e.a	$680$	$2$	680.e	5.b	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(2 i-1)q^{5}-4 i q^{7}+2 q^{9}+\cdots$
680.2.e.b	$680$	$2$	680.e	5.b	$2$	$10$	$10$	$5.430$	10.0.$\cdots$.1	$_{}$	None	None		✓			680.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+(-\beta _{3}-\beta _{8})q^{5}+(\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots$
680.2.e.c	$680$	$2$	680.e	5.b	$2$	$12$	$12$	$5.430$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		680.2.e.c	$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+\beta _{7}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
680.2.f.a	$680$	$2$	680.f	8.b	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.f.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}+i q^{3}+2 i q^{4}-i q^{5}+\cdots$
680.2.f.b	$680$	$2$	680.f	8.b	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.f.b	$2$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}-i q^{3}+2 i q^{4}+i q^{5}+\cdots$
680.2.f.c	$680$	$2$	680.f	8.b	$2$	$6$	$6$	$5.430$	6.0.399424.1	$_{}$	None	None		✓			680.2.f.c	$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
680.2.f.d	$680$	$2$	680.f	8.b	$2$	$24$	$24$	$5.430$		$_{}$	None	None		✓			680.2.f.d	$2$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.f.e	$680$	$2$	680.f	8.b	$2$	$30$	$30$	$5.430$		$_{}$	None	None		✓	✓		680.2.f.e	$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{2}]$
680.2.h.a	$680$	$2$	680.h	680.h	$2$	$16$	$16$	$5.430$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			680.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-1-\beta _{6})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
680.2.h.b	$680$	$2$	680.h	680.h	$2$	$40$	$40$	$5.430$		$_{}$	None	None		✓			680.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.h.c	$680$	$2$	680.h	680.h	$2$	$48$	$48$	$5.430$		$_{}$	None	None		✓	✓		680.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.j.a	$680$	$2$	680.j	40.f	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.j.a	$2$	$0$	$-2$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-1)q^{2}-q^{3}-2 i q^{4}+(-i-2)q^{5}+\cdots$
680.2.j.b	$680$	$2$	680.j	40.f	$2$	$2$	$2$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.j.a	$2$	$0$	$2$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}+q^{3}+2 i q^{4}+(i+2)q^{5}+\cdots$
680.2.j.c	$680$	$2$	680.j	40.f	$2$	$4$	$4$	$5.430$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			680.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots$
680.2.j.d	$680$	$2$	680.j	40.f	$2$	$4$	$4$	$5.430$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			680.2.j.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots$
680.2.j.e	$680$	$2$	680.j	40.f	$2$	$84$	$84$	$5.430$		$_{}$	None	None		✓	✓		680.2.j.e	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.l.a	$680$	$2$	680.l	136.h	$2$	$36$	$36$	$5.430$		$_{}$	None	None		✓			680.2.l.a	$2$	$0$	$0$	$-4$	$36$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.l.b	$680$	$2$	680.l	136.h	$2$	$36$	$36$	$5.430$		$_{}$	None	None		✓			680.2.l.a	$2$	$0$	$0$	$4$	$-36$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.o.a	$680$	$2$	680.o	85.c	$2$	$4$	$4$	$5.430$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			680.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2\zeta_{8}-2\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
680.2.o.b	$680$	$2$	680.o	85.c	$2$	$24$	$24$	$5.430$		$_{}$	None	None		✓	✓		680.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
680.2.t.a	$680$	$2$	680.t	680.t	$4$	$208$	$104$	$5.430$		$_{}$	None	None		✓	✓	✓	680.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
680.2.u.a	$680$	$2$	680.u	680.u	$4$	$8$	$4$	$5.430$	8.0.40960000.1	$_{}$	None	None		✓			680.2.u.a	$8$	$0$	$-8$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+2\beta _{3}q^{4}+\cdots$
680.2.u.b	$680$	$2$	680.u	680.u	$4$	$8$	$4$	$5.430$	8.0.$\cdots$.13	$_{}$	$\Q(\sqrt{-34}) $	None		✓			680.2.u.b	$8$	$0$	$-8$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots$
680.2.u.c	$680$	$2$	680.u	680.u	$4$	$8$	$4$	$5.430$	8.0.$\cdots$.13	$_{}$	$\Q(\sqrt{-34}) $	None		✓			680.2.u.c	$8$	$0$	$8$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
680.2.u.d	$680$	$2$	680.u	680.u	$4$	$184$	$92$	$5.430$		$_{}$	None	None		✓	✓		680.2.u.d	$8$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
680.2.z.a	$680$	$2$	680.z	85.j	$4$	$2$	$1$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.z.a	$2$	$0$	$0$	$-2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{3}+(-2 i+1)q^{5}+(-i-1)q^{7}+\cdots$
680.2.z.b	$680$	$2$	680.z	85.j	$4$	$2$	$1$	$5.430$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			680.2.z.a	$2$	$0$	$0$	$2$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{3}+(i-2)q^{5}+(i+1)q^{7}+\cdots$
680.2.z.c	$680$	$2$	680.z	85.j	$4$	$26$	$13$	$5.430$		$_{}$	None	None		✓			680.2.z.c	$2$	$0$	$0$	$-2$	$8$	$-2$			$\mathrm{SU}(2)[C_{4}]$
680.2.z.d	$680$	$2$	680.z	85.j	$4$	$26$	$13$	$5.430$		$_{}$	None	None		✓			680.2.z.c	$2$	$0$	$0$	$2$	$-2$	$2$			$\mathrm{SU}(2)[C_{4}]$
680.2.ba.a	$680$	$2$	680.ba	136.i	$4$	$4$	$2$	$5.430$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			680.2.ba.a	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
680.2.ba.b	$680$	$2$	680.ba	136.i	$4$	$140$	$70$	$5.430$		$_{}$	None	None		✓	✓		680.2.ba.b	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{4}]$
680.2.bd.a	$680$	$2$	680.bd	17.c	$4$	$16$	$8$	$5.430$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			680.2.bd.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}+\beta _{9}q^{5}+(-\beta _{10}+\beta _{13})q^{7}+\cdots$
680.2.bd.b	$680$	$2$	680.bd	17.c	$4$	$20$	$10$	$5.430$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		680.2.bd.b	$2$	$0$	$0$	$-4$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{3}-\beta _{4}q^{5}-\beta _{11}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots$
680.2.be.a	$680$	$2$	680.be	680.ae	$4$	$208$	$104$	$5.430$		$_{}$	None	None		✓	✓	✓	680.2.be.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.