LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 256 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
41.2.d.a	$41$	$2$	41.d	41.d	$5$	$8$	$2$	$0.327$	8.0.13140625.1	None		$2$	$0$	$-1$	$-6$	$3$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}-\beta _{7})q^{2}+(-1+\beta _{5})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
50.2.d.b	$50$	$2$	50.d	25.d	$5$	$8$	$2$	$0.399$	8.0.58140625.2	None		$2$	$0$	$-2$	$-3$	$0$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+\cdots$
55.2.g.a	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.159390625.1	None		$2$	$0$	$-4$	$1$	$-2$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
55.2.g.b	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.13140625.1	None		$2$	$0$	$-2$	$-5$	$2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
62.2.d.a	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.511890625.1	None		$2$	$0$	$-2$	$-4$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
62.2.d.b	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.1903140625.1	None		$2$	$0$	$2$	$-2$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
75.2.g.b	$75$	$2$	75.g	25.d	$5$	$8$	$2$	$0.599$	8.0.26265625.1	None		$2$	$0$	$-1$	$-2$	$-5$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
77.2.f.a	$77$	$2$	77.f	11.c	$5$	$8$	$2$	$0.615$	8.0.159390625.1	None		$2$	$0$	$-1$	$-4$	$3$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
11.4.c.a	$11$	$4$	11.c	11.c	$5$	$8$	$2$	$0.649$	8.0.$\cdots$.1	None		$2$	$0$	$-7$	$-3$	$-7$	$-35$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$
82.2.d.c	$82$	$2$	82.d	41.d	$5$	$8$	$2$	$0.655$	8.0.123765625.1	None		$2$	$0$	$-2$	$-10$	$-10$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-2-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots$
88.2.i.b	$88$	$2$	88.i	11.c	$5$	$8$	$2$	$0.703$	8.0.682515625.5	None		$2$	$0$	$0$	$-1$	$-3$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
93.2.f.a	$93$	$2$	93.f	31.d	$5$	$8$	$2$	$0.743$	$\Q(\zeta_{15})$	None		$2$	$0$	$3$	$2$	$-6$	$9$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{15}+\zeta_{15}^{3})q^{2}+(1+\zeta_{15}^{2}+\cdots)q^{3}+\cdots$
99.2.f.c	$99$	$2$	99.f	11.c	$5$	$8$	$2$	$0.791$	8.0.484000000.9	None		$4$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots$
110.2.g.c	$110$	$2$	110.g	11.c	$5$	$8$	$2$	$0.878$	8.0.682515625.5	None		$2$	$0$	$2$	$-4$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
142.2.c.b	$142$	$2$	142.c	71.c	$5$	$8$	$2$	$1.134$	8.0.159390625.1	None		$2$	$0$	$2$	$1$	$-5$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}-\beta _{2}q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
150.2.g.c	$150$	$2$	150.g	25.d	$5$	$8$	$2$	$1.198$	8.0.1064390625.3	None		$2$	$0$	$2$	$-2$	$-4$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
154.2.f.e	$154$	$2$	154.f	11.c	$5$	$8$	$2$	$1.230$	8.0.58140625.2	None		$2$	$0$	$2$	$-1$	$5$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots$
22.4.c.b	$22$	$4$	22.c	11.c	$5$	$8$	$2$	$1.298$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$4$	$3$	$5$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
165.2.m.a	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.13140625.1	None		$2$	$0$	$0$	$-2$	$2$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots$
165.2.m.b	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.819390625.1	None		$2$	$0$	$2$	$2$	$2$	$9$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
165.2.m.c	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	$\Q(\zeta_{15})$	None		$2$	$0$	$2$	$2$	$-2$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
165.2.m.d	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.13140625.1	None		$2$	$0$	$4$	$-2$	$-2$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots$
176.2.m.d	$176$	$2$	176.m	11.c	$5$	$8$	$2$	$1.405$	8.0.682515625.5	None		$2$	$0$	$0$	$1$	$-3$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
186.2.f.c	$186$	$2$	186.f	31.d	$5$	$8$	$2$	$1.485$	8.0.9240015625.1	None		$2$	$0$	$-2$	$2$	$2$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
187.2.g.d	$187$	$2$	187.g	11.c	$5$	$8$	$2$	$1.493$	8.0.324000000.3	None		$2$	$0$	$-4$	$6$	$4$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
187.2.g.e	$187$	$2$	187.g	11.c	$5$	$8$	$2$	$1.493$	8.0.13140625.1	None		$2$	$0$	$-1$	$3$	$-3$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{5})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
200.2.m.b	$200$	$2$	200.m	25.d	$5$	$8$	$2$	$1.597$	8.0.58140625.2	None		$2$	$0$	$0$	$-6$	$5$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
220.2.m.a	$220$	$2$	220.m	11.c	$5$	$8$	$2$	$1.757$	8.0.26265625.1	None		$2$	$0$	$0$	$-1$	$2$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
220.2.m.b	$220$	$2$	220.m	11.c	$5$	$8$	$2$	$1.757$	8.0.159390625.1	None		$2$	$0$	$0$	$5$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{3}+\beta _{4})q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
225.2.h.c	$225$	$2$	225.h	25.d	$5$	$8$	$2$	$1.797$	8.0.26265625.1	None		$2$	$0$	$1$	$0$	$5$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$
231.2.j.f	$231$	$2$	231.j	11.c	$5$	$8$	$2$	$1.845$	8.0.13140625.1	None		$2$	$0$	$2$	$2$	$2$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
242.2.c.f	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		$4$	$0$	$-2$	$2$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
242.2.c.g	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		$4$	$0$	$2$	$2$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
33.4.e.b	$33$	$4$	33.e	11.c	$5$	$8$	$2$	$1.947$	8.0.682515625.5	None		$2$	$0$	$-6$	$-6$	$9$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots$
246.2.g.e	$246$	$2$	246.g	41.d	$5$	$8$	$2$	$1.964$	8.0.$\cdots$.2	None		$2$	$0$	$2$	$-8$	$4$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{2}-\beta _{4}-\beta _{6})q^{2}-q^{3}-\beta _{6}q^{4}+\cdots$
250.2.d.b	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None		$2$	$0$	$-2$	$2$	$0$	$-16$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{20}q^{2}+(-\zeta_{20}^{3}+\zeta_{20}^{5})q^{3}+\zeta_{20}^{3}q^{4}+\cdots$
250.2.d.c	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None		$2$	$0$	$2$	$-2$	$0$	$16$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{20}^{4}q^{2}+(-\zeta_{20}+\zeta_{20}^{2})q^{3}-\zeta_{20}q^{4}+\cdots$
250.2.d.d	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	8.0.58140625.2	None		$2$	$0$	$2$	$3$	$0$	$-4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}-\beta _{3}-\beta _{6})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots$
264.2.q.e	$264$	$2$	264.q	11.c	$5$	$8$	$2$	$2.108$	8.0.185640625.1	None		$2$	$0$	$0$	$2$	$-1$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{3}+(-1+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
275.2.h.a	$275$	$2$	275.h	11.c	$5$	$8$	$2$	$2.196$	8.0.13140625.1	None		$2$	$0$	$2$	$5$	$0$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
275.2.h.b	$275$	$2$	275.h	11.c	$5$	$8$	$2$	$2.196$	8.0.159390625.1	None		$2$	$0$	$4$	$-1$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
279.2.i.b	$279$	$2$	279.i	31.d	$5$	$8$	$2$	$2.228$	$\Q(\zeta_{15})$	None		$2$	$0$	$-3$	$0$	$6$	$9$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{15}^{3}-\zeta_{15}^{4})q^{2}+(-\zeta_{15}+\cdots)q^{4}+\cdots$
286.2.h.b	$286$	$2$	286.h	11.c	$5$	$8$	$2$	$2.284$	8.0.159390625.1	None		$2$	$0$	$-2$	$4$	$7$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots$
300.2.m.a	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	$\Q(\zeta_{15})$	None		$2$	$0$	$0$	$-2$	$5$	$-8$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots$
300.2.m.b	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	8.0.26265625.1	None		$2$	$0$	$0$	$2$	$-5$	$8$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
308.2.j.b	$308$	$2$	308.j	11.c	$5$	$8$	$2$	$2.459$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-8$	$-1$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2-2\beta _{2}-\beta _{3}-\beta _{6})q^{3}+\beta _{7}q^{5}+\cdots$
310.2.h.c	$310$	$2$	310.h	31.d	$5$	$8$	$2$	$2.475$	8.0.484000000.9	None		$2$	$0$	$-2$	$0$	$-8$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{1}-\beta _{6}+\cdots)q^{3}+\cdots$
310.2.h.d	$310$	$2$	310.h	31.d	$5$	$8$	$2$	$2.475$	8.0.64000000.2	None		$2$	$0$	$-2$	$2$	$8$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots$
310.2.h.e	$310$	$2$	310.h	31.d	$5$	$8$	$2$	$2.475$	8.0.64000000.2	None		$2$	$0$	$2$	$2$	$-8$	$10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
328.2.m.a	$328$	$2$	328.m	41.d	$5$	$8$	$2$	$2.619$	8.0.4241265625.1	None		$2$	$0$	$0$	$0$	$1$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4})q^{5}+(-2+\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 256 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.