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 57 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				A-L signs				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6825.2.a.a	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				273.2.a.b	$1$	$1$	$-2$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
6825.2.a.b	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots$
6825.2.a.c	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.f.a	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots$
6825.2.a.d	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.f.b	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots$
6825.2.a.e	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.f	$1$	$0$	$-1$	$-1$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots$
6825.2.a.f	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.d	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots$
6825.2.a.g	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.c	$1$	$1$	$-1$	$1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots$
6825.2.a.h	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.b	$1$	$0$	$1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots$
6825.2.a.i	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.f.a	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$
6825.2.a.j	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.f.b	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$
6825.2.a.k	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				1365.2.a.a	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$
6825.2.a.l	$6825$	$2$	6825.a	1.a	$1$	$1$	$1$	$54.498$	$\Q$	None	✓				273.2.a.a	$1$	$0$	$2$	$1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots$
6825.2.a.m	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{2}) $	None	✓				273.2.a.c	$1$	$1$	$-2$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
6825.2.a.n	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{13}) $	None	✓				1365.2.a.n	$1$	$1$	$-1$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots$
6825.2.a.o	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓				1365.2.a.l	$1$	$0$	$-1$	$2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
6825.2.a.p	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓	✓			6825.2.a.p	$1$	$1$	$-1$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
6825.2.a.q	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{13}) $	None	✓				1365.2.a.m	$1$	$1$	$-1$	$2$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots$
6825.2.a.r	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓	✓			6825.2.a.p	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
6825.2.a.s	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓				1365.2.a.j	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
6825.2.a.t	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{13}) $	None	✓				1365.2.a.k	$1$	$0$	$1$	$-2$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots$
6825.2.a.u	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓				1365.2.a.h	$1$	$1$	$1$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
6825.2.a.v	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓				1365.2.a.i	$1$	$1$	$1$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
6825.2.a.w	$6825$	$2$	6825.a	1.a	$1$	$2$	$2$	$54.498$	$\Q(\sqrt{5}) $	None	✓				1365.2.a.g	$1$	$1$	$3$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots$
6825.2.a.x	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.229.1	None	✓				1365.2.a.r	$1$	$0$	$0$	$-3$	$0$	$-3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.y	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.621.1	None	✓				1365.2.a.s	$1$	$1$	$0$	$-3$	$0$	$3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.z	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.837.1	None	✓				1365.2.a.t	$1$	$0$	$0$	$-3$	$0$	$3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.ba	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.229.1	None	✓				1365.2.a.o	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.bb	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.229.1	None	✓				1365.2.a.p	$1$	$1$	$0$	$3$	$0$	$3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bc	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.621.1	None	✓				1365.2.a.q	$1$	$0$	$0$	$3$	$0$	$-3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bd	$6825$	$2$	6825.a	1.a	$1$	$3$	$3$	$54.498$	3.3.316.1	None	✓				273.2.a.d	$1$	$0$	$2$	$3$	$0$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots$
6825.2.a.be	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	$\Q(\zeta_{20})^+$	None	✓				1365.2.f.c	$1$	$1$	$-2$	$4$	$0$	$4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
6825.2.a.bf	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.14013.1	None	✓	✓	✓		6825.2.a.bf	$1$	$1$	$-1$	$-4$	$0$	$4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bg	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.17428.1	None	✓				273.2.a.e	$1$	$1$	$-1$	$-4$	$0$	$-4$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bh	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	$\Q(\zeta_{15})^+$	None	✓	✓	✓		6825.2.a.bh	$1$	$1$	$-1$	$4$	$0$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots$
6825.2.a.bi	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.3981.1	None	✓	✓			6825.2.a.bi	$1$	$1$	$-1$	$4$	$0$	$4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.bj	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.3981.1	None	✓	✓			6825.2.a.bi	$1$	$1$	$1$	$-4$	$0$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.bk	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	$\Q(\zeta_{15})^+$	None	✓	✓			6825.2.a.bh	$1$	$1$	$1$	$-4$	$0$	$4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
6825.2.a.bl	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.14013.1	None	✓	✓			6825.2.a.bf	$1$	$1$	$1$	$4$	$0$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bm	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	$\Q(\zeta_{20})^+$	None	✓				1365.2.f.c	$1$	$0$	$2$	$-4$	$0$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots$
6825.2.a.bn	$6825$	$2$	6825.a	1.a	$1$	$4$	$4$	$54.498$	4.4.2225.1	None	✓				1365.2.a.u	$1$	$0$	$3$	$-4$	$0$	$4$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
6825.2.a.bo	$6825$	$2$	6825.a	1.a	$1$	$5$	$5$	$54.498$	5.5.255877.1	None	✓				1365.2.a.v	$1$	$0$	$0$	$5$	$0$	$5$	$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(2+\beta _{1})q^{4}-\beta _{2}q^{6}+\cdots$
6825.2.a.bp	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.259521624.1	None	✓	✓	✓		6825.2.a.bp	$1$	$0$	$-3$	$6$	$0$	$-6$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
6825.2.a.bq	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.55102497.1	None	✓	✓	✓		6825.2.a.bq	$1$	$1$	$-2$	$6$	$0$	$6$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.br	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.78539816.1	None	✓	✓	✓		6825.2.a.br	$1$	$0$	$-1$	$-6$	$0$	$-6$	$+$	$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bs	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.78539816.1	None	✓	✓			6825.2.a.br	$1$	$0$	$1$	$6$	$0$	$6$	$-$	$-$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bt	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.55102497.1	None	✓	✓			6825.2.a.bq	$1$	$1$	$2$	$-6$	$0$	$-6$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.bu	$6825$	$2$	6825.a	1.a	$1$	$6$	$6$	$54.498$	6.6.259521624.1	None	✓	✓			6825.2.a.bp	$1$	$0$	$3$	$-6$	$0$	$6$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
6825.2.a.bv	$6825$	$2$	6825.a	1.a	$1$	$8$	$8$	$54.498$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		1365.2.f.d	$1$	$1$	$-2$	$-8$	$0$	$8$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
6825.2.a.bw	$6825$	$2$	6825.a	1.a	$1$	$8$	$8$	$54.498$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			6825.2.a.bw	$1$	$0$	$-2$	$8$	$0$	$-8$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
6825.2.a.bx	$6825$	$2$	6825.a	1.a	$1$	$8$	$8$	$54.498$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		6825.2.a.bx	$1$	$0$	$0$	$-8$	$0$	$-8$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$

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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.