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 52 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	53	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5194.2.a.a	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.e	$1$	$0$	$-1$	$-3$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
5194.2.a.b	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.d	$1$	$1$	$-1$	$-2$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{8}+\cdots$
5194.2.a.c	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				106.2.a.b	$1$	$1$	$-1$	$-2$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{8}+\cdots$
5194.2.a.d	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.c	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
5194.2.a.e	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.c	$1$	$1$	$-1$	$-2$	$4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+4q^{5}+2q^{6}-q^{8}+\cdots$
5194.2.a.f	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.b	$1$	$1$	$-1$	$0$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{8}-3q^{9}+4q^{10}+\cdots$
5194.2.a.g	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.b	$1$	$0$	$-1$	$0$	$-3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}-3q^{9}+3q^{10}+\cdots$
5194.2.a.h	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.a	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots$
5194.2.a.i	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.b	$1$	$0$	$-1$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{8}-3q^{9}-4q^{10}+\cdots$
5194.2.a.j	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				106.2.a.a	$1$	$0$	$-1$	$1$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots$
5194.2.a.k	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.c	$1$	$0$	$-1$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
5194.2.a.l	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.g	$1$	$1$	$1$	$-3$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+2q^{5}-3q^{6}+q^{8}+\cdots$
5194.2.a.m	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.a	$1$	$1$	$1$	$-2$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}+q^{8}+\cdots$
5194.2.a.n	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				106.2.a.d	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
5194.2.a.o	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.a.f	$1$	$1$	$1$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots$
5194.2.a.p	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				106.2.a.c	$1$	$1$	$1$	$2$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{8}+\cdots$
5194.2.a.q	$5194$	$2$	5194.a	1.a	$1$	$1$	$1$	$41.474$	$\Q$	None	✓				742.2.e.a	$1$	$0$	$1$	$2$	$4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{8}+\cdots$
5194.2.a.r	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓				742.2.e.d	$1$	$1$	$-2$	$-4$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2+\beta )q^{3}+q^{4}+2\beta q^{5}+\cdots$
5194.2.a.s	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.s	$1$	$1$	$-2$	$-2$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots$
5194.2.a.t	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.t	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-q^{8}-3q^{9}+\beta q^{10}+\cdots$
5194.2.a.u	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.u	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots$
5194.2.a.v	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.v	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots$
5194.2.a.w	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.w	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
5194.2.a.x	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓				742.2.a.i	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
5194.2.a.y	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓				742.2.a.h	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
5194.2.a.z	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.s	$1$	$1$	$-2$	$2$	$4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots$
5194.2.a.ba	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓				742.2.e.d	$1$	$0$	$-2$	$4$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(2+\beta )q^{3}+q^{4}+2\beta q^{5}+(-2+\cdots)q^{6}+\cdots$
5194.2.a.bb	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓				742.2.a.j	$1$	$1$	$2$	$0$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(-2+\beta )q^{5}+\beta q^{6}+\cdots$
5194.2.a.bc	$5194$	$2$	5194.a	1.a	$1$	$2$	$2$	$41.474$	$\Q(\sqrt{2}) $	None	✓	✓			5194.2.a.bc	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots$
5194.2.a.bd	$5194$	$2$	5194.a	1.a	$1$	$3$	$3$	$41.474$	3.3.257.1	None	✓				742.2.e.e	$1$	$1$	$-3$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots$
5194.2.a.be	$5194$	$2$	5194.a	1.a	$1$	$3$	$3$	$41.474$	3.3.257.1	None	✓				742.2.e.e	$1$	$0$	$-3$	$2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots$
5194.2.a.bf	$5194$	$2$	5194.a	1.a	$1$	$3$	$3$	$41.474$	3.3.940.1	None	✓				742.2.a.k	$1$	$0$	$-3$	$3$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{2})q^{5}+\cdots$
5194.2.a.bg	$5194$	$2$	5194.a	1.a	$1$	$3$	$3$	$41.474$	3.3.316.1	None	✓				742.2.a.l	$1$	$0$	$3$	$4$	$5$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(2-\beta _{1})q^{5}+\cdots$
5194.2.a.bh	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	4.4.147069.1	None	✓				742.2.e.f	$1$	$0$	$-4$	$-4$	$5$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
5194.2.a.bi	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	$\Q(\zeta_{24})^+$	None	✓	✓			5194.2.a.bi	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
5194.2.a.bj	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	$\Q(\sqrt{2}, \sqrt{7})$	None	✓	✓			5194.2.a.bj	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
5194.2.a.bk	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	$\Q(\sqrt{2}, \sqrt{7})$	None	✓	✓			5194.2.a.bk	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
5194.2.a.bl	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	$\Q(\zeta_{24})^+$	None	✓	✓			5194.2.a.bl	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$
5194.2.a.bm	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	4.4.147069.1	None	✓		✓		742.2.e.f	$1$	$1$	$-4$	$4$	$-5$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots$
5194.2.a.bn	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	$\Q(\zeta_{24})^+$	None	✓	✓			5194.2.a.bn	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{8}+\cdots$
5194.2.a.bo	$5194$	$2$	5194.a	1.a	$1$	$4$	$4$	$41.474$	4.4.9248.1	None	✓	✓			5194.2.a.bo	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
5194.2.a.bp	$5194$	$2$	5194.a	1.a	$1$	$6$	$6$	$41.474$	6.6.1229312.1	None	✓	✓	✓		5194.2.a.bp	$2$	$0$	$-6$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{4}-\beta _{5})q^{3}+q^{4}+\beta _{5}q^{5}+\cdots$
5194.2.a.bq	$5194$	$2$	5194.a	1.a	$1$	$6$	$6$	$41.474$	6.6.118210688.1	None	✓	✓			5194.2.a.bq	$2$	$0$	$-6$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+(-\beta _{1}+\beta _{5})q^{5}+\cdots$
5194.2.a.br	$5194$	$2$	5194.a	1.a	$1$	$6$	$6$	$41.474$	6.6.111663536.1	None	✓				742.2.a.m	$1$	$0$	$6$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
5194.2.a.bs	$5194$	$2$	5194.a	1.a	$1$	$7$	$7$	$41.474$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		742.2.e.g	$1$	$1$	$-7$	$-2$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
5194.2.a.bt	$5194$	$2$	5194.a	1.a	$1$	$7$	$7$	$41.474$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		742.2.e.g	$1$	$0$	$-7$	$2$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
5194.2.a.bu	$5194$	$2$	5194.a	1.a	$1$	$8$	$8$	$41.474$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		742.2.e.h	$1$	$1$	$8$	$-2$	$-5$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots$
5194.2.a.bv	$5194$	$2$	5194.a	1.a	$1$	$8$	$8$	$41.474$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				742.2.e.h	$1$	$0$	$8$	$2$	$5$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{1}q^{6}+\cdots$
5194.2.a.bw	$5194$	$2$	5194.a	1.a	$1$	$9$	$9$	$41.474$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		742.2.e.i	$1$	$1$	$9$	$-2$	$-9$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
5194.2.a.bx	$5194$	$2$	5194.a	1.a	$1$	$9$	$9$	$41.474$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				742.2.e.i	$1$	$0$	$9$	$2$	$9$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$

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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.