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 51 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6624.2.a.a	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.e	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}-6q^{11}+6q^{13}+2q^{17}+\cdots$
6624.2.a.b	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.e	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}+6q^{11}+6q^{13}+2q^{17}+\cdots$
6624.2.a.c	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-2q^{11}-2q^{13}-8q^{19}+\cdots$
6624.2.a.d	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.d	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+2q^{11}-2q^{13}+8q^{19}+\cdots$
6624.2.a.e	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+4q^{11}+2q^{13}-2q^{19}+q^{23}+\cdots$
6624.2.a.f	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.b	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots$
6624.2.a.g	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{11}-2q^{13}+6q^{17}-2q^{19}+\cdots$
6624.2.a.h	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-4q^{11}+2q^{13}+2q^{19}-q^{23}+\cdots$
6624.2.a.i	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.a	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}+2q^{11}+6q^{13}+4q^{19}+\cdots$
6624.2.a.j	$6624$	$2$	6624.a	1.a	$1$	$1$	$1$	$52.893$	$\Q$	None	✓				2208.2.a.a	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-2q^{11}+6q^{13}-4q^{19}+\cdots$
6624.2.a.k	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓				736.2.a.b	$1$	$0$	$0$	$0$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(-3-\beta )q^{7}+(3-\beta )q^{11}+\cdots$
6624.2.a.l	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓	✓			6624.2.a.l	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+2\beta q^{7}+(-3-\beta )q^{11}+\cdots$
6624.2.a.m	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓	✓			6624.2.a.l	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-2\beta q^{7}+(3+\beta )q^{11}+\cdots$
6624.2.a.n	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓				736.2.a.b	$1$	$1$	$0$	$0$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(3+\beta )q^{7}+(-3+\beta )q^{11}+\cdots$
6624.2.a.o	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓				2208.2.a.k	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(2-2\beta )q^{11}+\cdots$
6624.2.a.p	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓	✓			6624.2.a.l	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+\cdots$
6624.2.a.q	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓	✓			6624.2.a.l	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2\beta q^{7}+(3-\beta )q^{11}+2\beta q^{13}+\cdots$
6624.2.a.r	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{3}) $	None	✓				2208.2.a.k	$1$	$1$	$0$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-2+2\beta )q^{11}+\cdots$
6624.2.a.s	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{2}) $	None	✓				736.2.a.a	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2-\beta )q^{7}+3\beta q^{11}+\cdots$
6624.2.a.t	$6624$	$2$	6624.a	1.a	$1$	$2$	$2$	$52.893$	$\Q(\sqrt{2}) $	None	✓				736.2.a.a	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(2+\beta )q^{7}-3\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
6624.2.a.u	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓	✓			6624.2.a.u	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+(-1-\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots$
6624.2.a.v	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓	✓			6624.2.a.u	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+(1+\beta _{1})q^{7}+(2-2\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.w	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	$\Q(\zeta_{14})^+$	None	✓				2208.2.a.n	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.x	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	$\Q(\zeta_{14})^+$	None	✓				2208.2.a.n	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.y	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.316.1	None	✓				736.2.a.e	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
6624.2.a.z	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.316.1	None	✓				736.2.a.e	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
6624.2.a.ba	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓	✓			6624.2.a.u	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(-1-\beta _{1})q^{7}+(2-2\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.bb	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓				2208.2.a.m	$1$	$1$	$0$	$0$	$4$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.bc	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓				2208.2.a.m	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
6624.2.a.bd	$6624$	$2$	6624.a	1.a	$1$	$3$	$3$	$52.893$	3.3.148.1	None	✓	✓			6624.2.a.u	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(1+\beta _{1})q^{7}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots$
6624.2.a.be	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	4.4.13768.1	None	✓		✓		736.2.a.g	$1$	$1$	$0$	$0$	$-6$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2+\beta _{3})q^{5}+(-1+\beta _{1})q^{7}-\beta _{3}q^{11}+\cdots$
6624.2.a.bf	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	4.4.13768.1	None	✓				736.2.a.g	$1$	$1$	$0$	$0$	$-6$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots$
6624.2.a.bg	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓		6624.2.a.bg	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{1}q^{7}+(-1-\beta _{2})q^{13}+\cdots$
6624.2.a.bh	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓		6624.2.a.bg	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2})q^{13}+\cdots$
6624.2.a.bi	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	4.4.19796.1	None	✓				2208.2.a.q	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-1+\beta _{1}+\beta _{3})q^{11}+\cdots$
6624.2.a.bj	$6624$	$2$	6624.a	1.a	$1$	$4$	$4$	$52.893$	4.4.19796.1	None	✓				2208.2.a.q	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+(1-\beta _{1}-\beta _{3})q^{11}+\cdots$
6624.2.a.bk	$6624$	$2$	6624.a	1.a	$1$	$5$	$5$	$52.893$	5.5.218524.1	None	✓		✓		2208.2.a.s	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
6624.2.a.bl	$6624$	$2$	6624.a	1.a	$1$	$5$	$5$	$52.893$	5.5.218524.1	None	✓		✓		2208.2.a.s	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
6624.2.a.bm	$6624$	$2$	6624.a	1.a	$1$	$8$	$8$	$52.893$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		6624.2.a.bm	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{5}q^{7}+\beta _{3}q^{11}-\beta _{4}q^{13}+\cdots$
6624.2.a.bn	$6624$	$2$	6624.a	1.a	$1$	$8$	$8$	$52.893$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		6624.2.a.bm	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}-\beta _{5}q^{7}-\beta _{3}q^{11}-\beta _{4}q^{13}+\cdots$
6624.2.b.a	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.$\cdots$.17	$\Q(\sqrt{-46}) $					1656.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{5}+(-\beta _{5}+2\beta _{6})q^{11}+\beta _{2}q^{19}+\cdots$
6624.2.b.b	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.$\cdots$.17	$\Q(\sqrt{-46}) $					1656.2.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{5}-\beta _{4}q^{11}+(-\beta _{5}+\beta _{6})q^{19}+\cdots$
6624.2.b.c	$6624$	$2$	6624.b	552.b	$2$	$80$	$80$	$52.893$		None			✓		1656.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6624.2.e.a	$6624$	$2$	6624.e	12.b	$2$	$20$	$20$	$52.893$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			6624.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}+\beta _{4}q^{7}-\beta _{11}q^{11}+(-1+\cdots)q^{13}+\cdots$
6624.2.e.b	$6624$	$2$	6624.e	12.b	$2$	$20$	$20$	$52.893$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			6624.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}-\beta _{4}q^{7}+\beta _{11}q^{11}+(-1+\cdots)q^{13}+\cdots$
6624.2.e.c	$6624$	$2$	6624.e	12.b	$2$	$24$	$24$	$52.893$		None		✓			6624.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6624.2.e.d	$6624$	$2$	6624.e	12.b	$2$	$24$	$24$	$52.893$		None		✓			6624.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6624.2.j.a	$6624$	$2$	6624.j	24.f	$2$	$44$	$44$	$52.893$		None					1656.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6624.2.j.b	$6624$	$2$	6624.j	24.f	$2$	$44$	$44$	$52.893$		None					1656.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6624.2.m.a	$6624$	$2$	6624.m	69.c	$2$	$48$	$48$	$52.893$		None		✓			6624.2.m.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.