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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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
888.1.i.a	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓	✓			888.1.i.a	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
888.1.i.b	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓	✓			888.1.i.a	$2$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
888.1.i.c	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓	✓			888.1.i.a	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
888.1.i.d	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓	✓			888.1.i.a	$2$	$0$	$1$	$1$	$0$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
888.1.i.e	$888$	$1$	888.i	888.i	$2$	$8$	$8$	$0.443$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		✓	✓		888.1.i.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}-\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
888.2.a.a	$888$	$2$	888.a	1.a	$1$	$1$	$1$	$7.091$	$\Q$	$_{}$	None	None	✓	✓			888.2.a.a	$1$	$0$	$0$	$-1$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots$
888.2.a.b	$888$	$2$	888.a	1.a	$1$	$1$	$1$	$7.091$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	888.2.a.b	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-6q^{13}-4q^{17}+4q^{19}+\cdots$
888.2.a.c	$888$	$2$	888.a	1.a	$1$	$1$	$1$	$7.091$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	888.2.a.c	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
888.2.a.d	$888$	$2$	888.a	1.a	$1$	$1$	$1$	$7.091$	$\Q$	$_{}$	None	None	✓	✓			888.2.a.d	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}+2q^{13}+4q^{15}+\cdots$
888.2.a.e	$888$	$2$	888.a	1.a	$1$	$2$	$2$	$7.091$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	888.2.a.e	$1$	$1$	$0$	$-2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
888.2.a.f	$888$	$2$	888.a	1.a	$1$	$2$	$2$	$7.091$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		888.2.a.f	$1$	$0$	$0$	$-2$	$2$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+4q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots$
888.2.a.g	$888$	$2$	888.a	1.a	$1$	$2$	$2$	$7.091$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	888.2.a.g	$1$	$1$	$0$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+(-2-2\beta )q^{7}+\cdots$
888.2.a.h	$888$	$2$	888.a	1.a	$1$	$2$	$2$	$7.091$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	✓	✓		888.2.a.h	$1$	$0$	$0$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
888.2.a.i	$888$	$2$	888.a	1.a	$1$	$3$	$3$	$7.091$	3.3.316.1	$_{}$	None	None	✓	✓	✓	✓	888.2.a.i	$1$	$0$	$0$	$-3$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
888.2.a.j	$888$	$2$	888.a	1.a	$1$	$3$	$3$	$7.091$	3.3.568.1	$_{}$	None	None	✓	✓	✓	✓	888.2.a.j	$1$	$0$	$0$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
888.2.c.a	$888$	$2$	888.c	888.c	$2$	$16$	$16$	$7.091$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-111}) $	None		✓			888.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{13}q^{2}+\beta _{7}q^{3}-\beta _{15}q^{4}-\beta _{11}q^{5}+\cdots$
888.2.c.b	$888$	$2$	888.c	888.c	$2$	$16$	$16$	$7.091$	16.0.$\cdots$.2	$_{}$	None	None		✓			888.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{7}q^{3}+(1-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$
888.2.c.c	$888$	$2$	888.c	888.c	$2$	$20$	$20$	$7.091$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	$\Q(\sqrt{-74}) $	None		✓			888.2.c.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{12}q^{3}-2q^{4}+\beta _{16}q^{5}+\cdots$
888.2.c.d	$888$	$2$	888.c	888.c	$2$	$96$	$96$	$7.091$		$_{}$	None	None		✓	✓		888.2.c.d	$8$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
888.2.f.a	$888$	$2$	888.f	8.b	$2$	$28$	$28$	$7.091$		$_{}$	None	None		✓			888.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
888.2.f.b	$888$	$2$	888.f	8.b	$2$	$44$	$44$	$7.091$		$_{}$	None	None		✓	✓		888.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
888.2.h.a	$888$	$2$	888.h	37.b	$2$	$2$	$2$	$7.091$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			888.2.h.a	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+q^{9}+4 q^{11}-2\beta q^{13}+2\beta q^{17}+\cdots$
888.2.h.b	$888$	$2$	888.h	37.b	$2$	$6$	$6$	$7.091$	6.0.27206656.1	$_{}$	None	None		✓			888.2.h.b	$2$	$0$	$0$	$6$	$0$	$6$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
888.2.h.c	$888$	$2$	888.h	37.b	$2$	$10$	$10$	$7.091$	10.0.$\cdots$.1	$_{}$	None	None		✓	✓		888.2.h.c	$2$	$0$	$0$	$-10$	$0$	$-2$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
888.2.j.a	$888$	$2$	888.j	24.f	$2$	$4$	$4$	$7.091$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			888.2.j.a	$2$	$1$	$-2$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}-\beta_{2})q^{2}+(\beta_{3}-\beta_1+1)q^{3}+\cdots$
888.2.j.b	$888$	$2$	888.j	24.f	$2$	$4$	$4$	$7.091$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			888.2.j.a	$2$	$0$	$2$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+1)q^{2}+(\beta_{3}-\beta_1+1)q^{3}+\cdots$
888.2.j.c	$888$	$2$	888.j	24.f	$2$	$136$	$136$	$7.091$		$_{}$	None	None		✓	✓		888.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
888.2.o.a	$888$	$2$	888.o	296.e	$2$	$76$	$76$	$7.091$		$_{}$	None	None		✓	✓	✓	888.2.o.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
888.2.q.a	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			888.2.q.a	$2$	$1$	$0$	$-1$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$
888.2.q.b	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			888.2.q.b	$2$	$0$	$0$	$-1$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$
888.2.q.c	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			888.2.q.c	$2$	$1$	$0$	$1$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots$
888.2.q.d	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			888.2.q.d	$2$	$0$	$0$	$1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}+\zeta_{6}q^{5}+4\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots$
888.2.q.e	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.1415907.1	$_{}$	None	None		✓			888.2.q.e	$2$	$0$	$0$	$-3$	$-6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{3}+(-2+\beta _{1}-2\beta _{4}+\cdots)q^{5}+\cdots$
888.2.q.f	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.1415907.1	$_{}$	None	None		✓			888.2.q.f	$2$	$0$	$0$	$3$	$-2$	$-7$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
888.2.q.g	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.47545083.2	$_{}$	None	None		✓			888.2.q.g	$2$	$0$	$0$	$3$	$1$	$9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}-\beta _{5}q^{5}-3\beta _{4}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
888.2.q.h	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.50898483.1	$_{}$	None	None		✓			888.2.q.h	$2$	$0$	$0$	$3$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{5}-\beta _{3}q^{7}+\cdots$
888.2.q.i	$888$	$2$	888.q	37.c	$3$	$8$	$4$	$7.091$	$\Q(\sqrt{-3}, \sqrt{5}, \sqrt{13})$	$_{}$	None	None		✓	✓		888.2.q.i	$2$	$0$	$0$	$-4$	$1$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{3}+(-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$
888.2.r.a	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			888.2.r.a	$2$	$1$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(-2 i-2)q^{5}+\cdots$
888.2.r.b	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			888.2.r.b	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
888.2.r.c	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			888.2.r.a	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(2 i+2)q^{5}+\cdots$
888.2.r.d	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			888.2.r.b	$2$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}+i q^{3}-2 i q^{4}+(-2 i-2)q^{5}+\cdots$
888.2.r.e	$888$	$2$	888.r	296.j	$4$	$72$	$36$	$7.091$		$_{}$	None	None		✓			888.2.r.e	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
888.2.r.f	$888$	$2$	888.r	296.j	$4$	$72$	$36$	$7.091$		$_{}$	None	None		✓			888.2.r.f	$4$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
888.2.w.a	$888$	$2$	888.w	888.w	$4$	$296$	$148$	$7.091$		$_{}$	None	None		✓	✓	✓	888.2.w.a	$8$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{4}]$
888.2.y.a	$888$	$2$	888.y	111.g	$4$	$4$	$2$	$7.091$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			888.2.y.a	$4$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{3}+\beta_1)q^{3}+(\beta_{3}+\beta_{2})q^{5}+2 q^{7}+\cdots$
888.2.y.b	$888$	$2$	888.y	111.g	$4$	$16$	$8$	$7.091$	16.0.$\cdots$.1	$_{}$	None	None		✓			888.2.y.b	$4$	$0$	$0$	$0$	$0$	$-24$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{3}-\beta _{6}q^{5}+(-2+\beta _{2}-\beta _{7}+\cdots)q^{7}+\cdots$
888.2.y.c	$888$	$2$	888.y	111.g	$4$	$56$	$28$	$7.091$		$_{}$	None	None		✓	✓		888.2.y.c	$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{4}]$
888.2.z.a	$888$	$2$	888.z	296.q	$6$	$152$	$76$	$7.091$		$_{}$	None	None		✓	✓	✓	888.2.z.a	$4$	$0$	$6$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$
888.2.bd.a	$888$	$2$	888.bd	888.ad	$6$	$296$	$148$	$7.091$		$_{}$	None	None		✓	✓	✓	888.2.bd.a	$8$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
888.2.bh.a	$888$	$2$	888.bh	296.s	$6$	$152$	$76$	$7.091$		$_{}$	None	None		✓	✓	✓	888.2.bh.a	$4$	$0$	$-2$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$

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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.