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 196 matches)

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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
855.1.g.a	$855$	$1$	855.g	95.d	$2$	$1$	$1$	$0.427$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓				95.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots$
855.1.g.b	$855$	$1$	855.g	95.d	$2$	$2$	$2$	$0.427$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{285}) $		✓			855.1.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-i q^{5}+q^{16}-2 i q^{17}-q^{19}+\cdots$
855.1.g.c	$855$	$1$	855.g	95.d	$2$	$2$	$2$	$0.427$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓				95.1.d.b	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{2}+q^{4}+q^{5}-\beta q^{10}+\beta q^{13}+\cdots$
855.1.m.a	$855$	$1$	855.m	285.j	$4$	$4$	$2$	$0.427$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			855.1.m.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
855.1.m.b	$855$	$1$	855.m	285.j	$4$	$4$	$2$	$0.427$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			855.1.m.b	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(1+\zeta_{8}^{2})q^{7}+\cdots$
855.1.u.a	$855$	$1$	855.u	285.n	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	855.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}-\zeta_{24}^{4}q^{4}+\cdots$
855.1.v.a	$855$	$1$	855.v	95.h	$6$	$4$	$2$	$0.427$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	855.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
855.1.z.a	$855$	$1$	855.z	855.z	$6$	$2$	$1$	$0.427$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		✓			855.1.z.a	$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
855.1.z.b	$855$	$1$	855.z	855.z	$6$	$2$	$1$	$0.427$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		✓			855.1.z.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
855.1.z.c	$855$	$1$	855.z	855.z	$6$	$4$	$2$	$0.427$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-95}) $	None		✓			855.1.z.c	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{3}+(-1+\cdots)q^{4}+\cdots$
855.1.z.d	$855$	$1$	855.z	855.z	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-95}) $	None		✓	✓		855.1.z.d	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
855.1.ck.a	$855$	$1$	855.ck	95.m	$12$	$8$	$2$	$0.427$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	855.1.ck.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{7}q^{5}+\zeta_{24}^{3}q^{8}-\zeta_{24}^{8}q^{10}+\cdots$
855.1.cw.a	$855$	$1$	855.cw	95.o	$18$	$12$	$2$	$0.427$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	855.1.cw.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{36}^{7}+\zeta_{36}^{15})q^{2}+(\zeta_{36}^{4}-\zeta_{36}^{12}+\cdots)q^{4}+\cdots$
855.2.a.a	$855$	$2$	855.a	1.a	$1$	$1$	$1$	$6.827$	$\Q$	$_{}$	None	None	✓				285.2.a.c	$1$	$0$	$-1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
855.2.a.b	$855$	$2$	855.a	1.a	$1$	$1$	$1$	$6.827$	$\Q$	$_{}$	None	None	✓				285.2.a.b	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-2q^{7}+3q^{8}-q^{10}+\cdots$
855.2.a.c	$855$	$2$	855.a	1.a	$1$	$1$	$1$	$6.827$	$\Q$	$_{}$	None	None	✓				285.2.a.a	$1$	$0$	$1$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
855.2.a.d	$855$	$2$	855.a	1.a	$1$	$2$	$2$	$6.827$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		285.2.a.g	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots$
855.2.a.e	$855$	$2$	855.a	1.a	$1$	$2$	$2$	$6.827$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				285.2.a.f	$1$	$0$	$-2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots$
855.2.a.f	$855$	$2$	855.a	1.a	$1$	$2$	$2$	$6.827$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓	✓	285.2.a.e	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-\beta q^{8}+\cdots$
855.2.a.g	$855$	$2$	855.a	1.a	$1$	$2$	$2$	$6.827$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				285.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots$
855.2.a.h	$855$	$2$	855.a	1.a	$1$	$3$	$3$	$6.827$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	855.2.a.h	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots$
855.2.a.i	$855$	$2$	855.a	1.a	$1$	$3$	$3$	$6.827$	3.3.148.1	$_{}$	None	None	✓		✓		95.2.a.a	$1$	$0$	$-1$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+2\beta _{2}q^{7}+\cdots$
855.2.a.j	$855$	$2$	855.a	1.a	$1$	$3$	$3$	$6.827$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	855.2.a.j	$1$	$1$	$-1$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots$
855.2.a.k	$855$	$2$	855.a	1.a	$1$	$3$	$3$	$6.827$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	855.2.a.j	$1$	$0$	$1$	$0$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots$
855.2.a.l	$855$	$2$	855.a	1.a	$1$	$3$	$3$	$6.827$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	855.2.a.h	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots$
855.2.a.m	$855$	$2$	855.a	1.a	$1$	$4$	$4$	$6.827$	4.4.11344.1	$_{}$	None	None	✓		✓		95.2.a.b	$1$	$0$	$2$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots$
855.2.b.a	$855$	$2$	855.b	285.b	$2$	$4$	$4$	$6.827$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			855.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
855.2.b.b	$855$	$2$	855.b	285.b	$2$	$4$	$4$	$6.827$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			855.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{8}+\cdots$
855.2.b.c	$855$	$2$	855.b	285.b	$2$	$8$	$8$	$6.827$	8.0.8540717056.1	$_{}$	$\Q(\sqrt{-19}) $	None		✓			855.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+\beta _{6}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
855.2.b.d	$855$	$2$	855.b	285.b	$2$	$24$	$24$	$6.827$		$_{}$	None	None		✓	✓		855.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
855.2.c.a	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			855.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(-i-2)q^{5}+2 i q^{7}+\cdots$
855.2.c.b	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	$\Q(\sqrt{-1}) $	$_{}$	None	None					95.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(2 i+1)q^{5}+2 i q^{7}+\cdots$
855.2.c.c	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			855.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(-i+2)q^{5}-2 i q^{7}+\cdots$
855.2.c.d	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.16516096.1	$_{}$	None	None					95.2.b.b	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots$
855.2.c.e	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.350464.1	$_{}$	None	None					285.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
855.2.c.f	$855$	$2$	855.c	5.b	$2$	$12$	$12$	$6.827$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			855.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{6}q^{7}+\cdots$
855.2.c.g	$855$	$2$	855.c	5.b	$2$	$14$	$14$	$6.827$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None			✓		285.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
855.2.h.a	$855$	$2$	855.h	57.d	$2$	$24$	$24$	$6.827$		$_{}$	None	None		✓	✓	✓	855.2.h.a	$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{2}]$
855.2.i.a	$855$	$2$	855.i	9.c	$3$	$26$	$13$	$6.827$		$_{}$	None	None		✓			855.2.i.a	$2$	$0$	$3$	$-2$	$-13$	$10$			$\mathrm{SU}(2)[C_{3}]$
855.2.i.b	$855$	$2$	855.i	9.c	$3$	$30$	$15$	$6.827$		$_{}$	None	None		✓			855.2.i.b	$2$	$0$	$-3$	$2$	$15$	$2$			$\mathrm{SU}(2)[C_{3}]$
855.2.i.c	$855$	$2$	855.i	9.c	$3$	$42$	$21$	$6.827$		$_{}$	None	None		✓			855.2.i.c	$2$	$0$	$-3$	$-2$	$-21$	$-2$			$\mathrm{SU}(2)[C_{3}]$
855.2.i.d	$855$	$2$	855.i	9.c	$3$	$46$	$23$	$6.827$		$_{}$	None	None		✓	✓		855.2.i.d	$2$	$0$	$3$	$2$	$23$	$-10$			$\mathrm{SU}(2)[C_{3}]$
855.2.j.a	$855$	$2$	855.j	171.g	$3$	$80$	$40$	$6.827$		$_{}$	None	None		✓			855.2.j.a	$2$	$0$	$-2$	$1$	$-80$	$1$			$\mathrm{SU}(2)[C_{3}]$
855.2.j.b	$855$	$2$	855.j	171.g	$3$	$80$	$40$	$6.827$		$_{}$	None	None		✓			855.2.j.b	$2$	$0$	$-2$	$1$	$80$	$1$			$\mathrm{SU}(2)[C_{3}]$
855.2.k.a	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	$\Q(\sqrt{-3}) $	$_{}$	None	None					285.2.i.c	$2$	$0$	$-2$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
855.2.k.b	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	$\Q(\sqrt{-3}) $	$_{}$	None	None					95.2.e.a	$2$	$1$	$0$	$0$	$-1$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}-4q^{7}-3q^{11}+\cdots$
855.2.k.c	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	$\Q(\sqrt{-3}) $	$_{}$	None	None					285.2.i.b	$2$	$0$	$0$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+2q^{7}+3q^{11}+\cdots$
855.2.k.d	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	$\Q(\sqrt{-3}) $	$_{}$	None	None					285.2.i.a	$2$	$0$	$2$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
855.2.k.e	$855$	$2$	855.k	19.c	$3$	$4$	$2$	$6.827$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					285.2.i.e	$2$	$0$	$-1$	$0$	$-2$	$12$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
855.2.k.f	$855$	$2$	855.k	19.c	$3$	$4$	$2$	$6.827$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					285.2.i.d	$2$	$0$	$2$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$

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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.