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 226 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
273.1.o.a	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			273.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots$
273.1.o.b	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			273.1.o.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots$
273.1.s.a	$273$	$1$	273.s	273.s	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			273.1.s.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
273.1.s.b	$273$	$1$	273.s	273.s	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓		273.1.s.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
273.1.x.a	$273$	$1$	273.x	273.x	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	273.1.x.a	$4$	$0$	$0$	$-2$	$0$	$-1$		$1$		$q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
273.1.bm.a	$273$	$1$	273.bm	273.am	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			273.1.s.a	$4$	$0$	$0$	$2$	$0$	$-1$		$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
273.1.bm.b	$273$	$1$	273.bm	273.am	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓		273.1.s.b	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
273.1.bp.a	$273$	$1$	273.bp	273.ap	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	273.1.x.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
273.1.bs.a	$273$	$1$	273.bs	273.as	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
273.1.ch.a	$273$	$1$	273.ch	273.bh	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
273.2.a.a	$273$	$2$	273.a	1.a	$1$	$1$	$1$	$2.180$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	273.2.a.a	$1$	$1$	$-2$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots$
273.2.a.b	$273$	$2$	273.a	1.a	$1$	$1$	$1$	$2.180$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	273.2.a.b	$1$	$0$	$2$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
273.2.a.c	$273$	$2$	273.a	1.a	$1$	$2$	$2$	$2.180$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	273.2.a.c	$1$	$0$	$2$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
273.2.a.d	$273$	$2$	273.a	1.a	$1$	$3$	$3$	$2.180$	3.3.316.1	$_{}$	None	None	✓	✓	✓	✓	273.2.a.d	$1$	$1$	$-2$	$-3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots$
273.2.a.e	$273$	$2$	273.a	1.a	$1$	$4$	$4$	$2.180$	4.4.17428.1	$_{}$	None	None	✓	✓	✓	✓	273.2.a.e	$1$	$0$	$1$	$4$	$-3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
273.2.c.a	$273$	$2$	273.c	13.b	$2$	$2$	$2$	$2.180$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			273.2.c.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots$
273.2.c.b	$273$	$2$	273.c	13.b	$2$	$6$	$6$	$2.180$	6.0.350464.1	$_{}$	None	None		✓			273.2.c.b	$2$	$0$	$0$	$6$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
273.2.c.c	$273$	$2$	273.c	13.b	$2$	$8$	$8$	$2.180$	8.0.$\cdots$.1	$_{}$	None	None		✓	✓		273.2.c.c	$2$	$0$	$0$	$-8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
273.2.e.a	$273$	$2$	273.e	21.c	$2$	$32$	$32$	$2.180$		$_{}$	None	None		✓	✓	✓	273.2.e.a	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
273.2.g.a	$273$	$2$	273.g	273.g	$2$	$32$	$32$	$2.180$		$_{}$	None	None		✓	✓	✓	273.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
273.2.i.a	$273$	$2$	273.i	7.c	$3$	$2$	$1$	$2.180$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			273.2.i.a	$2$	$0$	$1$	$-1$	$-4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
273.2.i.b	$273$	$2$	273.i	7.c	$3$	$6$	$3$	$2.180$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			273.2.i.b	$2$	$0$	$0$	$3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$
273.2.i.c	$273$	$2$	273.i	7.c	$3$	$6$	$3$	$2.180$	6.0.64827.1	$_{}$	None	None		✓			273.2.i.c	$2$	$0$	$2$	$-3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(2\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
273.2.i.d	$273$	$2$	273.i	7.c	$3$	$8$	$4$	$2.180$	8.0.4868829729.1	$_{}$	None	None		✓			273.2.i.d	$2$	$0$	$1$	$-4$	$-3$	$9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$
273.2.i.e	$273$	$2$	273.i	7.c	$3$	$10$	$5$	$2.180$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		273.2.i.e	$2$	$0$	$0$	$5$	$3$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
273.2.j.a	$273$	$2$	273.j	91.g	$3$	$2$	$1$	$2.180$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			273.2.j.a	$2$	$0$	$0$	$2$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+q^{9}+\cdots$
273.2.j.b	$273$	$2$	273.j	91.g	$3$	$16$	$8$	$2.180$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			273.2.j.b	$2$	$0$	$0$	$-16$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots$
273.2.j.c	$273$	$2$	273.j	91.g	$3$	$20$	$10$	$2.180$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		273.2.j.c	$2$	$0$	$0$	$20$	$0$	$-9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(-\beta _{2}-2\beta _{7}+\cdots)q^{4}+\cdots$
273.2.k.a	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			273.2.k.a	$2$	$0$	$0$	$-3$	$12$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
273.2.k.b	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.6040683.1	$_{}$	None	None		✓			273.2.k.b	$2$	$0$	$0$	$3$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{4})q^{3}+(\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
273.2.k.c	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.64827.1	$_{}$	None	None		✓			273.2.k.c	$2$	$0$	$2$	$-3$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
273.2.k.d	$273$	$2$	273.k	13.c	$3$	$6$	$3$	$2.180$	6.0.771147.1	$_{}$	None	None		✓			273.2.k.d	$2$	$0$	$2$	$3$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots$
273.2.l.a	$273$	$2$	273.l	91.h	$3$	$2$	$1$	$2.180$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			273.2.j.a	$2$	$0$	$0$	$-1$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots$
273.2.l.b	$273$	$2$	273.l	91.h	$3$	$16$	$8$	$2.180$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			273.2.j.b	$2$	$0$	$0$	$8$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$
273.2.l.c	$273$	$2$	273.l	91.h	$3$	$20$	$10$	$2.180$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		273.2.j.c	$2$	$0$	$0$	$-10$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots$
273.2.n.a	$273$	$2$	273.n	39.f	$4$	$4$	$2$	$2.180$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			273.2.n.a	$2$	$1$	$-4$	$-4$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
273.2.n.b	$273$	$2$	273.n	39.f	$4$	$4$	$2$	$2.180$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			273.2.n.a	$2$	$0$	$4$	$-4$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$
273.2.n.c	$273$	$2$	273.n	39.f	$4$	$48$	$24$	$2.180$		$_{}$	None	None		✓	✓		273.2.n.c	$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
273.2.p.a	$273$	$2$	273.p	91.i	$4$	$4$	$2$	$2.180$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			273.2.p.a	$2$	$0$	$0$	$0$	$-8$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-2+2\beta _{2}+\cdots)q^{5}+\cdots$
273.2.p.b	$273$	$2$	273.p	91.i	$4$	$4$	$2$	$2.180$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			273.2.p.b	$2$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
273.2.p.c	$273$	$2$	273.p	91.i	$4$	$4$	$2$	$2.180$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			273.2.p.b	$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}-2\beta _{2}q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$
273.2.p.d	$273$	$2$	273.p	91.i	$4$	$4$	$2$	$2.180$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			273.2.p.a	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots$
273.2.p.e	$273$	$2$	273.p	91.i	$4$	$12$	$6$	$2.180$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			273.2.p.e	$2$	$0$	$0$	$0$	$-12$	$12$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{2}-\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots$
273.2.p.f	$273$	$2$	273.p	91.i	$4$	$12$	$6$	$2.180$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			273.2.p.e	$2$	$0$	$0$	$0$	$12$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{2}+\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots$
273.2.r.a	$273$	$2$	273.r	273.r	$6$	$2$	$1$	$2.180$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			273.2.r.a	$4$	$0$	$0$	$-3$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots$
273.2.r.b	$273$	$2$	273.r	273.r	$6$	$64$	$32$	$2.180$		$_{}$	None	None		✓	✓		273.2.r.b	$4$	$0$	$0$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
273.2.t.a	$273$	$2$	273.t	91.k	$6$	$2$	$1$	$2.180$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			273.2.t.a	$2$	$0$	$0$	$1$	$-6$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots$
273.2.t.b	$273$	$2$	273.t	91.k	$6$	$4$	$2$	$2.180$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			273.2.t.b	$2$	$0$	$0$	$-2$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
273.2.t.c	$273$	$2$	273.t	91.k	$6$	$12$	$6$	$2.180$	12.0.$\cdots$.1	$_{}$	None	None		✓			273.2.t.c	$2$	$0$	$0$	$-6$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots$
273.2.t.d	$273$	$2$	273.t	91.k	$6$	$20$	$10$	$2.180$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		273.2.t.d	$2$	$0$	$0$	$10$	$6$	$2$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$

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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.