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 165 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
364.1.d.a	$364$	$1$	364.d	91.b	$2$	$1$	$1$	$0.182$	$\Q$	$D_{3}$	$\Q(\sqrt{-91}) $	None	✓	✓			364.1.d.a	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-q^{5}+q^{7}+q^{9}+q^{13}-q^{19}-q^{23}+\cdots$
364.1.d.b	$364$	$1$	364.d	91.b	$2$	$1$	$1$	$0.182$	$\Q$	$D_{3}$	$\Q(\sqrt{-91}) $	None	✓	✓			364.1.d.a	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{5}-q^{7}+q^{9}-q^{13}+q^{19}-q^{23}+\cdots$
364.1.bl.a	$364$	$1$	364.bl	364.al	$6$	$2$	$1$	$0.182$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		✓			364.1.bl.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
364.1.bl.b	$364$	$1$	364.bl	364.al	$6$	$2$	$1$	$0.182$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		✓			364.1.bl.a	$4$	$0$	$1$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-q^{8}-\zeta_{6}q^{9}+\cdots$
364.2.a.a	$364$	$2$	364.a	1.a	$1$	$1$	$1$	$2.907$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	364.2.a.a	$1$	$1$	$0$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
364.2.a.b	$364$	$2$	364.a	1.a	$1$	$1$	$1$	$2.907$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	364.2.a.b	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots$
364.2.a.c	$364$	$2$	364.a	1.a	$1$	$2$	$2$	$2.907$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓	✓	✓	364.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+3q^{9}+\cdots$
364.2.a.d	$364$	$2$	364.a	1.a	$1$	$2$	$2$	$2.907$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	364.2.a.d	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots$
364.2.f.a	$364$	$2$	364.f	28.d	$2$	$4$	$4$	$2.907$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			364.2.f.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+\cdots$
364.2.f.b	$364$	$2$	364.f	28.d	$2$	$16$	$16$	$2.907$	16.0.$\cdots$.1	$_{}$	None	None		✓			364.2.f.b	$4$	$0$	$2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{8}-\beta _{11})q^{3}-\beta _{10}q^{4}+\cdots$
364.2.f.c	$364$	$2$	364.f	28.d	$2$	$28$	$28$	$2.907$		$_{}$	None	None		✓	✓		364.2.f.c	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
364.2.g.a	$364$	$2$	364.g	13.b	$2$	$8$	$8$	$2.907$	8.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	364.2.g.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{4})q^{5}+\beta _{3}q^{7}+\cdots$
364.2.h.a	$364$	$2$	364.h	364.h	$2$	$4$	$4$	$2.907$	$\Q(\sqrt{2}, \sqrt{-13})$	$_{}$	$\Q(\sqrt{-13}) $	None		✓			364.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots$
364.2.h.b	$364$	$2$	364.h	364.h	$2$	$48$	$48$	$2.907$		$_{}$	None	None		✓	✓		364.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
364.2.i.a	$364$	$2$	364.i	91.h	$3$	$18$	$9$	$2.907$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.i.a	$2$	$0$	$0$	$-1$	$0$	$4$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(\beta _{5}+\beta _{8})q^{5}-\beta _{14}q^{7}+(-\beta _{6}+\cdots)q^{9}+\cdots$
364.2.j.a	$364$	$2$	364.j	7.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.j.a	$2$	$0$	$0$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
364.2.j.b	$364$	$2$	364.j	7.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.j.b	$2$	$0$	$0$	$-1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
364.2.j.c	$364$	$2$	364.j	7.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.j.c	$2$	$0$	$0$	$2$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
364.2.j.d	$364$	$2$	364.j	7.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.j.d	$2$	$0$	$0$	$3$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
364.2.j.e	$364$	$2$	364.j	7.c	$3$	$8$	$4$	$2.907$	8.0.856615824.2	$_{}$	None	None		✓	✓		364.2.j.e	$2$	$0$	$0$	$-3$	$1$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
364.2.k.a	$364$	$2$	364.k	13.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.k.a	$2$	$0$	$0$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots$
364.2.k.b	$364$	$2$	364.k	13.c	$3$	$2$	$1$	$2.907$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			364.2.k.b	$2$	$0$	$0$	$0$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots$
364.2.k.c	$364$	$2$	364.k	13.c	$3$	$4$	$2$	$2.907$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			364.2.k.c	$2$	$0$	$0$	$-1$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
364.2.k.d	$364$	$2$	364.k	13.c	$3$	$4$	$2$	$2.907$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			364.2.k.d	$2$	$0$	$0$	$1$	$-6$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(-2+\beta _{2})q^{5}+\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots$
364.2.l.a	$364$	$2$	364.l	91.g	$3$	$18$	$9$	$2.907$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.i.a	$2$	$0$	$0$	$2$	$0$	$1$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{3}-\beta _{8}q^{5}+\beta _{10}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$
364.2.m.a	$364$	$2$	364.m	52.f	$4$	$84$	$42$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.m.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
364.2.n.a	$364$	$2$	364.n	91.i	$4$	$16$	$8$	$2.907$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.n.a	$4$	$0$	$0$	$0$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{9}q^{3}+(-\beta _{5}-\beta _{13})q^{5}+\beta _{8}q^{7}+\cdots$
364.2.u.a	$364$	$2$	364.u	13.e	$6$	$16$	$8$	$2.907$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.u.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{2}+\beta _{14})q^{3}+(\beta _{2}+\beta _{12}-\beta _{13}+\cdots)q^{5}+\cdots$
364.2.v.a	$364$	$2$	364.v	364.v	$6$	$4$	$2$	$2.907$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			364.2.v.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
364.2.v.b	$364$	$2$	364.v	364.v	$6$	$4$	$2$	$2.907$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			364.2.v.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
364.2.v.c	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.592240896.1	$_{}$	None	None		✓			364.2.v.c	$4$	$0$	$-4$	$-6$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}-\beta _{3})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\cdots$
364.2.v.d	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.592240896.1	$_{}$	None	None		✓			364.2.v.c	$4$	$0$	$-4$	$6$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{2}+\beta _{3}+\beta _{7})q^{2}+(1-2\beta _{3}+\cdots)q^{3}+\cdots$
364.2.v.e	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.49787136.1	$_{}$	None	None		✓			364.2.v.e	$8$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+(\beta _{3}-2\beta _{7})q^{3}+\cdots$
364.2.v.f	$364$	$2$	364.v	364.v	$6$	$72$	$36$	$2.907$		$_{}$	None	None		✓	✓		364.2.v.f	$8$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.w.a	$364$	$2$	364.w	364.w	$6$	$104$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.x.a	$364$	$2$	364.x	364.x	$6$	$8$	$4$	$2.907$	8.0.$\cdots$.6	$_{}$	$\Q(\sqrt{-13}) $	None		✓			364.2.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-\beta _{2}+\beta _{6})q^{2}+(-2+2\beta _{3})q^{4}+\cdots$
364.2.x.b	$364$	$2$	364.x	364.x	$6$	$96$	$48$	$2.907$		$_{}$	None	None		✓	✓		364.2.x.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.y.a	$364$	$2$	364.y	91.r	$6$	$8$	$4$	$2.907$	8.0.$\cdots$.8	$_{}$	None	None		✓			364.2.y.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+\cdots$
364.2.y.b	$364$	$2$	364.y	91.r	$6$	$12$	$6$	$2.907$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		364.2.y.b	$4$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{3}+(-\beta _{7}-\beta _{8}-\beta _{9}-\beta _{11})q^{5}+\cdots$
364.2.z.a	$364$	$2$	364.z	28.f	$6$	$96$	$48$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.z.a	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.ba.a	$364$	$2$	364.ba	364.aa	$6$	$104$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.ba.a	$4$	$0$	$-2$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.bb.a	$364$	$2$	364.bb	91.k	$6$	$18$	$9$	$2.907$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.bb.a	$2$	$0$	$0$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{5}+(-\beta _{7}-\beta _{13})q^{7}+\cdots$
364.2.bc.a	$364$	$2$	364.bc	364.ac	$6$	$104$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.bc.a	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.bp.a	$364$	$2$	364.bp	364.ap	$6$	$104$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.w.a	$4$	$0$	$-3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.bq.a	$364$	$2$	364.bq	91.u	$6$	$18$	$9$	$2.907$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	364.2.bb.a	$2$	$0$	$0$	$-2$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{3}+\beta _{11}q^{5}-\beta _{7}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
364.2.br.a	$364$	$2$	364.br	364.ar	$6$	$104$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.ba.a	$4$	$0$	$1$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
364.2.bs.a	$364$	$2$	364.bs	91.w	$12$	$36$	$9$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.bs.a	$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{12}]$
364.2.bt.a	$364$	$2$	364.bt	364.at	$12$	$208$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.bt.a	$4$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{12}]$
364.2.ca.a	$364$	$2$	364.ca	364.ba	$12$	$208$	$52$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.bt.a	$4$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{12}]$
364.2.cb.a	$364$	$2$	364.cb	91.ac	$12$	$40$	$10$	$2.907$		$_{}$	None	None		✓	✓	✓	364.2.cb.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$

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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.