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 265 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
315.1.bg.a	$315$	$1$	315.bg	315.ag	$6$	$2$	$1$	$0.157$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			315.1.bg.a	$4$	$0$	$0$	$-2$	$1$	$1$		$1$		$q-q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
315.1.bg.b	$315$	$1$	315.bg	315.ag	$6$	$2$	$1$	$0.157$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			315.1.bg.a	$4$	$0$	$0$	$2$	$-1$	$-1$		$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
315.2.a.a	$315$	$2$	315.a	1.a	$1$	$1$	$1$	$2.515$	$\Q$	$_{}$	None	None	✓		✓	✓	105.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots$
315.2.a.b	$315$	$2$	315.a	1.a	$1$	$1$	$1$	$2.515$	$\Q$	$_{}$	None	None	✓				35.2.a.a	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}+3q^{11}+5q^{13}+\cdots$
315.2.a.c	$315$	$2$	315.a	1.a	$1$	$2$	$2$	$2.515$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	315.2.a.c	$1$	$1$	$-2$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-q^{7}+\cdots$
315.2.a.d	$315$	$2$	315.a	1.a	$1$	$2$	$2$	$2.515$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		105.2.a.b	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}+q^{5}+q^{7}-\beta q^{8}-\beta q^{10}+\cdots$
315.2.a.e	$315$	$2$	315.a	1.a	$1$	$2$	$2$	$2.515$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓	✓	35.2.a.b	$1$	$0$	$1$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots$
315.2.a.f	$315$	$2$	315.a	1.a	$1$	$2$	$2$	$2.515$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	315.2.a.c	$1$	$0$	$2$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-q^{7}+\cdots$
315.2.b.a	$315$	$2$	315.b	21.c	$2$	$4$	$4$	$2.515$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			315.2.b.a	$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots$
315.2.b.b	$315$	$2$	315.b	21.c	$2$	$4$	$4$	$2.515$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			315.2.b.a	$2$	$0$	$0$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots$
315.2.d.a	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	$\Q(\sqrt{-1}) $	$_{}$	None	None					35.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}+(-i+2)q^{5}+i q^{7}+\cdots$
315.2.d.b	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			315.2.d.b	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(i-2)q^{5}+i q^{7}+\cdots$
315.2.d.c	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	$\Q(\sqrt{-1}) $	$_{}$	None	None					105.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(-2 i-1)q^{5}-i q^{7}+\cdots$
315.2.d.d	$315$	$2$	315.d	5.b	$2$	$2$	$2$	$2.515$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			315.2.d.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(i+2)q^{5}-i q^{7}+\cdots$
315.2.d.e	$315$	$2$	315.d	5.b	$2$	$6$	$6$	$2.515$	6.0.350464.1	$_{}$	None	None			✓		105.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
315.2.g.a	$315$	$2$	315.g	105.g	$2$	$16$	$16$	$2.515$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	315.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(1+\beta _{14})q^{4}-\beta _{4}q^{5}-\beta _{12}q^{7}+\cdots$
315.2.i.a	$315$	$2$	315.i	9.c	$3$	$2$	$1$	$2.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			315.2.i.a	$2$	$1$	$-2$	$-3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
315.2.i.b	$315$	$2$	315.i	9.c	$3$	$2$	$1$	$2.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			315.2.i.b	$2$	$0$	$0$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
315.2.i.c	$315$	$2$	315.i	9.c	$3$	$8$	$4$	$2.515$	8.0.142635249.1	$_{}$	None	None		✓			315.2.i.c	$2$	$0$	$1$	$-1$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\cdots$
315.2.i.d	$315$	$2$	315.i	9.c	$3$	$8$	$4$	$2.515$	$\Q(\zeta_{15})$	$_{}$	None	None		✓			315.2.i.d	$2$	$0$	$1$	$3$	$4$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{3}-\beta_{2}+\beta_1+1)q^{2}+(-\beta_{6}-\beta_{4}+1)q^{3}+\cdots$
315.2.i.e	$315$	$2$	315.i	9.c	$3$	$12$	$6$	$2.515$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			315.2.i.e	$2$	$0$	$3$	$1$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{9}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
315.2.i.f	$315$	$2$	315.i	9.c	$3$	$16$	$8$	$2.515$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		315.2.i.f	$2$	$0$	$1$	$1$	$-8$	$8$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{13})q^{2}+\beta _{5}q^{3}+(-2-2\beta _{3}+\cdots)q^{4}+\cdots$
315.2.j.a	$315$	$2$	315.j	7.c	$3$	$2$	$1$	$2.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.b	$2$	$0$	$-2$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
315.2.j.b	$315$	$2$	315.j	7.c	$3$	$2$	$1$	$2.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.a	$2$	$0$	$0$	$0$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
315.2.j.c	$315$	$2$	315.j	7.c	$3$	$4$	$2$	$2.515$	$\Q(\zeta_{12})$	$_{}$	None	None					105.2.i.d	$2$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$
315.2.j.d	$315$	$2$	315.j	7.c	$3$	$4$	$2$	$2.515$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					105.2.i.c	$2$	$0$	$0$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
315.2.j.e	$315$	$2$	315.j	7.c	$3$	$4$	$2$	$2.515$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					35.2.e.a	$2$	$0$	$2$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$
315.2.j.f	$315$	$2$	315.j	7.c	$3$	$6$	$3$	$2.515$	6.0.4406832.1	$_{}$	None	None		✓			315.2.j.f	$2$	$0$	$-2$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
315.2.j.g	$315$	$2$	315.j	7.c	$3$	$6$	$3$	$2.515$	6.0.4406832.1	$_{}$	None	None		✓			315.2.j.f	$2$	$0$	$2$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
315.2.k.a	$315$	$2$	315.k	63.g	$3$	$4$	$2$	$2.515$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			315.2.k.a	$2$	$0$	$1$	$0$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
315.2.k.b	$315$	$2$	315.k	63.g	$3$	$24$	$12$	$2.515$		$_{}$	None	None		✓			315.2.k.b	$2$	$0$	$-1$	$1$	$-24$	$7$			$\mathrm{SU}(2)[C_{3}]$
315.2.k.c	$315$	$2$	315.k	63.g	$3$	$36$	$18$	$2.515$		$_{}$	None	None		✓	✓		315.2.k.c	$2$	$0$	$0$	$-1$	$36$	$-1$			$\mathrm{SU}(2)[C_{3}]$
315.2.l.a	$315$	$2$	315.l	63.h	$3$	$4$	$2$	$2.515$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			315.2.k.a	$2$	$0$	$-2$	$6$	$2$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(2-\beta _{3})q^{4}+\cdots$
315.2.l.b	$315$	$2$	315.l	63.h	$3$	$24$	$12$	$2.515$		$_{}$	None	None		✓			315.2.k.b	$2$	$0$	$2$	$-5$	$12$	$-11$			$\mathrm{SU}(2)[C_{3}]$
315.2.l.c	$315$	$2$	315.l	63.h	$3$	$36$	$18$	$2.515$		$_{}$	None	None		✓	✓		315.2.k.c	$2$	$0$	$0$	$-1$	$-18$	$-1$			$\mathrm{SU}(2)[C_{3}]$
315.2.m.a	$315$	$2$	315.m	15.e	$4$	$12$	$6$	$2.515$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			315.2.m.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(\beta _{5}+\beta _{6}-\beta _{8})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
315.2.m.b	$315$	$2$	315.m	15.e	$4$	$12$	$6$	$2.515$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			315.2.m.a	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}+\beta _{8}+\beta _{9})q^{2}+(-\beta _{5}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$
315.2.p.a	$315$	$2$	315.p	35.f	$4$	$4$	$2$	$2.515$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			315.2.p.a	$4$	$0$	$0$	$0$	$-8$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-2+\beta _{2})q^{5}+\cdots$
315.2.p.b	$315$	$2$	315.p	35.f	$4$	$4$	$2$	$2.515$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			315.2.p.a	$4$	$0$	$0$	$0$	$8$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$
315.2.p.c	$315$	$2$	315.p	35.f	$4$	$4$	$2$	$2.515$	$\Q(i, \sqrt{10})$	$_{}$	None	None					35.2.f.a	$4$	$0$	$4$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+\beta _{1}q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots$
315.2.p.d	$315$	$2$	315.p	35.f	$4$	$8$	$4$	$2.515$	$\Q(i, \sqrt{2}, \sqrt{5})$	$_{}$	None	None		✓			315.2.p.d	$8$	$0$	$0$	$0$	$0$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{4}+\beta _{5}q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots$
315.2.p.e	$315$	$2$	315.p	35.f	$4$	$16$	$8$	$2.515$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		105.2.m.a	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(-\beta _{6}-\beta _{7}+\beta _{13})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
315.2.r.a	$315$	$2$	315.r	315.r	$6$	$4$	$2$	$2.515$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			315.2.r.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}^{3}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+q^{4}+\cdots$
315.2.r.b	$315$	$2$	315.r	315.r	$6$	$84$	$42$	$2.515$		$_{}$	None	None		✓	✓		315.2.r.b	$4$	$0$	$0$	$0$	$3$	$0$			$\mathrm{SU}(2)[C_{6}]$
315.2.t.a	$315$	$2$	315.t	63.i	$6$	$2$	$1$	$2.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			315.2.t.a	$2$	$0$	$0$	$-3$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-q^{4}+\cdots$
315.2.t.b	$315$	$2$	315.t	63.i	$6$	$30$	$15$	$2.515$		$_{}$	None	None		✓			315.2.t.b	$2$	$0$	$0$	$4$	$15$	$-3$			$\mathrm{SU}(2)[C_{6}]$
315.2.t.c	$315$	$2$	315.t	63.i	$6$	$32$	$16$	$2.515$		$_{}$	None	None		✓	✓		315.2.t.c	$2$	$0$	$0$	$-1$	$-16$	$1$			$\mathrm{SU}(2)[C_{6}]$
315.2.u.a	$315$	$2$	315.u	315.u	$6$	$88$	$44$	$2.515$		$_{}$	None	None		✓	✓	✓	315.2.u.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
315.2.z.a	$315$	$2$	315.z	315.z	$6$	$8$	$4$	$2.515$	$\Q(\sqrt{-3}, \sqrt{-5}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-35}) $	None		✓			315.2.z.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{5}q^{3}+(2+2\beta _{4})q^{4}+(\beta _{1}-\beta _{6})q^{5}+\cdots$
315.2.z.b	$315$	$2$	315.z	315.z	$6$	$80$	$40$	$2.515$		$_{}$	None	None		✓	✓		315.2.z.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.