LMFDB - Newform search results

Refine search

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

				Sort order	Select

Results (1-50 of 153 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
930.2.a.a	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓	✓	✓	930.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
930.2.a.b	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓	✓	✓	930.2.a.b	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
930.2.a.c	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.c	$1$	$1$	$-1$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
930.2.a.d	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.d	$1$	$1$	$-1$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
930.2.a.e	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓	✓	✓	930.2.a.e	$1$	$0$	$-1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
930.2.a.f	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.f	$1$	$0$	$-1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
930.2.a.g	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.g	$1$	$0$	$-1$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
930.2.a.h	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓	✓	✓	930.2.a.h	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
930.2.a.i	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.i	$1$	$0$	$-1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
930.2.a.j	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.j	$1$	$0$	$-1$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
930.2.a.k	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.k	$1$	$0$	$1$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
930.2.a.l	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓	✓	✓	930.2.a.l	$1$	$1$	$1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
930.2.a.m	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.m	$1$	$0$	$1$	$-1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots$
930.2.a.n	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.n	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
930.2.a.o	$930$	$2$	930.a	1.a	$1$	$1$	$1$	$7.426$	$\Q$	None	✓	✓			930.2.a.o	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
930.2.a.p	$930$	$2$	930.a	1.a	$1$	$2$	$2$	$7.426$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	930.2.a.p	$1$	$0$	$2$	$-2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots$
930.2.a.q	$930$	$2$	930.a	1.a	$1$	$2$	$2$	$7.426$	$\Q(\sqrt{65}) $	None	✓	✓	✓		930.2.a.q	$1$	$0$	$2$	$2$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots$
930.2.a.r	$930$	$2$	930.a	1.a	$1$	$2$	$2$	$7.426$	$\Q(\sqrt{33}) $	None	✓	✓	✓		930.2.a.r	$1$	$0$	$2$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$
930.2.d.a	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(2 i-1)q^{5}+\cdots$
930.2.d.b	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
930.2.d.c	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.c	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(2 i+1)q^{5}+\cdots$
930.2.d.d	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.d	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
930.2.d.e	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.e	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
930.2.d.f	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	$\Q(\sqrt{-1}) $	None		✓			930.2.d.f	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(-i+2)q^{5}+\cdots$
930.2.d.g	$930$	$2$	930.d	5.b	$2$	$4$	$4$	$7.426$	$\Q(\zeta_{8})$	None		✓			930.2.d.g	$2$	$0$	$0$	$0$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+\beta_1 q^{3}-q^{4}+(\beta_1+2)q^{5}+\cdots$
930.2.d.h	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.3534400.1	None		✓			930.2.d.h	$2$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots$
930.2.d.i	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.11669056.1	None		✓			930.2.d.i	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
930.2.e.a	$930$	$2$	930.e	465.g	$2$	$32$	$32$	$7.426$		None		✓			930.2.e.a	$4$	$0$	$-32$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
930.2.e.b	$930$	$2$	930.e	465.g	$2$	$32$	$32$	$7.426$		None		✓			930.2.e.a	$4$	$0$	$32$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
930.2.h.a	$930$	$2$	930.h	93.c	$2$	$4$	$4$	$7.426$	$\Q(i, \sqrt{6})$	None		✓			930.2.h.a	$4$	$0$	$0$	$0$	$0$	$-16$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
930.2.h.b	$930$	$2$	930.h	93.c	$2$	$4$	$4$	$7.426$	$\Q(\zeta_{12})$	None		✓			930.2.h.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}-\beta_{3} q^{3}-q^{4}-\beta_1 q^{5}+\cdots$
930.2.h.c	$930$	$2$	930.h	93.c	$2$	$16$	$16$	$7.426$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			930.2.h.c	$4$	$0$	$0$	$0$	$0$	$-20$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
930.2.h.d	$930$	$2$	930.h	93.c	$2$	$16$	$16$	$7.426$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			930.2.h.d	$4$	$0$	$0$	$0$	$0$	$4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-\beta _{12}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{5}q^{6}+\cdots$
930.2.i.a	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.a	$2$	$0$	$-2$	$-1$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots$
930.2.i.b	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.b	$2$	$0$	$-2$	$1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots$
930.2.i.c	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.c	$2$	$0$	$-2$	$1$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots$
930.2.i.d	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.d	$2$	$0$	$2$	$-1$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
930.2.i.e	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.e	$2$	$0$	$2$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
930.2.i.f	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.f	$2$	$0$	$2$	$-1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
930.2.i.g	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.g	$2$	$0$	$2$	$1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots$
930.2.i.h	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.h	$2$	$0$	$2$	$1$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots$
930.2.i.i	$930$	$2$	930.i	31.c	$3$	$2$	$1$	$7.426$	$\Q(\sqrt{-3}) $	None		✓			930.2.i.i	$2$	$0$	$2$	$1$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots$
930.2.i.j	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	$\Q(\sqrt{-3}, \sqrt{7})$	None		✓			930.2.i.j	$2$	$0$	$-4$	$-2$	$-2$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots$
930.2.i.k	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			930.2.i.k	$2$	$0$	$-4$	$-2$	$2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots$
930.2.i.l	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			930.2.i.l	$2$	$0$	$4$	$-2$	$2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots$
930.2.i.m	$930$	$2$	930.i	31.c	$3$	$4$	$2$	$7.426$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			930.2.i.m	$2$	$0$	$4$	$2$	$-2$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots$
930.2.i.n	$930$	$2$	930.i	31.c	$3$	$6$	$3$	$7.426$	6.0.3636603.4	None		✓	✓		930.2.i.n	$2$	$0$	$-6$	$3$	$-3$	$-4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots$
930.2.j.a	$930$	$2$	930.j	15.e	$4$	$4$	$2$	$7.426$	$\Q(\zeta_{8})$	None		✓			930.2.j.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
930.2.j.b	$930$	$2$	930.j	15.e	$4$	$4$	$2$	$7.426$	$\Q(\zeta_{8})$	None		✓			930.2.j.b	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
930.2.j.c	$930$	$2$	930.j	15.e	$4$	$8$	$4$	$7.426$	8.0.1698758656.6	None		✓			930.2.j.c	$2$	$0$	$0$	$-8$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 153 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.