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 373 matches)

Next Download displayed columns for results to

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
336.1.o.a	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	✓			336.1.o.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots$
336.1.o.b	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	✓			336.1.o.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{9}-2q^{19}-q^{21}-q^{25}+\cdots$
336.1.z.a	$336$	$1$	336.z	84.j	$6$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			336.1.z.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots$
336.1.z.b	$336$	$1$	336.z	84.j	$6$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			336.1.z.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots$
336.1.bn.a	$336$	$1$	336.bn	21.h	$6$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	84.1.p.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
336.2.a.a	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓		✓	✓	21.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
336.2.a.b	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓		✓	✓	84.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$
336.2.a.c	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓		✓	✓	168.2.a.b	$1$	$0$	$0$	$-1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$
336.2.a.d	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓				42.2.a.a	$1$	$0$	$0$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
336.2.a.e	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓		✓	✓	168.2.a.a	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots$
336.2.a.f	$336$	$2$	336.a	1.a	$1$	$1$	$1$	$2.683$	$\Q$	$_{}$	None	None	✓				84.2.a.a	$1$	$0$	$0$	$1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
336.2.b.a	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			336.2.b.a	$2$	$0$	$0$	$-2$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-\beta-2)q^{7}+q^{9}-2\beta q^{11}+\cdots$
336.2.b.b	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	$\Q(\sqrt{-6}) $	$_{}$	None	None		✓			336.2.b.b	$2$	$0$	$0$	$-2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
336.2.b.c	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	$\Q(\sqrt{-6}) $	$_{}$	None	None		✓			336.2.b.b	$2$	$0$	$0$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
336.2.b.d	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			336.2.b.a	$2$	$0$	$0$	$2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(\beta+2)q^{7}+q^{9}+2\beta q^{11}+\cdots$
336.2.h.a	$336$	$2$	336.h	12.b	$2$	$4$	$4$	$2.683$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			336.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{3}+\beta_1)q^{3}-\beta_{2} q^{5}-\beta_1 q^{7}+\cdots$
336.2.h.b	$336$	$2$	336.h	12.b	$2$	$8$	$8$	$2.683$	8.0.56070144.2	$_{}$	None	None		✓	✓		336.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots$
336.2.k.a	$336$	$2$	336.k	21.c	$2$	$2$	$2$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					84.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+(-\beta-2)q^{7}-3 q^{9}-4\beta q^{13}+\cdots$
336.2.k.b	$336$	$2$	336.k	21.c	$2$	$4$	$4$	$2.683$	$\Q(i, \sqrt{6})$	$_{}$	None	None					42.2.d.a	$4$	$0$	$0$	$0$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots$
336.2.k.c	$336$	$2$	336.k	21.c	$2$	$8$	$8$	$2.683$	8.0.342102016.5	$_{}$	None	None			✓		168.2.k.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots$
336.2.q.a	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					168.2.q.b	$2$	$1$	$0$	$-1$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
336.2.q.b	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					42.2.e.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
336.2.q.c	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.i.a	$2$	$0$	$0$	$-1$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$
336.2.q.d	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					42.2.e.b	$2$	$0$	$0$	$1$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$
336.2.q.e	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					168.2.q.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
336.2.q.f	$336$	$2$	336.q	7.c	$3$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.e.a	$2$	$0$	$0$	$1$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
336.2.q.g	$336$	$2$	336.q	7.c	$3$	$4$	$2$	$2.683$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None			✓		168.2.q.c	$2$	$0$	$0$	$-2$	$1$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
336.2.s.a	$336$	$2$	336.s	48.k	$4$	$4$	$2$	$2.683$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			336.2.s.a	$2$	$1$	$-4$	$-4$	$-4$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1-1)q^{2}+(\beta_{2}-1)q^{3}-2\beta_1 q^{4}+\cdots$
336.2.s.b	$336$	$2$	336.s	48.k	$4$	$4$	$2$	$2.683$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			336.2.s.a	$2$	$0$	$4$	$0$	$4$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1+1)q^{2}+(-\beta_{3}-\beta_1)q^{3}+\cdots$
336.2.s.c	$336$	$2$	336.s	48.k	$4$	$40$	$20$	$2.683$		$_{}$	None	None		✓			336.2.s.c	$4$	$0$	$0$	$4$	$0$	$-40$			$\mathrm{SU}(2)[C_{4}]$
336.2.s.d	$336$	$2$	336.s	48.k	$4$	$48$	$24$	$2.683$		$_{}$	None	None		✓	✓		336.2.s.d	$4$	$0$	$0$	$0$	$0$	$48$			$\mathrm{SU}(2)[C_{4}]$
336.2.u.a	$336$	$2$	336.u	112.j	$4$	$64$	$32$	$2.683$		$_{}$	None	None		✓	✓	✓	336.2.u.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
336.2.w.a	$336$	$2$	336.w	16.e	$4$	$20$	$10$	$2.683$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			336.2.w.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}-\beta _{7}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6}-\beta _{16}+\cdots)q^{4}+\cdots$
336.2.w.b	$336$	$2$	336.w	16.e	$4$	$28$	$14$	$2.683$		$_{}$	None	None		✓	✓		336.2.w.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
336.2.y.a	$336$	$2$	336.y	336.y	$4$	$120$	$60$	$2.683$		$_{}$	None	None		✓	✓	✓	336.2.y.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
336.2.bc.a	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					84.2.k.c	$4$	$0$	$0$	$-3$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
336.2.bc.b	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.k.a	$2$	$0$	$0$	$0$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
336.2.bc.c	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					21.2.g.a	$4$	$0$	$0$	$3$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
336.2.bc.d	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.k.a	$2$	$0$	$0$	$3$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
336.2.bc.e	$336$	$2$	336.bc	21.g	$6$	$4$	$2$	$2.683$	$\Q(\zeta_{12})$	$_{}$	None	None					42.2.f.a	$4$	$0$	$0$	$0$	$0$	$10$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta_{2} q^{3}+(\beta_{3}-\beta_{2})q^{5}+(\beta_1+2)q^{7}+\cdots$
336.2.bc.f	$336$	$2$	336.bc	21.g	$6$	$16$	$8$	$2.683$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		168.2.u.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots$
336.2.bj.a	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			336.2.bj.a	$4$	$1$	$0$	$-3$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots$
336.2.bj.b	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			336.2.bj.b	$4$	$0$	$0$	$-3$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$
336.2.bj.c	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			336.2.bj.b	$4$	$0$	$0$	$3$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(2-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$
336.2.bj.d	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			336.2.bj.a	$4$	$0$	$0$	$3$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(2-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$
336.2.bj.e	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.8275904784.2	$_{}$	None	None		✓			336.2.bj.e	$4$	$0$	$0$	$-3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
336.2.bj.f	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.303595776.1	$_{}$	None	None		✓			336.2.bj.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(1-2\beta _{2}+\beta _{4}+2\beta _{6})q^{5}+\cdots$
336.2.bj.g	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.8275904784.2	$_{}$	None	None		✓			336.2.bj.e	$4$	$0$	$0$	$3$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots$
336.2.bl.a	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			336.2.bl.a	$2$	$1$	$0$	$-1$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$
336.2.bl.b	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			336.2.bl.b	$2$	$1$	$0$	$-1$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots$

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 373 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.