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 291 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
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	112.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}+i q^{7}-i q^{8}-i q^{9}+\cdots$
112.2.a.a	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	$_{}$	None	None	✓		✓	✓	56.2.a.b	$1$	$1$	$0$	$-2$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots$
112.2.a.b	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	$_{}$	None	None	✓		✓	✓	56.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots$
112.2.a.c	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	$_{}$	None	None	✓		✓	✓	14.2.a.a	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}-4q^{13}+6q^{17}+\cdots$
112.2.f.a	$112$	$2$	112.f	28.d	$2$	$2$	$2$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			112.2.f.a	$2$	$0$	$0$	$-4$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}-2\beta q^{5}+(-\beta+2)q^{7}+q^{9}+\cdots$
112.2.f.b	$112$	$2$	112.f	28.d	$2$	$2$	$2$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			112.2.f.a	$2$	$0$	$0$	$4$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{3}+2\beta q^{5}+(-\beta-2)q^{7}+q^{9}+\cdots$
112.2.i.a	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None					56.2.i.b	$2$	$0$	$0$	$-1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
112.2.i.b	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$0$	$0$	$1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
112.2.i.c	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None					56.2.i.a	$2$	$0$	$0$	$3$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
112.2.j.a	$112$	$2$	112.j	112.j	$4$	$4$	$2$	$0.894$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			112.2.j.a	$4$	$0$	$-4$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots$
112.2.j.b	$112$	$2$	112.j	112.j	$4$	$4$	$2$	$0.894$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			112.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots$
112.2.j.c	$112$	$2$	112.j	112.j	$4$	$4$	$2$	$0.894$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			112.2.j.c	$4$	$0$	$4$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1+1)q^{2}+(-\beta_{3}+\beta_{2})q^{3}+\cdots$
112.2.j.d	$112$	$2$	112.j	112.j	$4$	$16$	$8$	$0.894$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		112.2.j.d	$4$	$0$	$-4$	$0$	$0$	$8$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{9}q^{2}+\beta _{15}q^{3}+(-1-\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
112.2.m.a	$112$	$2$	112.m	16.e	$4$	$2$	$1$	$0.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			112.2.m.a	$2$	$1$	$-2$	$-4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+(2 i-2)q^{3}-2 i q^{4}+\cdots$
112.2.m.b	$112$	$2$	112.m	16.e	$4$	$2$	$1$	$0.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			112.2.m.b	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
112.2.m.c	$112$	$2$	112.m	16.e	$4$	$8$	$4$	$0.894$	8.0.214798336.3	$_{}$	None	None		✓			112.2.m.c	$2$	$0$	$2$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots$
112.2.m.d	$112$	$2$	112.m	16.e	$4$	$12$	$6$	$0.894$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓		112.2.m.d	$2$	$0$	$2$	$4$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{10})q^{3}+\beta _{1}q^{4}+\cdots$
112.2.p.a	$112$	$2$	112.p	28.f	$6$	$2$	$1$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			112.2.p.a	$2$	$0$	$0$	$-1$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
112.2.p.b	$112$	$2$	112.p	28.f	$6$	$2$	$1$	$0.894$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			112.2.p.a	$2$	$0$	$0$	$1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
112.2.p.c	$112$	$2$	112.p	28.f	$6$	$4$	$2$	$0.894$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		✓	✓		112.2.p.c	$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$
112.2.v.a	$112$	$2$	112.v	112.v	$12$	$56$	$14$	$0.894$		$_{}$	None	None		✓	✓	✓	112.2.v.a	$4$	$0$	$-2$	$-6$	$-6$	$-8$			$\mathrm{SU}(2)[C_{12}]$
112.2.w.a	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			112.2.w.a	$2$	$0$	$-2$	$-4$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$
112.2.w.b	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			112.2.w.a	$2$	$0$	$4$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
112.2.w.c	$112$	$2$	112.w	112.w	$12$	$48$	$12$	$0.894$		$_{}$	None	None		✓	✓		112.2.w.c	$4$	$0$	$-4$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{12}]$
112.3.c.a	$112$	$3$	112.c	7.b	$2$	$1$	$1$	$3.052$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓				7.3.b.a	$2$	$0$	$0$	$0$	$0$	$7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{7}+9q^{9}+6q^{11}-18q^{23}+5^{2}q^{25}+\cdots$
112.3.c.b	$112$	$3$	112.c	7.b	$2$	$2$	$2$	$3.052$	$\Q(\sqrt{-6}) $	$_{}$	None	None					28.3.b.a	$2$	$0$	$0$	$0$	$0$	$-10$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}+(-5-\beta )q^{7}-15q^{9}+\cdots$
112.3.c.c	$112$	$3$	112.c	7.b	$2$	$4$	$4$	$3.052$	4.0.2048.2	$_{}$	None	None			✓		56.3.c.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
112.3.d.a	$112$	$3$	112.d	4.b	$2$	$2$	$2$	$3.052$	$\Q(\sqrt{-7}) $	$_{}$	None	None		✓			112.3.d.a	$2$	$0$	$0$	$0$	$16$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{3}+8q^{5}+\beta q^{7}-19q^{9}-4\beta q^{11}+\cdots$
112.3.d.b	$112$	$3$	112.d	4.b	$2$	$4$	$4$	$3.052$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓	✓		112.3.d.b	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots$
112.3.k.a	$112$	$3$	112.k	16.f	$4$	$48$	$24$	$3.052$		$_{}$	None	None		✓	✓	✓	112.3.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
112.3.l.a	$112$	$3$	112.l	112.l	$4$	$4$	$2$	$3.052$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			112.3.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(-2+3\beta _{2})q^{4}+7\beta _{3}q^{7}+\cdots$
112.3.l.b	$112$	$3$	112.l	112.l	$4$	$56$	$28$	$3.052$		$_{}$	None	None		✓	✓		112.3.l.b	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
112.3.r.a	$112$	$3$	112.r	28.g	$6$	$4$	$2$	$3.052$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			112.3.r.a	$4$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(3\beta _{1}-\beta _{3})q^{7}-2\beta _{2}q^{9}+\cdots$
112.3.r.b	$112$	$3$	112.r	28.g	$6$	$6$	$3$	$3.052$	6.0.259470000.1	$_{}$	None	None		✓			112.3.r.b	$2$	$0$	$0$	$-3$	$-1$	$-14$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
112.3.r.c	$112$	$3$	112.r	28.g	$6$	$6$	$3$	$3.052$	6.0.259470000.1	$_{}$	None	None		✓			112.3.r.b	$2$	$0$	$0$	$3$	$-1$	$14$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
112.3.s.a	$112$	$3$	112.s	7.d	$6$	$2$	$1$	$3.052$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.3.h.a	$2$	$0$	$0$	$-3$	$3$	$14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+7q^{7}+\cdots$
112.3.s.b	$112$	$3$	112.s	7.d	$6$	$4$	$2$	$3.052$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					14.3.d.a	$2$	$0$	$0$	$6$	$-6$	$-8$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(2+\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
112.3.s.c	$112$	$3$	112.s	7.d	$6$	$8$	$4$	$3.052$	8.0.$\cdots$.2	$_{}$	None	None			✓		56.3.o.a	$2$	$0$	$0$	$0$	$0$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{3}-\beta _{7}q^{5}+(2-3\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
112.3.u.a	$112$	$3$	112.u	112.u	$12$	$120$	$30$	$3.052$		$_{}$	None	None		✓	✓	✓	112.3.u.a	$4$	$0$	$-2$	$-2$	$-2$	$-8$			$\mathrm{SU}(2)[C_{12}]$
112.3.x.a	$112$	$3$	112.x	112.x	$12$	$120$	$30$	$3.052$		$_{}$	None	None		✓	✓	✓	112.3.x.a	$4$	$0$	$-2$	$-6$	$-6$	$0$			$\mathrm{SU}(2)[C_{12}]$
112.4.a.a	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				14.4.a.a	$1$	$0$	$0$	$-8$	$-14$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}-14q^{5}+7q^{7}+37q^{9}+28q^{11}+\cdots$
112.4.a.b	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				56.4.a.b	$1$	$1$	$0$	$-6$	$8$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{3}+8q^{5}+7q^{7}+9q^{9}-56q^{11}+\cdots$
112.4.a.c	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				28.4.a.b	$1$	$1$	$0$	$-4$	$6$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+6q^{5}-7q^{7}-11q^{9}+12q^{11}+\cdots$
112.4.a.d	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				56.4.a.a	$1$	$1$	$0$	$2$	$-16$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2^{4}q^{5}+7q^{7}-23q^{9}-24q^{11}+\cdots$
112.4.a.e	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				14.4.a.b	$1$	$1$	$0$	$2$	$-12$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-12q^{5}-7q^{7}-23q^{9}-48q^{11}+\cdots$
112.4.a.f	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				7.4.a.a	$1$	$0$	$0$	$2$	$16$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2^{4}q^{5}+7q^{7}-23q^{9}+8q^{11}+\cdots$
112.4.a.g	$112$	$4$	112.a	1.a	$1$	$1$	$1$	$6.608$	$\Q$	$_{}$	None	None	✓				28.4.a.a	$1$	$0$	$0$	$10$	$-8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+10q^{3}-8q^{5}+7q^{7}+73q^{9}+40q^{11}+\cdots$
112.4.a.h	$112$	$4$	112.a	1.a	$1$	$2$	$2$	$6.608$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓		✓	✓	56.4.a.c	$1$	$0$	$0$	$2$	$22$	$-14$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(11+\beta )q^{5}-7q^{7}+(31+\cdots)q^{9}+\cdots$
112.4.f.a	$112$	$4$	112.f	28.d	$2$	$4$	$4$	$6.608$	$\Q(\sqrt{-5}, \sqrt{7})$	$_{}$	None	None		✓			112.4.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
112.4.f.b	$112$	$4$	112.f	28.d	$2$	$8$	$8$	$6.608$	8.0.$\cdots$.7	$_{}$	None	None		✓	✓		112.4.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+2\beta _{3}-\beta _{7})q^{7}+\cdots$

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 291 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.