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 239 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
300.1.b.a	$300$	$1$	300.b	15.d	$2$	$2$	$2$	$0.150$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	300.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-i q^{7}-q^{9}+i q^{13}+q^{19}+\cdots$
300.1.g.a	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			300.1.g.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots$
300.1.g.b	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			300.1.g.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		✓	✓	✓	300.1.l.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
300.2.a.a	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓		✓	✓	60.2.d.a	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots$
300.2.a.b	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	300.2.a.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots$
300.2.a.c	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	✓			300.2.a.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots$
300.2.a.d	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓				60.2.d.a	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots$
300.2.d.a	$300$	$2$	300.d	5.b	$2$	$2$	$2$	$2.396$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	✓	✓	300.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{7}-q^{9}+6 q^{11}+5 i q^{13}+\cdots$
300.2.e.a	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None					60.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$
300.2.e.b	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None					60.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots$
300.2.e.c	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None					60.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
300.2.e.d	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	$_{}$	None	None		✓			300.2.e.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.e.e	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	$_{}$	None	None		✓			300.2.e.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.h.a	$300$	$2$	300.h	60.h	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None					60.2.e.a	$4$	$0$	$-2$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.b	$300$	$2$	300.h	60.h	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None					60.2.e.a	$4$	$0$	$2$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.c	$300$	$2$	300.h	60.h	$2$	$16$	$16$	$2.396$	16.0.$\cdots$.3	$_{}$	None	None		✓	✓		300.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots$
300.2.i.a	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{5})$	$_{}$	None	None					60.2.i.a	$4$	$0$	$0$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
300.2.i.b	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			300.2.i.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots$
300.2.i.c	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			300.2.i.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots$
300.2.j.a	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			300.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{5}-\beta_{4}+\beta_1)q^{2}+\beta_1 q^{3}+(\beta_{6}-\beta_{2})q^{4}+\cdots$
300.2.j.b	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	$\Q(i, \sqrt{2}, \sqrt{7})$	$_{}$	None	None		✓			300.2.j.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots$
300.2.j.c	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			300.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta_{7}-\beta_1)q^{2}-\beta_{5} q^{3}+(-\beta_{6}+\beta_{2})q^{4}+\cdots$
300.2.j.d	$300$	$2$	300.j	20.e	$4$	$12$	$6$	$2.396$	12.0.$\cdots$.1	$_{}$	None	None			✓		60.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots$
300.2.m.a	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	$\Q(\zeta_{15})$	$_{}$	None	None		✓			300.2.m.a	$2$	$0$	$0$	$-2$	$5$	$-8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta_{5} q^{3}+(\beta_{7}-\beta_{6}-\beta_{5}+\cdots-1)q^{5}+\cdots$
300.2.m.b	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	8.0.26265625.1	$_{}$	None	None		✓			300.2.m.b	$2$	$0$	$0$	$2$	$-5$	$8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
300.2.n.a	$300$	$2$	300.n	300.n	$10$	$224$	$56$	$2.396$		$_{}$	None	None		✓	✓	✓	300.2.n.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.o.a	$300$	$2$	300.o	25.e	$10$	$24$	$6$	$2.396$		$_{}$	None	None		✓	✓	✓	300.2.o.a	$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.r.a	$300$	$2$	300.r	300.r	$10$	$224$	$56$	$2.396$		$_{}$	None	None		✓	✓	✓	300.2.r.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.w.a	$300$	$2$	300.w	100.l	$20$	$240$	$30$	$2.396$		$_{}$	None	None		✓	✓	✓	300.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
300.2.x.a	$300$	$2$	300.x	75.l	$20$	$80$	$10$	$2.396$		$_{}$	None	None		✓	✓	✓	300.2.x.a	$4$	$0$	$0$	$-2$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
300.3.b.a	$300$	$3$	300.b	15.d	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None					12.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3 i q^{3}+2 i q^{7}-9 q^{9}+22 i q^{13}+\cdots$
300.3.b.b	$300$	$3$	300.b	15.d	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			300.3.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3 i q^{3}-13 i q^{7}-9 q^{9}-23 i q^{13}+\cdots$
300.3.b.c	$300$	$3$	300.b	15.d	$2$	$4$	$4$	$8.174$	$\Q(i, \sqrt{5})$	$_{}$	None	None					60.3.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots$
300.3.b.d	$300$	$3$	300.b	15.d	$2$	$4$	$4$	$8.174$	$\Q(i, \sqrt{35})$	$_{}$	None	None		✓			300.3.g.f	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots$
300.3.c.a	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None					60.3.f.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta-1)q^{2}+\beta q^{3}+(2\beta-2)q^{4}+\cdots$
300.3.c.b	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None					12.3.d.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{2}-\beta q^{3}+(2\beta-2)q^{4}+\cdots$
300.3.c.c	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None					60.3.f.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{2}-\beta q^{3}+(2\beta-2)q^{4}+\cdots$
300.3.c.d	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.85100625.1	$_{}$	None	None					60.3.c.a	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.e	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	$_{}$	None	None		✓			300.3.c.e	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.f	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.6080256576.2	$_{}$	None	None					60.3.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.g	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	$_{}$	None	None		✓			300.3.c.e	$2$	$0$	$2$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.f.a	$300$	$3$	300.f	20.d	$2$	$4$	$4$	$8.174$	$\Q(\zeta_{12})$	$_{}$	None	None					12.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+\beta_1)q^{2}+\beta_{3} q^{3}+(2\beta_{2}+2)q^{4}+\cdots$
300.3.f.b	$300$	$3$	300.f	20.d	$2$	$16$	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					60.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots$
300.3.f.c	$300$	$3$	300.f	20.d	$2$	$16$	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			300.3.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{20}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.g.a	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			300.3.g.a	$2$	$0$	$0$	$-3$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots$
300.3.g.b	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				12.3.c.a	$2$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots$
300.3.g.c	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			300.3.g.a	$2$	$0$	$0$	$3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots$
300.3.g.d	$300$	$3$	300.g	3.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-5}) $	$_{}$	None	None					60.3.g.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots$
300.3.g.e	$300$	$3$	300.g	3.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-5}) $	$_{}$	None	None					60.3.b.a	$2$	$0$	$0$	$-4$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 239 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.