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 93 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
1521.1.j.a	$1521$	$1$	1521.j	13.d	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1521.1.j.a	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q+(-i-1)q^{2}+i q^{4}+(i+1)q^{5}+\cdots$
1521.1.j.b	$1521$	$1$	1521.j	13.d	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None					117.1.j.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-i q^{4}+(-i+1)q^{7}-q^{16}+(i+1)q^{19}+\cdots$
1521.1.j.c	$1521$	$1$	1521.j	13.d	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1521.1.j.a	$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+(i+1)q^{2}+i q^{4}+(-i-1)q^{5}+\cdots$
1521.1.bd.a	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1521.1.j.a	$8$	$0$	$-2$	$0$	$-4$	$0$		$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(-1+\cdots)q^{5}+\cdots$
1521.1.bd.b	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-3}) $	None					117.1.j.a	$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}q^{4}+(\zeta_{12}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots$
1521.1.bd.c	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-3}) $	None					117.1.j.a	$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots$
1521.1.bd.d	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1521.1.j.a	$8$	$0$	$2$	$0$	$4$	$0$		$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(1+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
1521.1.bm.a	$1521$	$1$	1521.bm	169.j	$52$	$24$	$1$	$0.759$	$\Q(\zeta_{52})$	$D_{52}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1521.1.bm.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{52}^{17}q^{4}+(-\zeta_{52}^{5}-\zeta_{52}^{20})q^{7}+\cdots$
1521.2.a.a	$1521$	$2$	1521.a	1.a	$1$	$1$	$1$	$12.145$	$\Q$	$_{}$	None	None	✓				39.2.e.a	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots$
1521.2.a.b	$1521$	$2$	1521.a	1.a	$1$	$1$	$1$	$12.145$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				117.2.g.a	$2$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}+4q^{16}+8q^{19}-5q^{25}+\cdots$
1521.2.a.c	$1521$	$2$	1521.a	1.a	$1$	$1$	$1$	$12.145$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				117.2.g.a	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{7}+4q^{16}-8q^{19}-5q^{25}+\cdots$
1521.2.a.d	$1521$	$2$	1521.a	1.a	$1$	$1$	$1$	$12.145$	$\Q$	$_{}$	None	None	✓				39.2.e.a	$1$	$0$	$1$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-q^{10}+\cdots$
1521.2.a.e	$1521$	$2$	1521.a	1.a	$1$	$1$	$1$	$12.145$	$\Q$	$_{}$	None	None	✓				39.2.a.a	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+4q^{7}-3q^{8}+2q^{10}+\cdots$
1521.2.a.f	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				39.2.a.b	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots$
1521.2.a.g	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				39.2.e.b	$1$	$0$	$-1$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+(2-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
1521.2.a.h	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				39.2.j.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2\beta q^{5}-\beta q^{7}-2\beta q^{11}+4q^{16}+\cdots$
1521.2.a.i	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓				117.2.q.b	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-3\beta q^{7}+4q^{16}-2\beta q^{19}+\cdots$
1521.2.a.j	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				117.2.a.b	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}-2\beta q^{11}+\cdots$
1521.2.a.k	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				13.2.e.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots$
1521.2.a.l	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				39.2.b.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2\beta q^{7}-\beta q^{8}+2\beta q^{11}+\cdots$
1521.2.a.m	$1521$	$2$	1521.a	1.a	$1$	$2$	$2$	$12.145$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				39.2.e.b	$1$	$0$	$1$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+(-2+\beta )q^{5}+(1+\cdots)q^{7}+\cdots$
1521.2.a.n	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				507.2.a.i	$1$	$1$	$-3$	$0$	$-6$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots$
1521.2.a.o	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				169.2.a.b	$1$	$1$	$-2$	$0$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
1521.2.a.p	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				507.2.a.j	$1$	$0$	$-1$	$0$	$-4$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots$
1521.2.a.q	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				507.2.a.j	$1$	$1$	$1$	$0$	$4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$
1521.2.a.r	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				169.2.a.b	$1$	$0$	$2$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1521.2.a.s	$1521$	$2$	1521.a	1.a	$1$	$3$	$3$	$12.145$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				507.2.a.i	$1$	$0$	$3$	$0$	$6$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots$
1521.2.a.t	$1521$	$2$	1521.a	1.a	$1$	$4$	$4$	$12.145$	4.4.8112.1	$_{}$	$\Q(\sqrt{-39}) $	None	✓				117.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	$q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$
1521.2.a.u	$1521$	$2$	1521.a	1.a	$1$	$4$	$4$	$12.145$	$\Q(\sqrt{3}, \sqrt{5})$	$_{}$	None	None	✓				117.2.q.d	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+3q^{4}+\beta _{3}q^{5}+2\beta _{1}q^{7}+\cdots$
1521.2.a.v	$1521$	$2$	1521.a	1.a	$1$	$6$	$6$	$12.145$	6.6.1997632.1	$_{}$	None	None	✓	✓	✓		1521.2.a.v	$2$	$1$	$0$	$0$	$0$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}+(-2\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
1521.2.a.w	$1521$	$2$	1521.a	1.a	$1$	$6$	$6$	$12.145$	6.6.1997632.1	$_{}$	None	None	✓	✓	✓		1521.2.a.v	$2$	$0$	$0$	$0$	$0$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}+(-2\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
1521.2.b.a	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-3}) $	$_{}$	None	None					13.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{4}+\beta q^{5}-\beta q^{8}+3 q^{10}+\cdots$
1521.2.b.b	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-1}) $	$_{}$	None	None					39.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+2 i q^{5}-4 i q^{7}+3 i q^{8}+\cdots$
1521.2.b.c	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-1}) $	$_{}$	None	None					39.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}-i q^{5}+2 i q^{7}+3 i q^{8}+\cdots$
1521.2.b.d	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					117.2.q.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+3\beta q^{7}+4 q^{16}-2\beta q^{19}+\cdots$
1521.2.b.e	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None					117.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+i q^{7}+4 q^{16}+8 i q^{19}+\cdots$
1521.2.b.f	$1521$	$2$	1521.b	13.b	$2$	$2$	$2$	$12.145$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{4}+2\beta q^{5}+\beta q^{7}+2\beta q^{11}+\cdots$
1521.2.b.g	$1521$	$2$	1521.b	13.b	$2$	$4$	$4$	$12.145$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None					117.2.q.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{5}-2\beta _{2}q^{7}+\cdots$
1521.2.b.h	$1521$	$2$	1521.b	13.b	$2$	$4$	$4$	$12.145$	$\Q(i, \sqrt{17})$	$_{}$	None	None					39.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$
1521.2.b.i	$1521$	$2$	1521.b	13.b	$2$	$4$	$4$	$12.145$	$\Q(\zeta_{12})$	$_{}$	None	None					117.2.a.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}-q^{4}+\beta_1 q^{7}+\beta_{2} q^{8}+\cdots$
1521.2.b.j	$1521$	$2$	1521.b	13.b	$2$	$4$	$4$	$12.145$	$\Q(\zeta_{8})$	$_{}$	None	None					39.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+(-\beta_{3}-1)q^{4}+(\beta_{2}-\beta_1)q^{5}+\cdots$
1521.2.b.k	$1521$	$2$	1521.b	13.b	$2$	$6$	$6$	$12.145$	6.0.153664.1	$_{}$	None	None					507.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-3-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
1521.2.b.l	$1521$	$2$	1521.b	13.b	$2$	$6$	$6$	$12.145$	6.0.153664.1	$_{}$	None	None					169.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{5})q^{2}+(1-2\beta _{2}-\beta _{4})q^{4}+\cdots$
1521.2.b.m	$1521$	$2$	1521.b	13.b	$2$	$6$	$6$	$12.145$	6.0.153664.1	$_{}$	None	None					507.2.a.j	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots$
1521.2.b.n	$1521$	$2$	1521.b	13.b	$2$	$12$	$12$	$12.145$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		1521.2.a.v	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+(-2-\beta _{2}+2\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1521.2.i.a	$1521$	$2$	1521.i	39.f	$4$	$4$	$2$	$12.145$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1521.2.i.a	$4$	$0$	$0$	$0$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(-3+\cdots)q^{7}+\cdots$
1521.2.i.b	$1521$	$2$	1521.i	39.f	$4$	$4$	$2$	$12.145$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1521.2.i.a	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(3+3\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
1521.2.i.c	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	$\Q(\zeta_{24})$	$_{}$	None	None					117.2.ba.b	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_1 q^{2}-\beta_{3} q^{4}+(-\beta_{7}-\beta_{4}+2\beta_1)q^{5}+\cdots$
1521.2.i.d	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	$\Q(\zeta_{24})$	$_{}$	None	None					117.2.ba.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{7}-\beta_{5})q^{2}+2\beta_{3} q^{4}+(-\beta_{7}+\beta_{5}+\beta_{2})q^{5}+\cdots$
1521.2.i.e	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	$\Q(\zeta_{24})$	$_{}$	None	None					117.2.ba.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{7}-\beta_{5})q^{2}+2\beta_{3} q^{4}+(-\beta_{7}+\beta_{5}+\beta_{2})q^{5}+\cdots$

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 93 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.