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 146 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
1575.1.e.a	$1575$	$1$	1575.e	35.c	$2$	$2$	$2$	$0.786$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None					175.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{7}-i q^{8}+q^{11}-q^{14}+\cdots$
1575.1.e.b	$1575$	$1$	1575.e	35.c	$2$	$2$	$2$	$0.786$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $					63.1.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-i q^{7}+q^{16}-i q^{28}-2 i q^{37}+\cdots$
1575.1.e.c	$1575$	$1$	1575.e	35.c	$2$	$4$	$4$	$0.786$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓	✓		1575.1.h.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
1575.1.h.a	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓				175.1.d.a	$2$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}-q^{7}+q^{8}+q^{11}+q^{14}-q^{16}+\cdots$
1575.1.h.b	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓				63.1.d.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-q^{4}+q^{7}+q^{16}-q^{28}+2q^{37}+\cdots$
1575.1.h.c	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓				175.1.d.a	$2$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots$
1575.1.h.d	$1575$	$1$	1575.h	7.b	$2$	$2$	$2$	$0.786$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None	✓	✓			1575.1.h.d	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}-\beta q^{11}+\cdots$
1575.1.h.e	$1575$	$1$	1575.h	7.b	$2$	$2$	$2$	$0.786$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None	✓	✓			1575.1.h.d	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta q^{2}+2q^{4}+q^{7}-\beta q^{8}+\beta q^{11}+\cdots$
1575.1.n.a	$1575$	$1$	1575.n	105.k	$4$	$4$	$2$	$0.786$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1575.1.n.a	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-1-\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots$
1575.1.n.b	$1575$	$1$	1575.n	105.k	$4$	$4$	$2$	$0.786$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1575.1.n.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots$
1575.1.n.c	$1575$	$1$	1575.n	105.k	$4$	$8$	$4$	$0.786$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		✓			1575.1.n.c	$8$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$		$q+(\zeta_{24}^{8}+\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots$
1575.1.n.d	$1575$	$1$	1575.n	105.k	$4$	$8$	$4$	$0.786$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		✓			1575.1.n.c	$8$	$0$	$4$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{24}^{8}-\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
1575.1.x.a	$1575$	$1$	1575.x	7.d	$6$	$2$	$1$	$0.786$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1575.1.x.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}q^{4}-\zeta_{6}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\cdots$
1575.1.x.b	$1575$	$1$	1575.x	7.d	$6$	$2$	$1$	$0.786$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1575.1.x.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots$
1575.1.y.a	$1575$	$1$	1575.y	63.l	$6$	$4$	$2$	$0.786$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-35}) $	None			✓	✓	315.1.bg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-q^{9}+\cdots$
1575.1.bj.a	$1575$	$1$	1575.bj	35.i	$6$	$4$	$2$	$0.786$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1575.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{13}+\cdots$
1575.1.cb.a	$1575$	$1$	1575.cb	315.at	$12$	$8$	$2$	$0.786$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	1575.1.cb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots$
1575.1.ci.a	$1575$	$1$	1575.ci	35.l	$12$	$8$	$2$	$0.786$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1575.1.ci.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{13}+\cdots$
1575.1.cn.a	$1575$	$1$	1575.cn	315.bf	$12$	$8$	$2$	$0.786$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓	✓	✓	1575.1.cn.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{7}+\cdots$
1575.1.cp.a	$1575$	$1$	1575.cp	315.bh	$12$	$8$	$2$	$0.786$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	1575.1.cb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{6}+\cdots$
1575.2.a.a	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				35.2.b.a	$1$	$1$	$-2$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}+3q^{11}+q^{13}+\cdots$
1575.2.a.b	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				315.2.d.b	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+4q^{13}+q^{14}+\cdots$
1575.2.a.c	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				21.2.a.a	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-4q^{11}+2q^{13}+\cdots$
1575.2.a.d	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				315.2.d.b	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-4q^{13}-q^{14}+\cdots$
1575.2.a.e	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				105.2.d.a	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+6q^{11}+2q^{13}+\cdots$
1575.2.a.f	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				35.2.a.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+3q^{11}-5q^{13}+4q^{16}+\cdots$
1575.2.a.g	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				315.2.d.b	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+4q^{13}-q^{14}+\cdots$
1575.2.a.h	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				105.2.a.a	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+6q^{13}-q^{14}+\cdots$
1575.2.a.i	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				105.2.d.a	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+6q^{11}-2q^{13}+\cdots$
1575.2.a.j	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				315.2.d.b	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-4q^{13}+q^{14}+\cdots$
1575.2.a.k	$1575$	$2$	1575.a	1.a	$1$	$1$	$1$	$12.576$	$\Q$	$_{}$	None	None	✓				35.2.b.a	$1$	$0$	$2$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}+3q^{11}-q^{13}+\cdots$
1575.2.a.l	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				525.2.a.e	$1$	$0$	$-3$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}-q^{7}+(-1+\cdots)q^{8}+\cdots$
1575.2.a.m	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				315.2.a.c	$1$	$0$	$-2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots$
1575.2.a.n	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				175.2.a.d	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
1575.2.a.o	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				525.2.a.f	$1$	$0$	$-1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{7}-3q^{8}+3q^{11}+\cdots$
1575.2.a.p	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				35.2.a.b	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+q^{7}+(-4-\beta )q^{8}+\cdots$
1575.2.a.q	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓	✓	63.2.a.b	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}-2\beta q^{11}+\cdots$
1575.2.a.r	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				105.2.a.b	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-q^{7}-\beta q^{8}+(-2-2\beta )q^{11}+\cdots$
1575.2.a.s	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				175.2.a.d	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-q^{7}+(1-2\beta )q^{8}+\cdots$
1575.2.a.t	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				525.2.a.f	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}+3q^{11}+\cdots$
1575.2.a.u	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				315.2.a.c	$1$	$0$	$2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{7}+(3+\beta )q^{8}+\cdots$
1575.2.a.v	$1575$	$2$	1575.a	1.a	$1$	$2$	$2$	$12.576$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				525.2.a.e	$1$	$0$	$3$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+q^{7}+(1+4\beta )q^{8}+\cdots$
1575.2.a.w	$1575$	$2$	1575.a	1.a	$1$	$3$	$3$	$12.576$	3.3.148.1	$_{}$	None	None	✓		✓		105.2.d.b	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{7}+(-2+\cdots)q^{8}+\cdots$
1575.2.a.x	$1575$	$2$	1575.a	1.a	$1$	$3$	$3$	$12.576$	3.3.148.1	$_{}$	None	None	✓		✓		105.2.d.b	$1$	$0$	$1$	$0$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{7}+(2+\cdots)q^{8}+\cdots$
1575.2.a.y	$1575$	$2$	1575.a	1.a	$1$	$4$	$4$	$12.576$	4.4.174928.1	$_{}$	None	None	✓	✓	✓		1575.2.a.y	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{7}+(2\beta _{1}+\beta _{3})q^{8}+\cdots$
1575.2.a.z	$1575$	$2$	1575.a	1.a	$1$	$4$	$4$	$12.576$	4.4.174928.1	$_{}$	None	None	✓	✓	✓		1575.2.a.y	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+q^{7}+(2\beta _{1}+\beta _{3})q^{8}+\cdots$
1575.2.b.a	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None					63.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
1575.2.b.b	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					315.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots$
1575.2.b.c	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					315.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots$
1575.2.b.d	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			1575.2.b.d	$4$	$0$	$0$	$0$	$0$	$-2$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{7}-2\beta _{1}q^{8}-\beta _{1}q^{11}+\cdots$

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 146 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.