LMFDB - Newform search results

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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

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Results (1-50 of 140 matches)

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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
2475.1.b.a	$2475$	$1$	2475.b	11.b	$2$	$1$	$1$	$1.235$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓				55.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{11}+q^{16}-2q^{31}+q^{44}+\cdots$
2475.1.b.b	$2475$	$1$	2475.b	11.b	$2$	$2$	$2$	$1.235$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None					495.1.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{2}-q^{4}-\beta q^{7}-q^{11}-\beta q^{13}+\cdots$
2475.1.b.c	$2475$	$1$	2475.b	11.b	$2$	$2$	$2$	$1.235$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None					495.1.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}-q^{4}-\beta q^{7}+q^{11}-\beta q^{13}+\cdots$
2475.1.m.a	$2475$	$1$	2475.m	165.l	$4$	$8$	$4$	$1.235$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		✓			2475.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$		$q+(-\zeta_{16}+\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
2475.1.m.b	$2475$	$1$	2475.m	165.l	$4$	$8$	$4$	$1.235$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		✓			2475.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$		$q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
2475.1.t.a	$2475$	$1$	2475.t	495.o	$6$	$4$	$2$	$1.235$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-11}) $	None			✓	✓	99.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{11}+\cdots$
2475.1.y.a	$2475$	$1$	2475.y	99.h	$6$	$2$	$1$	$1.235$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					99.1.h.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{11}+\cdots$
2475.1.y.b	$2475$	$1$	2475.y	99.h	$6$	$4$	$2$	$1.235$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None			✓		495.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{11}+\cdots$
2475.1.bs.a	$2475$	$1$	2475.bs	275.s	$10$	$4$	$1$	$1.235$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.s.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{10}^{4}q^{4}+q^{5}+\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots$
2475.1.bu.a	$2475$	$1$	2475.bu	275.v	$10$	$4$	$1$	$1.235$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.v.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{10}^{4}q^{4}-q^{5}-\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots$
2475.1.cr.a	$2475$	$1$	2475.cr	495.ad	$12$	$4$	$1$	$1.235$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None					495.1.bd.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{11}+\cdots$
2475.1.cr.b	$2475$	$1$	2475.cr	495.ad	$12$	$4$	$1$	$1.235$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None					495.1.bd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{11}+\cdots$
2475.1.eu.a	$2475$	$1$	2475.eu	2475.du	$30$	$8$	$1$	$1.235$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.eu.a	$4$	$0$	$0$	$1$	$-4$	$0$		$1$		$q+\zeta_{30}^{2}q^{3}+\zeta_{30}^{8}q^{4}+\zeta_{30}^{10}q^{5}+\cdots$
2475.1.eu.b	$2475$	$1$	2475.eu	2475.du	$30$	$8$	$1$	$1.235$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.eu.a	$4$	$0$	$0$	$1$	$8$	$0$		$1$		$q+\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+q^{5}-\zeta_{30}^{13}q^{9}+\cdots$
2475.1.ev.a	$2475$	$1$	2475.ev	2475.dv	$30$	$8$	$1$	$1.235$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.ev.a	$4$	$0$	$0$	$-1$	$-8$	$0$		$1$		$q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{4}q^{4}-q^{5}+\zeta_{30}^{14}q^{9}+\cdots$
2475.1.ev.b	$2475$	$1$	2475.ev	2475.dv	$30$	$8$	$1$	$1.235$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.ev.a	$4$	$0$	$0$	$1$	$4$	$0$		$1$		$q-\zeta_{30}q^{3}-\zeta_{30}^{4}q^{4}+\zeta_{30}^{5}q^{5}+\zeta_{30}^{2}q^{9}+\cdots$
2475.1.fy.a	$2475$	$1$	2475.fy	2475.ey	$60$	$16$	$1$	$1.235$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.fy.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{60}^{8}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{25}q^{5}+\cdots$
2475.1.fy.b	$2475$	$1$	2475.fy	2475.ey	$60$	$16$	$1$	$1.235$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-11}) $	None		✓			2475.1.fy.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{60}^{11}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{15}q^{5}+\cdots$
2475.2.a.a	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				11.2.a.a	$1$	$0$	$-2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{7}-q^{11}-4q^{13}+\cdots$
2475.2.a.b	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓	✓			2475.2.a.b	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots$
2475.2.a.c	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$0$	$-1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots$
2475.2.a.d	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓	✓			2475.2.a.b	$1$	$1$	$-1$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{7}+3q^{8}-q^{11}-2q^{13}+\cdots$
2475.2.a.e	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				825.2.a.b	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+q^{11}-q^{13}+4q^{16}+\cdots$
2475.2.a.f	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				825.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+q^{11}+q^{13}+4q^{16}+\cdots$
2475.2.a.g	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots$
2475.2.a.h	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓	✓			2475.2.a.b	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots$
2475.2.a.i	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				55.2.a.a	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}+q^{11}-2q^{13}+\cdots$
2475.2.a.j	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$1$	$1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots$
2475.2.a.k	$2475$	$2$	2475.a	1.a	$1$	$1$	$1$	$19.763$	$\Q$	$_{}$	None	None	✓	✓			2475.2.a.b	$1$	$0$	$1$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{7}-3q^{8}+q^{11}-2q^{13}+\cdots$
2475.2.a.l	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				825.2.a.d	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-1-\beta )q^{7}+\cdots$
2475.2.a.m	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				165.2.a.a	$1$	$1$	$-2$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2+2\beta )q^{7}+\cdots$
2475.2.a.n	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				275.2.a.d	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(2-3\beta )q^{7}+\cdots$
2475.2.a.o	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				275.2.a.e	$1$	$0$	$-1$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+(2+\beta )q^{7}-3q^{8}+\cdots$
2475.2.a.p	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2475.2.a.p	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{7}+(-4-\beta )q^{8}+\cdots$
2475.2.a.q	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2475.2.a.p	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+q^{7}+(-4-\beta )q^{8}+\cdots$
2475.2.a.r	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				165.2.a.b	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+q^{11}+\cdots$
2475.2.a.s	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				275.2.a.d	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{7}+\cdots$
2475.2.a.t	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				275.2.a.e	$1$	$1$	$1$	$0$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(-2-\beta )q^{7}+3q^{8}+\cdots$
2475.2.a.u	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2475.2.a.p	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}-q^{7}+(4+\beta )q^{8}+\cdots$
2475.2.a.v	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2475.2.a.p	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+q^{7}+(4+\beta )q^{8}+\cdots$
2475.2.a.w	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				825.2.a.d	$1$	$0$	$2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1-\beta )q^{7}+\cdots$
2475.2.a.x	$2475$	$2$	2475.a	1.a	$1$	$2$	$2$	$19.763$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				55.2.a.b	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{7}+(3+\cdots)q^{8}+\cdots$
2475.2.a.y	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.148.1	$_{}$	None	None	✓				165.2.c.a	$1$	$0$	$-3$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2475.2.a.z	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.568.1	$_{}$	None	None	✓				825.2.a.i	$1$	$1$	$-2$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots$
2475.2.a.ba	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.148.1	$_{}$	None	None	✓				165.2.c.b	$1$	$1$	$-1$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
2475.2.a.bb	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.148.1	$_{}$	None	None	✓				165.2.a.c	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2475.2.a.bc	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.148.1	$_{}$	None	None	✓				165.2.c.b	$1$	$1$	$1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
2475.2.a.bd	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.568.1	$_{}$	None	None	✓				825.2.a.i	$1$	$0$	$2$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
2475.2.a.be	$2475$	$2$	2475.a	1.a	$1$	$3$	$3$	$19.763$	3.3.148.1	$_{}$	None	None	✓				165.2.c.a	$1$	$0$	$3$	$0$	$0$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-3+\cdots)q^{7}+\cdots$
2475.2.a.bf	$2475$	$2$	2475.a	1.a	$1$	$4$	$4$	$19.763$	4.4.48704.2	$_{}$	None	None	✓		✓		495.2.a.f	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.