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 70 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6075.2.a.a	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.a	$1$	$1$	$-2$	$0$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{7}-4q^{11}+2q^{13}+\cdots$
6075.2.a.b	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.b	$1$	$1$	$-2$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{11}-2q^{13}-4q^{16}+\cdots$
6075.2.a.c	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.a	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{11}-q^{13}-4q^{16}+\cdots$
6075.2.a.d	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.b	$1$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{11}+2q^{13}-4q^{16}+\cdots$
6075.2.a.e	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.a	$1$	$1$	$-2$	$0$	$0$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{7}+4q^{11}-2q^{13}+\cdots$
6075.2.a.f	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.d	$1$	$2$	$-1$	$0$	$0$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{7}+3q^{8}-5q^{11}+\cdots$
6075.2.a.g	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.g	$1$	$0$	$-1$	$0$	$0$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{7}+3q^{8}+4q^{11}+\cdots$
6075.2.a.h	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.c	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{7}+3q^{8}+4q^{11}+\cdots$
6075.2.a.i	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.i	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-2q^{11}-q^{13}+\cdots$
6075.2.a.j	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.i	$1$	$1$	$-1$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+2q^{11}+q^{13}+\cdots$
6075.2.a.k	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.g	$1$	$0$	$-1$	$0$	$0$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{7}+3q^{8}-4q^{11}+\cdots$
6075.2.a.l	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.b	$1$	$1$	$-1$	$0$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{7}+3q^{8}+q^{11}-4q^{13}+\cdots$
6075.2.a.m	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓				243.2.a.b	$2$	$1$	$0$	$0$	$0$	$-5$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+8q^{19}+\cdots$
6075.2.a.n	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.n	$2$	$0$	$0$	$0$	$0$	$-5$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-5q^{7}+7q^{13}+4q^{16}-7q^{19}+\cdots$
6075.2.a.o	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.o	$2$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-4q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots$
6075.2.a.p	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.p	$2$	$0$	$0$	$0$	$0$	$-1$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots$
6075.2.a.q	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.q	$2$	$1$	$0$	$0$	$0$	$-1$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots$
6075.2.a.r	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.e	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-6q^{11}-2q^{13}+4q^{16}+\cdots$
6075.2.a.s	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.q	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{7}-2q^{13}+4q^{16}-q^{19}+\cdots$
6075.2.a.t	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.p	$2$	$0$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{7}+7q^{13}+4q^{16}+8q^{19}+\cdots$
6075.2.a.u	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.e	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+6q^{11}-2q^{13}+4q^{16}+\cdots$
6075.2.a.v	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.o	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+4q^{7}-2q^{13}+4q^{16}-7q^{19}+\cdots$
6075.2.a.w	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓				243.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+4q^{7}+7q^{13}+4q^{16}-q^{19}+\cdots$
6075.2.a.x	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			6075.2.a.n	$2$	$0$	$0$	$0$	$0$	$5$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+5q^{7}-7q^{13}+4q^{16}-7q^{19}+\cdots$
6075.2.a.y	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.g	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{7}-3q^{8}-4q^{11}+\cdots$
6075.2.a.z	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.c	$1$	$1$	$1$	$0$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{7}-3q^{8}-4q^{11}+\cdots$
6075.2.a.ba	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.d	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{7}-3q^{8}+5q^{11}+\cdots$
6075.2.a.bb	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.i	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}-2q^{11}+q^{13}+\cdots$
6075.2.a.bc	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.i	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}+2q^{11}-q^{13}+\cdots$
6075.2.a.bd	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.b	$1$	$1$	$1$	$0$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{7}-3q^{8}-q^{11}-4q^{13}+\cdots$
6075.2.a.be	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.g	$1$	$0$	$1$	$0$	$0$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{7}-3q^{8}+4q^{11}+\cdots$
6075.2.a.bf	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.a	$1$	$1$	$2$	$0$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{7}+4q^{11}+2q^{13}+\cdots$
6075.2.a.bg	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓				1215.2.a.a	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{11}-q^{13}-4q^{16}+\cdots$
6075.2.a.bh	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.b	$1$	$1$	$2$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{11}+2q^{13}-4q^{16}+\cdots$
6075.2.a.bi	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.b	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{11}-2q^{13}-4q^{16}+\cdots$
6075.2.a.bj	$6075$	$2$	6075.a	1.a	$1$	$1$	$1$	$48.509$	$\Q$	None	✓	✓			6075.2.a.a	$1$	$1$	$2$	$0$	$0$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{7}-4q^{11}-2q^{13}+\cdots$
6075.2.a.bk	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{13}) $	None	✓				1215.2.a.k	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+(1-\beta )q^{7}-3q^{8}+\cdots$
6075.2.a.bl	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{21}) $	None	✓				1215.2.a.l	$1$	$0$	$-1$	$0$	$0$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(3+\beta )q^{4}+(1+\beta )q^{7}+(-5+\cdots)q^{8}+\cdots$
6075.2.a.bm	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{3}) $	None	✓				243.2.a.c	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{7}-\beta q^{8}+2\beta q^{11}+\cdots$
6075.2.a.bn	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{6}) $	None	✓				243.2.a.d	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}-2q^{7}+2\beta q^{8}-\beta q^{11}+\cdots$
6075.2.a.bo	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{13}) $	None	✓				1215.2.a.k	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(1-\beta )q^{7}+3q^{8}+\cdots$
6075.2.a.bp	$6075$	$2$	6075.a	1.a	$1$	$2$	$2$	$48.509$	$\Q(\sqrt{21}) $	None	✓				1215.2.a.l	$1$	$0$	$1$	$0$	$0$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3+\beta )q^{4}+(1+\beta )q^{7}+(5+2\beta )q^{8}+\cdots$
6075.2.a.bq	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	$\Q(\zeta_{18})^+$	None	✓				243.2.a.e	$1$	$1$	$-3$	$0$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
6075.2.a.br	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	3.3.564.1	None	✓				1215.2.a.o	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-2\beta _{1})q^{7}+\cdots$
6075.2.a.bs	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	$\Q(\zeta_{18})^+$	None	✓				1215.2.a.p	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{8}+\cdots$
6075.2.a.bt	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	$\Q(\zeta_{18})^+$	None	✓				1215.2.a.p	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{8}+\cdots$
6075.2.a.bu	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	3.3.564.1	None	✓				1215.2.a.o	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-2\beta _{1})q^{7}+\cdots$
6075.2.a.bv	$6075$	$2$	6075.a	1.a	$1$	$3$	$3$	$48.509$	$\Q(\zeta_{18})^+$	None	✓				243.2.a.e	$1$	$0$	$3$	$0$	$0$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots$
6075.2.a.bw	$6075$	$2$	6075.a	1.a	$1$	$4$	$4$	$48.509$	4.4.92160.2	None	✓	✓			6075.2.a.bw	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{2}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots$
6075.2.a.bx	$6075$	$2$	6075.a	1.a	$1$	$4$	$4$	$48.509$	4.4.29952.1	None	✓	✓			6075.2.a.bx	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-2\beta _{2}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$

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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.