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 88 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8700.2.a.a	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓	✓			8700.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-6q^{11}-q^{13}+\cdots$
8700.2.a.b	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.h	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
8700.2.a.c	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				348.2.a.d	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}+3q^{13}+3q^{17}+\cdots$
8700.2.a.d	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.e	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}+q^{13}-3q^{17}+\cdots$
8700.2.a.e	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓	✓			8700.2.a.e	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots$
8700.2.a.f	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.g.a	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
8700.2.a.g	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.g.b	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+5q^{11}-4q^{17}+\cdots$
8700.2.a.h	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.g	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
8700.2.a.i	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				348.2.a.c	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}-q^{11}+3q^{13}+\cdots$
8700.2.a.j	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.f	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots$
8700.2.a.k	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.d	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots$
8700.2.a.l	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.c	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
8700.2.a.m	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.g.a	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
8700.2.a.n	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.g.b	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+5q^{11}+4q^{17}+\cdots$
8700.2.a.o	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓	✓			8700.2.a.e	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}+5q^{13}+\cdots$
8700.2.a.p	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				348.2.a.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots$
8700.2.a.q	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.a	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-6q^{11}-6q^{13}-4q^{17}+\cdots$
8700.2.a.r	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				1740.2.a.b	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
8700.2.a.s	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓	✓			8700.2.a.a	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-6q^{11}+q^{13}+\cdots$
8700.2.a.t	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	$\Q$	None	✓				348.2.a.b	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots$
8700.2.a.u	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{57}) $	None	✓				1740.2.a.n	$1$	$0$	$0$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots$
8700.2.a.v	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.m	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
8700.2.a.w	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{33}) $	None	✓				1740.2.a.l	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}+q^{9}+(2-\beta )q^{11}+(2+\cdots)q^{13}+\cdots$
8700.2.a.x	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.j	$1$	$1$	$0$	$2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots$
8700.2.a.y	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{33}) $	None	✓				1740.2.a.i	$1$	$0$	$0$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+(2+\beta )q^{11}+(2+\cdots)q^{13}+\cdots$
8700.2.a.z	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.k	$1$	$1$	$0$	$2$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(3-\beta )q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots$
8700.2.a.ba	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.321.1	None	✓	✓	✓		8700.2.a.ba	$1$	$0$	$0$	$-3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
8700.2.a.bb	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.257.1	None	✓	✓	✓		8700.2.a.bb	$1$	$1$	$0$	$-3$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
8700.2.a.bc	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.257.1	None	✓	✓			8700.2.a.bb	$1$	$1$	$0$	$3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
8700.2.a.bd	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.321.1	None	✓	✓			8700.2.a.ba	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
8700.2.a.be	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.8524696.1	None	✓	✓			8700.2.a.be	$1$	$1$	$0$	$-5$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{4}q^{7}+q^{9}+(-2+\beta _{3})q^{11}+\cdots$
8700.2.a.bf	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.40563468.1	None	✓	✓			8700.2.a.bf	$1$	$0$	$0$	$-5$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
8700.2.a.bg	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.8524696.1	None	✓	✓	✓		8700.2.a.be	$1$	$1$	$0$	$5$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{4}q^{7}+q^{9}+(-2+\beta _{3})q^{11}+\cdots$
8700.2.a.bh	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.40563468.1	None	✓	✓	✓		8700.2.a.bf	$1$	$0$	$0$	$5$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
8700.2.a.bi	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.41017664.1	None	✓		✓		1740.2.g.c	$1$	$1$	$0$	$-6$	$0$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{3}q^{7}+q^{9}+(-\beta _{3}-\beta _{4})q^{11}+\cdots$
8700.2.a.bj	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.71480896.1	None	✓		✓		1740.2.g.d	$1$	$0$	$0$	$-6$	$0$	$6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{2})q^{7}+q^{9}+(\beta _{4}+\beta _{5})q^{11}+\cdots$
8700.2.a.bk	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.71480896.1	None	✓		✓		1740.2.g.d	$1$	$1$	$0$	$6$	$0$	$-6$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{2})q^{7}+q^{9}+(\beta _{4}+\beta _{5})q^{11}+\cdots$
8700.2.a.bl	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.41017664.1	None	✓		✓		1740.2.g.c	$1$	$0$	$0$	$6$	$0$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{3}q^{7}+q^{9}+(-\beta _{3}-\beta _{4})q^{11}+\cdots$
8700.2.b.a	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					1740.2.l.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+i q^{7}+q^{9}+3 i q^{11}-7 i q^{13}+\cdots$
8700.2.b.b	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+3 i q^{7}+q^{9}-3 i q^{11}-5 i q^{13}+\cdots$
8700.2.b.c	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					1740.2.l.b	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+4 i q^{7}+q^{9}+3 i q^{11}+2 q^{17}+\cdots$
8700.2.b.d	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.b	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2\beta q^{7}+q^{9}-2\beta q^{11}-\beta q^{13}+\cdots$
8700.2.b.e	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.c	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+i q^{7}+q^{9}+5 i q^{11}+i q^{13}+\cdots$
8700.2.b.f	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.c	$2$	$1$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+i q^{7}+q^{9}-5 i q^{11}+i q^{13}+\cdots$
8700.2.b.g	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.b	$2$	$1$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2\beta q^{7}+q^{9}+2\beta q^{11}-\beta q^{13}+\cdots$
8700.2.b.h	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					1740.2.l.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+4 i q^{7}+q^{9}-3 i q^{11}-2 q^{17}+\cdots$
8700.2.b.i	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					348.2.h.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+3 i q^{7}+q^{9}+3 i q^{11}-5 i q^{13}+\cdots$
8700.2.b.j	$8700$	$2$	8700.b	145.d	$2$	$2$	$2$	$69.470$	$\Q(\sqrt{-1}) $	None					1740.2.l.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+i q^{7}+q^{9}-3 i q^{11}-7 i q^{13}+\cdots$
8700.2.b.k	$8700$	$2$	8700.b	145.d	$2$	$6$	$6$	$69.470$	6.0.399424.1	None					1740.2.l.c	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-\beta _{1}-\beta _{4})q^{7}+q^{9}+(\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$
8700.2.b.l	$8700$	$2$	8700.b	145.d	$2$	$6$	$6$	$69.470$	6.0.399424.1	None					1740.2.l.c	$2$	$0$	$0$	$6$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(-\beta _{1}-\beta _{4})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$

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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.