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 53 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
9300.2.a.a	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				372.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}-2q^{13}+4q^{19}+\cdots$
9300.2.a.b	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				1860.2.a.c	$1$	$2$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
9300.2.a.c	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.c	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-3q^{11}+4q^{13}-q^{17}+\cdots$
9300.2.a.d	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				372.2.a.d	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}-q^{21}+\cdots$
9300.2.a.e	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				1860.2.a.b	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
9300.2.a.f	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.f	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+4q^{13}-3q^{17}+\cdots$
9300.2.a.g	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.g	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots$
9300.2.a.h	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				372.2.a.b	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
9300.2.a.i	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.f	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-4q^{13}+3q^{17}+\cdots$
9300.2.a.j	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.g	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
9300.2.a.k	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓	✓			9300.2.a.c	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-3q^{11}-4q^{13}+q^{17}+\cdots$
9300.2.a.l	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				1860.2.a.a	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2q^{13}+4q^{17}-4q^{19}+\cdots$
9300.2.a.m	$9300$	$2$	9300.a	1.a	$1$	$1$	$1$	$74.261$	$\Q$	None	✓				372.2.a.a	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+6q^{13}+8q^{17}+\cdots$
9300.2.a.n	$9300$	$2$	9300.a	1.a	$1$	$2$	$2$	$74.261$	$\Q(\sqrt{3}) $	None	✓				1860.2.a.e	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}-4q^{11}+\cdots$
9300.2.a.o	$9300$	$2$	9300.a	1.a	$1$	$2$	$2$	$74.261$	$\Q(\sqrt{33}) $	None	✓	✓			9300.2.a.o	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+\beta q^{11}+(1+2\beta )q^{17}+\cdots$
9300.2.a.p	$9300$	$2$	9300.a	1.a	$1$	$2$	$2$	$74.261$	$\Q(\sqrt{6}) $	None	✓				1860.2.a.d	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+(2-\beta )q^{13}-2q^{17}+\cdots$
9300.2.a.q	$9300$	$2$	9300.a	1.a	$1$	$2$	$2$	$74.261$	$\Q(\sqrt{33}) $	None	✓	✓			9300.2.a.o	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+\beta q^{11}+(-1-2\beta )q^{17}+\cdots$
9300.2.a.r	$9300$	$2$	9300.a	1.a	$1$	$2$	$2$	$74.261$	$\Q(\sqrt{17}) $	None	✓				372.2.a.e	$1$	$1$	$0$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9300.2.a.s	$9300$	$2$	9300.a	1.a	$1$	$3$	$3$	$74.261$	3.3.404.1	None	✓	✓			9300.2.a.s	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
9300.2.a.t	$9300$	$2$	9300.a	1.a	$1$	$3$	$3$	$74.261$	3.3.7636.1	None	✓				1860.2.a.h	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{7}+q^{9}+2q^{11}-\beta _{1}q^{13}+\cdots$
9300.2.a.u	$9300$	$2$	9300.a	1.a	$1$	$3$	$3$	$74.261$	3.3.404.1	None	✓				1860.2.a.g	$1$	$1$	$0$	$-3$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{2})q^{7}+q^{9}+2\beta _{2}q^{11}+\cdots$
9300.2.a.v	$9300$	$2$	9300.a	1.a	$1$	$3$	$3$	$74.261$	3.3.564.1	None	✓		✓		1860.2.a.f	$1$	$1$	$0$	$3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}-2\beta _{1}q^{11}+\cdots$
9300.2.a.w	$9300$	$2$	9300.a	1.a	$1$	$3$	$3$	$74.261$	3.3.404.1	None	✓	✓			9300.2.a.s	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
9300.2.a.x	$9300$	$2$	9300.a	1.a	$1$	$4$	$4$	$74.261$	4.4.224148.1	None	✓				1860.2.a.i	$1$	$0$	$0$	$4$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
9300.2.a.y	$9300$	$2$	9300.a	1.a	$1$	$6$	$6$	$74.261$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		9300.2.a.y	$1$	$0$	$0$	$-6$	$0$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{5})q^{7}+q^{9}+(-1-\beta _{4}+\cdots)q^{11}+\cdots$
9300.2.a.z	$9300$	$2$	9300.a	1.a	$1$	$6$	$6$	$74.261$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			9300.2.a.z	$1$	$0$	$0$	$-6$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}-\beta _{4}q^{11}+\cdots$
9300.2.a.ba	$9300$	$2$	9300.a	1.a	$1$	$6$	$6$	$74.261$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			9300.2.a.y	$1$	$0$	$0$	$6$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{5})q^{7}+q^{9}+(-1-\beta _{4}+\cdots)q^{11}+\cdots$
9300.2.a.bb	$9300$	$2$	9300.a	1.a	$1$	$6$	$6$	$74.261$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		9300.2.a.z	$1$	$0$	$0$	$6$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{7}+q^{9}-\beta _{4}q^{11}+\cdots$
9300.2.a.bc	$9300$	$2$	9300.a	1.a	$1$	$7$	$7$	$74.261$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1860.2.g.a	$1$	$1$	$0$	$-7$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{7}+q^{9}+(1-\beta _{4}+\cdots)q^{11}+\cdots$
9300.2.a.bd	$9300$	$2$	9300.a	1.a	$1$	$7$	$7$	$74.261$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1860.2.g.b	$1$	$0$	$0$	$-7$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{4})q^{7}+q^{9}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots$
9300.2.a.be	$9300$	$2$	9300.a	1.a	$1$	$7$	$7$	$74.261$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1860.2.g.b	$1$	$1$	$0$	$7$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{4})q^{7}+q^{9}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots$
9300.2.a.bf	$9300$	$2$	9300.a	1.a	$1$	$7$	$7$	$74.261$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1860.2.g.a	$1$	$0$	$0$	$7$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{2})q^{7}+q^{9}+(1-\beta _{4})q^{11}+\cdots$
9300.2.g.a	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					1860.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{7}-q^{9}-4 q^{11}-4 i q^{13}+\cdots$
9300.2.g.b	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					1860.2.a.c	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{7}-q^{9}-4 q^{11}-4 i q^{13}+\cdots$
9300.2.g.c	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None		✓			9300.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{9}-3 q^{11}-4 i q^{13}-i q^{17}+\cdots$
9300.2.g.d	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					372.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+i q^{7}-q^{9}-6 i q^{13}+8 i q^{17}+\cdots$
9300.2.g.e	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					372.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{7}-q^{9}-2 i q^{13}+\cdots$
9300.2.g.f	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None		✓			9300.2.a.f	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{7}-q^{9}-4 i q^{13}+\cdots$
9300.2.g.g	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					372.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{7}-q^{9}+2 i q^{13}+q^{19}+\cdots$
9300.2.g.h	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					1860.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-q^{9}-2 i q^{13}+4 i q^{17}+\cdots$
9300.2.g.i	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None					372.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+5 i q^{7}-q^{9}+2 q^{11}-4 i q^{13}+\cdots$
9300.2.g.j	$9300$	$2$	9300.g	5.b	$2$	$2$	$2$	$74.261$	$\Q(\sqrt{-1}) $	None		✓			9300.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{7}-q^{9}+3 q^{11}+2 i q^{13}+\cdots$
9300.2.g.k	$9300$	$2$	9300.g	5.b	$2$	$4$	$4$	$74.261$	$\Q(\zeta_{12})$	None					1860.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+(-\beta_{2}+\beta_1)q^{7}-q^{9}+\cdots$
9300.2.g.l	$9300$	$2$	9300.g	5.b	$2$	$4$	$4$	$74.261$	$\Q(i, \sqrt{6})$	None					1860.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}-q^{9}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
9300.2.g.m	$9300$	$2$	9300.g	5.b	$2$	$4$	$4$	$74.261$	$\Q(i, \sqrt{33})$	None		✓			9300.2.a.o	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-q^{9}+(1-\beta _{3})q^{11}+(-2\beta _{1}+\cdots)q^{17}+\cdots$
9300.2.g.n	$9300$	$2$	9300.g	5.b	$2$	$4$	$4$	$74.261$	$\Q(i, \sqrt{17})$	None					372.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(2-2\beta _{3})q^{11}+\cdots$
9300.2.g.o	$9300$	$2$	9300.g	5.b	$2$	$6$	$6$	$74.261$	6.0.2611456.1	None		✓			9300.2.a.s	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{4}-\beta _{5})q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots$
9300.2.g.p	$9300$	$2$	9300.g	5.b	$2$	$6$	$6$	$74.261$	6.0.5089536.1	None					1860.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(\beta _{2}+2\beta _{4}-\beta _{5})q^{7}-q^{9}+\cdots$
9300.2.g.q	$9300$	$2$	9300.g	5.b	$2$	$6$	$6$	$74.261$	6.0.2611456.1	None					1860.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{3}-\beta _{4})q^{7}-q^{9}-2\beta _{2}q^{11}+\cdots$
9300.2.g.r	$9300$	$2$	9300.g	5.b	$2$	$6$	$6$	$74.261$	6.0.932935936.2	None					1860.2.a.h	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+2q^{11}+\beta _{1}q^{13}+\cdots$

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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.