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 (49 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
7644.2.a.a	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				156.2.a.b	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-q^{13}+6q^{17}-2q^{19}+\cdots$
7644.2.a.b	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓	✓			7644.2.a.b	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+2q^{11}-q^{13}-q^{15}+\cdots$
7644.2.a.c	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				1092.2.a.e	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots$
7644.2.a.d	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓	✓			7644.2.a.d	$1$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
7644.2.a.e	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓	✓			7644.2.a.d	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
7644.2.a.f	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				1092.2.a.d	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-6q^{11}+q^{13}-q^{15}+\cdots$
7644.2.a.g	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓	✓			7644.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+2q^{11}+q^{13}-q^{15}+\cdots$
7644.2.a.h	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				1092.2.a.c	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}+q^{13}-4q^{17}+\cdots$
7644.2.a.i	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				1092.2.a.b	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{11}-q^{13}+q^{15}+\cdots$
7644.2.a.j	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				1092.2.a.a	$1$	$1$	$0$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+q^{13}+2q^{15}+\cdots$
7644.2.a.k	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	$\Q$	None	✓				156.2.a.a	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}-4q^{11}-q^{13}+\cdots$
7644.2.a.l	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{7}) $	None	✓	✓			7644.2.a.l	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+q^{9}+(-3+\beta )q^{11}+\cdots$
7644.2.a.m	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{3}) $	None	✓	✓			7644.2.a.m	$1$	$0$	$0$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+q^{9}+(1-3\beta )q^{11}+\cdots$
7644.2.a.n	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{33}) $	None	✓				1092.2.a.g	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
7644.2.a.o	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{2}) $	None	✓				1092.2.q.a	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{5}+q^{9}+(-1-\beta )q^{11}+\cdots$
7644.2.a.p	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{5}) $	None	✓				1092.2.a.f	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots$
7644.2.a.q	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{2}) $	None	✓				1092.2.q.a	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2\beta q^{5}+q^{9}+(-1+\beta )q^{11}+\cdots$
7644.2.a.r	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{7}) $	None	✓	✓			7644.2.a.l	$1$	$1$	$0$	$2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots$
7644.2.a.s	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	$\Q(\sqrt{3}) $	None	✓	✓			7644.2.a.m	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+q^{9}+(1+3\beta )q^{11}+\cdots$
7644.2.a.t	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.1373.1	None	✓				1092.2.a.h	$1$	$1$	$0$	$-3$	$-1$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+q^{9}+\beta _{1}q^{11}-q^{13}+\cdots$
7644.2.a.u	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.b	$1$	$1$	$0$	$-3$	$-1$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots$
7644.2.a.v	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓		✓		1092.2.q.c	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+q^{9}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$
7644.2.a.w	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.d	$1$	$0$	$0$	$-3$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2-\beta _{1})q^{5}+q^{9}-\beta _{2}q^{11}+\cdots$
7644.2.a.x	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓		✓		1092.2.q.d	$1$	$1$	$0$	$3$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta _{1})q^{5}+q^{9}-\beta _{2}q^{11}+\cdots$
7644.2.a.y	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.c	$1$	$1$	$0$	$3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+q^{9}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$
7644.2.a.z	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.b	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots$
7644.2.a.ba	$7644$	$2$	7644.a	1.a	$1$	$5$	$5$	$61.038$	5.5.20094696.1	None	✓				1092.2.q.e	$1$	$1$	$0$	$-5$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+q^{9}+(\beta _{1}-\beta _{4})q^{11}+\cdots$
7644.2.a.bb	$7644$	$2$	7644.a	1.a	$1$	$5$	$5$	$61.038$	5.5.20094696.1	None	✓		✓		1092.2.q.e	$1$	$0$	$0$	$5$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+q^{9}+(\beta _{1}-\beta _{4})q^{11}+\cdots$
7644.2.a.bc	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.566222848.1	None	✓	✓	✓		7644.2.a.bc	$1$	$0$	$0$	$-6$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+q^{9}+(2-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
7644.2.a.bd	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.71950336.1	None	✓	✓	✓		7644.2.a.bd	$1$	$1$	$0$	$-6$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{3}q^{5}+q^{9}+(-2-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$
7644.2.a.be	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.71950336.1	None	✓	✓	✓		7644.2.a.bd	$1$	$1$	$0$	$6$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{3}q^{5}+q^{9}+(-2-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$
7644.2.a.bf	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.566222848.1	None	✓	✓	✓		7644.2.a.bc	$1$	$0$	$0$	$6$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+q^{9}+(2-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
7644.2.e.a	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.cu.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2 i q^{5}+q^{9}-i q^{11}+(-2 i-3)q^{13}+\cdots$
7644.2.e.b	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					156.2.b.b	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta q^{5}+q^{9}+3\beta q^{11}+(-\beta-3)q^{13}+\cdots$
7644.2.e.c	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.e.d	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+i q^{5}+q^{9}+(3 i-2)q^{13}+\cdots$
7644.2.e.d	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.e.c	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+q^{9}-2\beta q^{11}+(-\beta+3)q^{13}+\cdots$
7644.2.e.e	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.e.b	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2\beta q^{5}+q^{9}+(\beta+3)q^{13}+\cdots$
7644.2.e.f	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.e.a	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-\beta-3)q^{13}+\cdots$
7644.2.e.g	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-3}) $	None					156.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(-\beta+1)q^{13}+\cdots$
7644.2.e.h	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	$\Q(\sqrt{-1}) $	None					1092.2.cu.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2 i q^{5}+q^{9}+i q^{11}+(-2 i+3)q^{13}+\cdots$
7644.2.e.i	$7644$	$2$	7644.e	13.b	$2$	$4$	$4$	$61.038$	$\Q(i, \sqrt{17})$	None					1092.2.e.e	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
7644.2.e.j	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.50922496.1	None		✓			7644.2.e.j	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}+q^{9}+\beta _{4}q^{11}+(-1+\cdots)q^{13}+\cdots$
7644.2.e.k	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.3375599808.1	None					1092.2.cu.b	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{5}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots$
7644.2.e.l	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.3375599808.1	None					1092.2.cu.b	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{5}q^{11}+(-1+\cdots)q^{13}+\cdots$
7644.2.e.m	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.50922496.1	None		✓			7644.2.e.j	$2$	$0$	$0$	$6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{1}q^{5}+q^{9}-\beta _{4}q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots$
7644.2.e.n	$7644$	$2$	7644.e	13.b	$2$	$10$	$10$	$61.038$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					1092.2.cu.c	$2$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{9}q^{11}-\beta _{5}q^{13}+\cdots$
7644.2.e.o	$7644$	$2$	7644.e	13.b	$2$	$10$	$10$	$61.038$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					1092.2.cu.c	$2$	$0$	$0$	$10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{9}q^{11}-\beta _{6}q^{13}+\cdots$
7644.2.e.p	$7644$	$2$	7644.e	13.b	$2$	$16$	$16$	$61.038$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			7644.2.e.p	$2$	$0$	$0$	$-16$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{7}q^{11}+\beta _{11}q^{13}+\cdots$
7644.2.e.q	$7644$	$2$	7644.e	13.b	$2$	$16$	$16$	$61.038$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			7644.2.e.p	$2$	$0$	$0$	$16$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{7}q^{11}+\beta _{10}q^{13}+\cdots$

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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.