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 62 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9522.2.a.a	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓	✓			9522.2.a.a	$1$	$0$	$-1$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
9522.2.a.b	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				3174.2.a.f	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{13}+\cdots$
9522.2.a.c	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				3174.2.a.f	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{13}+\cdots$
9522.2.a.d	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				138.2.a.c	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-2q^{13}+\cdots$
9522.2.a.e	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓	✓			9522.2.a.a	$1$	$0$	$-1$	$0$	$2$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
9522.2.a.f	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				1058.2.a.a	$1$	$0$	$1$	$0$	$-3$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots$
9522.2.a.g	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				1058.2.a.d	$1$	$0$	$1$	$0$	$-2$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots$
9522.2.a.h	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓	✓			9522.2.a.a	$1$	$1$	$1$	$0$	$-2$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
9522.2.a.i	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				138.2.a.a	$1$	$0$	$1$	$0$	$-2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots$
9522.2.a.j	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				3174.2.a.a	$1$	$0$	$1$	$0$	$-2$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+5q^{7}+q^{8}-2q^{10}+\cdots$
9522.2.a.k	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				138.2.a.b	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{13}-2q^{14}+\cdots$
9522.2.a.l	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				3174.2.a.a	$1$	$0$	$1$	$0$	$2$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-5q^{7}+q^{8}+2q^{10}+\cdots$
9522.2.a.m	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓	✓			9522.2.a.a	$1$	$1$	$1$	$0$	$2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
9522.2.a.n	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				1058.2.a.d	$1$	$0$	$1$	$0$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots$
9522.2.a.o	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				1058.2.a.a	$1$	$0$	$1$	$0$	$3$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-2q^{7}+q^{8}+3q^{10}+\cdots$
9522.2.a.p	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	$\Q$	None	✓				46.2.a.a	$1$	$0$	$1$	$0$	$4$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+4q^{7}+q^{8}+4q^{10}+\cdots$
9522.2.a.q	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{5}) $	None	✓				138.2.a.d	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}-2\beta q^{7}+\cdots$
9522.2.a.r	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{41}) $	None	✓				3174.2.a.o	$1$	$1$	$-2$	$0$	$-1$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}+(1+\beta )q^{7}-q^{8}+\cdots$
9522.2.a.s	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				3174.2.a.m	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3\beta q^{5}-\beta q^{7}-q^{8}-3\beta q^{10}+\cdots$
9522.2.a.t	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓				1058.2.a.g	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
9522.2.a.u	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓	✓			9522.2.a.u	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}+3\beta q^{11}+\cdots$
9522.2.a.v	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{6}) $	None	✓	✓			9522.2.a.v	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-\beta q^{11}+\cdots$
9522.2.a.w	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓				3174.2.a.p	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+\beta q^{11}+\cdots$
9522.2.a.x	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓				3174.2.a.q	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}-\beta q^{11}+4q^{13}+\cdots$
9522.2.a.y	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				3174.2.a.n	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+\beta q^{7}-q^{8}-2\beta q^{10}+\cdots$
9522.2.a.z	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				1058.2.a.h	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{7}-q^{8}+3\beta q^{11}+\cdots$
9522.2.a.ba	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{41}) $	None	✓				3174.2.a.o	$1$	$1$	$-2$	$0$	$1$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots$
9522.2.a.bb	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{7}) $	None	✓				414.2.a.e	$1$	$0$	$-2$	$0$	$2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots$
9522.2.a.bc	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{7}) $	None	✓				414.2.a.e	$1$	$1$	$2$	$0$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots$
9522.2.a.bd	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓				3174.2.a.j	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-5q^{13}+\cdots$
9522.2.a.be	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓	✓			9522.2.a.u	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{7}+q^{8}-3\beta q^{11}+\cdots$
9522.2.a.bf	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{6}) $	None	✓				3174.2.a.k	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{7}+q^{8}-\beta q^{11}-2q^{13}+\cdots$
9522.2.a.bg	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				3174.2.a.l	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
9522.2.a.bh	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{6}) $	None	✓	✓			9522.2.a.v	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-\beta q^{11}+\cdots$
9522.2.a.bi	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				3174.2.a.h	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{7}+q^{8}+\beta q^{14}+q^{16}+\cdots$
9522.2.a.bj	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{3}) $	None	✓				1058.2.a.f	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}-2\beta q^{7}+q^{8}+\cdots$
9522.2.a.bk	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	$\Q(\sqrt{2}) $	None	✓				3174.2.a.i	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
9522.2.a.bl	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	$\Q(\zeta_{24})^+$	None	✓				3174.2.a.v	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots$
9522.2.a.bm	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	$\Q(\zeta_{24})^+$	None	✓				1058.2.a.i	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
9522.2.a.bn	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	$\Q(\zeta_{24})^+$	None	✓				3174.2.a.u	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
9522.2.a.bo	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	$\Q(\sqrt{3}, \sqrt{35})$	None	✓				3174.2.a.t	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
9522.2.a.bp	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				46.2.c.a	$1$	$0$	$-5$	$0$	$-8$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta _{1}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots$
9522.2.a.bq	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.a	$1$	$1$	$-5$	$0$	$-7$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{3}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots$
9522.2.a.br	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.b	$1$	$1$	$-5$	$0$	$-1$	$-11$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(-3+\cdots)q^{7}+\cdots$
9522.2.a.bs	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.b	$1$	$0$	$-5$	$0$	$1$	$11$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-2\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots$
9522.2.a.bt	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.a	$1$	$0$	$-5$	$0$	$7$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{3}-\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots$
9522.2.a.bu	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				46.2.c.a	$1$	$1$	$-5$	$0$	$8$	$-7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots$
9522.2.a.bv	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.c	$1$	$1$	$5$	$0$	$-11$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-3-\beta _{2}+2\beta _{3}-\beta _{4})q^{5}+\cdots$
9522.2.a.bw	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				46.2.c.b	$1$	$0$	$5$	$0$	$-2$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots$
9522.2.a.bx	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	$\Q(\zeta_{22})^+$	None	✓				138.2.e.d	$1$	$1$	$5$	$0$	$-1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(\beta _{2}-\beta _{3}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots$

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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.