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 58 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	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6525.2.a.a	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				1305.2.a.a	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{7}-3q^{11}+4q^{13}+\cdots$
6525.2.a.b	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.c.a	$1$	$1$	$-2$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{7}+3q^{11}-4q^{13}+\cdots$
6525.2.a.c	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.c.b	$1$	$1$	$-1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{13}+\cdots$
6525.2.a.d	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				145.2.a.a	$1$	$1$	$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{7}+3q^{8}+6q^{11}+\cdots$
6525.2.a.e	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.a.a	$1$	$0$	$-1$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{7}+3q^{8}-6q^{13}+\cdots$
6525.2.a.f	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{7}-3q^{11}-2q^{13}+4q^{16}+\cdots$
6525.2.a.g	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				2175.2.a.e	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+2q^{11}+3q^{13}+4q^{16}+\cdots$
6525.2.a.h	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				2175.2.a.e	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+2q^{11}-3q^{13}+4q^{16}+\cdots$
6525.2.a.i	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.a.b	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-q^{11}-6q^{13}+4q^{16}+\cdots$
6525.2.a.j	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.a.d	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}+4q^{11}+\cdots$
6525.2.a.k	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.c.b	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}-4q^{13}+\cdots$
6525.2.a.l	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				435.2.c.a	$1$	$1$	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{7}+3q^{11}+4q^{13}+\cdots$
6525.2.a.m	$6525$	$2$	6525.a	1.a	$1$	$1$	$1$	$52.102$	$\Q$	None	✓				1305.2.a.a	$1$	$0$	$2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{7}+3q^{11}+4q^{13}+\cdots$
6525.2.a.n	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				435.2.c.c	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+\beta q^{7}+3q^{8}+(2-\beta )q^{11}+\cdots$
6525.2.a.o	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				29.2.a.a	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{7}+\cdots$
6525.2.a.p	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				145.2.a.b	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2+2\beta )q^{7}+\cdots$
6525.2.a.q	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				261.2.a.a	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{7}+\cdots$
6525.2.a.r	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				1305.2.a.h	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
6525.2.a.s	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				435.2.a.e	$1$	$0$	$-1$	$0$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+3q^{7}+(-1+\cdots)q^{8}+\cdots$
6525.2.a.t	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{21}) $	None	✓				435.2.a.f	$1$	$0$	$-1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(3+\beta )q^{4}-q^{7}+(-5-2\beta )q^{8}+\cdots$
6525.2.a.u	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				1305.2.c.c	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{4}-2\beta q^{7}-5q^{11}+2\beta q^{13}+\cdots$
6525.2.a.v	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				1305.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{4}+2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots$
6525.2.a.w	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				2175.2.a.n	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{7}-2\beta q^{8}+2q^{11}-q^{13}+\cdots$
6525.2.a.x	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				2175.2.a.n	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{7}-2\beta q^{8}+2q^{11}+q^{13}+\cdots$
6525.2.a.y	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				435.2.a.g	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-2q^{7}-\beta q^{8}+2q^{11}+\cdots$
6525.2.a.z	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				261.2.a.a	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{7}+\cdots$
6525.2.a.ba	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				87.2.a.a	$1$	$1$	$1$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
6525.2.a.bb	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{5}) $	None	✓				1305.2.a.h	$1$	$1$	$1$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
6525.2.a.bc	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{17}) $	None	✓				435.2.a.h	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$
6525.2.a.bd	$6525$	$2$	6525.a	1.a	$1$	$2$	$2$	$52.102$	$\Q(\sqrt{2}) $	None	✓				435.2.c.c	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-\beta q^{7}-3q^{8}+(2-\beta )q^{11}+\cdots$
6525.2.a.be	$6525$	$2$	6525.a	1.a	$1$	$3$	$3$	$52.102$	3.3.148.1	None	✓				145.2.a.c	$1$	$1$	$1$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
6525.2.a.bf	$6525$	$2$	6525.a	1.a	$1$	$3$	$3$	$52.102$	3.3.469.1	None	✓				435.2.a.i	$1$	$1$	$1$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
6525.2.a.bg	$6525$	$2$	6525.a	1.a	$1$	$3$	$3$	$52.102$	3.3.229.1	None	✓				87.2.a.b	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
6525.2.a.bh	$6525$	$2$	6525.a	1.a	$1$	$3$	$3$	$52.102$	3.3.148.1	None	✓				145.2.a.d	$1$	$0$	$3$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots$
6525.2.a.bi	$6525$	$2$	6525.a	1.a	$1$	$4$	$4$	$52.102$	4.4.2225.1	None	✓				435.2.a.j	$1$	$1$	$-3$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
6525.2.a.bj	$6525$	$2$	6525.a	1.a	$1$	$4$	$4$	$52.102$	$\Q(\zeta_{24})^+$	None	✓				145.2.b.b	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots$
6525.2.a.bk	$6525$	$2$	6525.a	1.a	$1$	$4$	$4$	$52.102$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓				145.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{4}-2\beta _{1}q^{7}-\beta _{2}q^{8}+(-3+\cdots)q^{11}+\cdots$
6525.2.a.bl	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.246832.1	None	✓				435.2.c.e	$1$	$1$	$-3$	$0$	$0$	$8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
6525.2.a.bm	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.240881.1	None	✓				725.2.a.h	$1$	$0$	$-2$	$0$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
6525.2.a.bn	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.331312.1	None	✓				435.2.c.d	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+(1+\cdots)q^{7}+\cdots$
6525.2.a.bo	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.294577.1	None	✓				725.2.a.i	$1$	$1$	$0$	$0$	$0$	$-10$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
6525.2.a.bp	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.294577.1	None	✓				725.2.a.i	$1$	$0$	$0$	$0$	$0$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
6525.2.a.bq	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.240881.1	None	✓				725.2.a.h	$1$	$1$	$2$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
6525.2.a.br	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.331312.1	None	✓				435.2.c.d	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+(-1+\cdots)q^{7}+\cdots$
6525.2.a.bs	$6525$	$2$	6525.a	1.a	$1$	$5$	$5$	$52.102$	5.5.246832.1	None	✓				435.2.c.e	$1$	$1$	$3$	$0$	$0$	$-8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{7}+\cdots$
6525.2.a.bt	$6525$	$2$	6525.a	1.a	$1$	$6$	$6$	$52.102$	6.6.337383424.1	None	✓				145.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots$
6525.2.a.bu	$6525$	$2$	6525.a	1.a	$1$	$7$	$7$	$52.102$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		2175.2.a.ba	$1$	$1$	$-2$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\beta _{6})q^{7}+\cdots$
6525.2.a.bv	$6525$	$2$	6525.a	1.a	$1$	$7$	$7$	$52.102$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				1305.2.a.s	$1$	$1$	$-1$	$0$	$0$	$-10$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{5})q^{7}+\cdots$
6525.2.a.bw	$6525$	$2$	6525.a	1.a	$1$	$7$	$7$	$52.102$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				1305.2.a.s	$1$	$0$	$1$	$0$	$0$	$-10$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{5})q^{7}+\cdots$
6525.2.a.bx	$6525$	$2$	6525.a	1.a	$1$	$7$	$7$	$52.102$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		2175.2.a.ba	$1$	$0$	$2$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$

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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.