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				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	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7569.2.a.a	$7569$	$2$	7569.a	1.a	$1$	$1$	$1$	$60.439$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			7569.2.a.a	$2$	$0$	$0$	$0$	$0$	$-1$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots$
7569.2.a.b	$7569$	$2$	7569.a	1.a	$1$	$1$	$1$	$60.439$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			7569.2.a.a	$2$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}+2q^{13}+4q^{16}+q^{19}+\cdots$
7569.2.a.c	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{2}) $	None	✓				29.2.a.a	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+2\beta q^{7}+\cdots$
7569.2.a.d	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				841.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots$
7569.2.a.e	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				2523.2.a.b	$1$	$1$	$-1$	$0$	$1$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+(2+\cdots)q^{7}+\cdots$
7569.2.a.f	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				87.2.c.a	$1$	$1$	$-1$	$0$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.g	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				2523.2.a.a	$1$	$1$	$-1$	$0$	$3$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.h	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				261.2.a.a	$1$	$1$	$-1$	$0$	$4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.i	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				29.2.b.a	$2$	$1$	$0$	$0$	$-6$	$4$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-3q^{5}+2q^{7}-\beta q^{8}+\cdots$
7569.2.a.j	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				261.2.a.a	$1$	$1$	$1$	$0$	$-4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.k	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				87.2.a.a	$1$	$0$	$1$	$0$	$-2$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots$
7569.2.a.l	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				841.2.a.a	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots$
7569.2.a.m	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				2523.2.a.b	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+(2+\cdots)q^{7}+\cdots$
7569.2.a.n	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				87.2.c.a	$1$	$1$	$1$	$0$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.o	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	$\Q(\sqrt{5}) $	None	✓				2523.2.a.a	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.p	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	$\Q(\zeta_{14})^+$	None	✓				29.2.d.a	$1$	$0$	$-1$	$0$	$3$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{1}+\beta _{2})q^{5}+\cdots$
7569.2.a.q	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.733.1	None	✓				2523.2.a.i	$1$	$0$	$-1$	$0$	$-3$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
7569.2.a.r	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	$\Q(\zeta_{14})^+$	None	✓				29.2.d.a	$1$	$0$	$1$	$0$	$3$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{1}+\beta _{2})q^{5}+\cdots$
7569.2.a.s	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.733.1	None	✓				2523.2.a.i	$1$	$1$	$1$	$0$	$-3$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
7569.2.a.t	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.229.1	None	✓				87.2.a.b	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots$
7569.2.a.u	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	$\Q(\zeta_{15})^+$	$\Q(\sqrt{-3}) $	✓	✓			7569.2.a.u	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-1+3\beta _{1}-\beta _{3})q^{7}+(4\beta _{2}+\cdots)q^{13}+\cdots$
7569.2.a.v	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	$\Q(\zeta_{15})^+$	$\Q(\sqrt{-3}) $	✓	✓			7569.2.a.u	$2$	$0$	$0$	$0$	$0$	$1$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-1+3\beta _{1}-\beta _{3})q^{7}+(4\beta _{2}+\cdots)q^{13}+\cdots$
7569.2.a.w	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	4.4.7600.1	None	✓	✓			7569.2.a.w	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots$
7569.2.a.x	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	4.4.7600.1	None	✓	✓			7569.2.a.w	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots$
7569.2.a.y	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.11973625.1	None	✓				841.2.a.g	$1$	$1$	$-2$	$0$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
7569.2.a.z	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.8902000.1	None	✓				2523.2.a.k	$1$	$0$	$-1$	$0$	$-5$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
7569.2.a.ba	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.160016229.2	$\Q(\sqrt{-87}) $	✓				261.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{3}$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
7569.2.a.bb	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.8902000.1	None	✓				2523.2.a.k	$1$	$1$	$1$	$0$	$-5$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
7569.2.a.bc	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.11973625.1	None	✓				841.2.a.g	$1$	$0$	$2$	$0$	$2$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
7569.2.a.bd	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.2841328125.1	None	✓				841.2.a.i	$1$	$1$	$-4$	$0$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{6})q^{5}+\cdots$
7569.2.a.be	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.5878828125.1	None	✓				2523.2.a.m	$1$	$0$	$-1$	$0$	$9$	$-12$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
7569.2.a.bf	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.$\cdots$.2	None	✓	✓			7569.2.a.bf	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$
7569.2.a.bg	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.$\cdots$.2	None	✓	✓			7569.2.a.bf	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{6}-\beta _{7})q^{5}+\cdots$
7569.2.a.bh	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.5878828125.1	None	✓				2523.2.a.m	$1$	$1$	$1$	$0$	$9$	$-12$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
7569.2.a.bi	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.2841328125.1	None	✓				841.2.a.i	$1$	$0$	$4$	$0$	$1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{6})q^{5}+\cdots$
7569.2.a.bj	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				87.2.g.a	$1$	$0$	$-5$	$0$	$4$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
7569.2.a.bk	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				87.2.g.b	$1$	$0$	$-1$	$0$	$0$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
7569.2.a.bl	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				87.2.g.b	$1$	$0$	$1$	$0$	$0$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
7569.2.a.bm	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				87.2.g.a	$1$	$0$	$5$	$0$	$4$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots$
7569.2.a.bn	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				87.2.i.a	$1$	$1$	$-6$	$0$	$-2$	$-10$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
7569.2.a.bo	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				2523.2.a.t	$1$	$1$	$-1$	$0$	$-7$	$9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{3}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots$
7569.2.a.bp	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	12.12.$\cdots$.1	None	✓				29.2.e.a	$2$	$1$	$0$	$0$	$-8$	$10$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{11}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots$
7569.2.a.bq	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				261.2.k.d	$2$	$1$	$0$	$0$	$0$	$-14$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.br	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				261.2.k.d	$2$	$1$	$0$	$0$	$0$	$-14$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots$
7569.2.a.bs	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		2523.2.a.t	$1$	$0$	$1$	$0$	$-7$	$9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots$
7569.2.a.bt	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				87.2.i.a	$1$	$1$	$6$	$0$	$-2$	$-10$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
7569.2.a.bu	$7569$	$2$	7569.a	1.a	$1$	$16$	$16$	$60.439$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓		7569.2.a.bu	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{10}+\cdots)q^{5}+\cdots$
7569.2.a.bv	$7569$	$2$	7569.a	1.a	$1$	$16$	$16$	$60.439$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓			7569.2.a.bu	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{10})q^{5}+\cdots$
7569.2.a.bw	$7569$	$2$	7569.a	1.a	$1$	$36$	$36$	$60.439$		None	✓		✓		261.2.o.c	$4$	$0$	$0$	$0$	$0$	$28$	$+$	$-$	$-$		$\mathrm{SU}(2)$

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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.