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 63 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1540.1.b.a	$1540$	$1$	1540.b	1540.b	$2$	$4$	$4$	$0.769$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1540.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\cdots$
1540.1.b.b	$1540$	$1$	1540.b	1540.b	$2$	$4$	$4$	$0.769$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1540.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}+\cdots$
1540.1.bj.a	$1540$	$1$	1540.bj	1540.aj	$6$	$8$	$4$	$0.769$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		✓			1540.1.bj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}+\zeta_{24}^{10}q^{5}+\cdots$
1540.1.bj.b	$1540$	$1$	1540.bj	1540.aj	$6$	$8$	$4$	$0.769$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		✓			1540.1.bj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{10}q^{5}+\cdots$
1540.1.bq.a	$1540$	$1$	1540.bq	385.y	$10$	$8$	$2$	$0.769$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-35}) $	None		✓			1540.1.bq.a	$4$	$0$	$0$	$-3$	$-2$	$-2$		$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{3}-\zeta_{30}^{3}q^{5}-\zeta_{30}^{9}q^{7}+\cdots$
1540.1.bq.b	$1540$	$1$	1540.bq	385.y	$10$	$8$	$2$	$0.769$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-35}) $	None		✓			1540.1.bq.a	$4$	$0$	$0$	$3$	$2$	$2$		$1$		$q+(\zeta_{30}^{5}+\zeta_{30}^{7})q^{3}+\zeta_{30}^{3}q^{5}+\zeta_{30}^{9}q^{7}+\cdots$
1540.2.a.a	$1540$	$2$	1540.a	1.a	$1$	$1$	$1$	$12.297$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.a	$1$	$1$	$0$	$-2$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
1540.2.a.b	$1540$	$2$	1540.a	1.a	$1$	$1$	$1$	$12.297$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.b	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{9}-q^{11}+2q^{13}+\cdots$
1540.2.a.c	$1540$	$2$	1540.a	1.a	$1$	$1$	$1$	$12.297$	$\Q$	$_{}$	None	None	✓	✓			1540.2.a.c	$1$	$0$	$0$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
1540.2.a.d	$1540$	$2$	1540.a	1.a	$1$	$2$	$2$	$12.297$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-q^{7}-q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots$
1540.2.a.e	$1540$	$2$	1540.a	1.a	$1$	$2$	$2$	$12.297$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.e	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots$
1540.2.a.f	$1540$	$2$	1540.a	1.a	$1$	$3$	$3$	$12.297$	3.3.564.1	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.f	$1$	$1$	$0$	$-2$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots$
1540.2.a.g	$1540$	$2$	1540.a	1.a	$1$	$3$	$3$	$12.297$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.g	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots$
1540.2.a.h	$1540$	$2$	1540.a	1.a	$1$	$3$	$3$	$12.297$	3.3.3028.1	$_{}$	None	None	✓	✓	✓		1540.2.a.h	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+q^{7}+(4+\beta _{1}+\beta _{2})q^{9}+\cdots$
1540.2.a.i	$1540$	$2$	1540.a	1.a	$1$	$4$	$4$	$12.297$	4.4.111028.1	$_{}$	None	None	✓	✓	✓	✓	1540.2.a.i	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}-q^{7}+(2+\beta _{2})q^{9}+q^{11}+\cdots$
1540.2.e.a	$1540$	$2$	1540.e	5.b	$2$	$12$	$12$	$12.297$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1540.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{9}+\beta _{11})q^{5}+\beta _{6}q^{7}+\beta _{2}q^{9}+\cdots$
1540.2.e.b	$1540$	$2$	1540.e	5.b	$2$	$16$	$16$	$12.297$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		1540.2.e.b	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{4}q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots$
1540.2.h.a	$1540$	$2$	1540.h	77.b	$2$	$32$	$32$	$12.297$		$_{}$	None	None		✓	✓	✓	1540.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1540.2.l.a	$1540$	$2$	1540.l	385.h	$2$	$4$	$4$	$12.297$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1540.2.l.a	$4$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
1540.2.l.b	$1540$	$2$	1540.l	385.h	$2$	$4$	$4$	$12.297$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1540.2.l.a	$4$	$0$	$0$	$8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+q^{9}+\cdots$
1540.2.l.c	$1540$	$2$	1540.l	385.h	$2$	$8$	$8$	$12.297$	8.0.121550625.1	$_{}$	$\Q(\sqrt{-35}) $	None		✓			1540.2.l.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{4}+\beta _{6})q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
1540.2.l.d	$1540$	$2$	1540.l	385.h	$2$	$32$	$32$	$12.297$		$_{}$	None	None		✓	✓		1540.2.l.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1540.2.q.a	$1540$	$2$	1540.q	7.c	$3$	$2$	$1$	$12.297$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1540.2.q.a	$2$	$0$	$0$	$-2$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
1540.2.q.b	$1540$	$2$	1540.q	7.c	$3$	$2$	$1$	$12.297$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1540.2.q.b	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
1540.2.q.c	$1540$	$2$	1540.q	7.c	$3$	$2$	$1$	$12.297$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1540.2.q.c	$2$	$1$	$0$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
1540.2.q.d	$1540$	$2$	1540.q	7.c	$3$	$2$	$1$	$12.297$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1540.2.q.d	$2$	$0$	$0$	$2$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
1540.2.q.e	$1540$	$2$	1540.q	7.c	$3$	$8$	$4$	$12.297$	8.0.447703281.1	$_{}$	None	None		✓			1540.2.q.e	$2$	$0$	$0$	$1$	$4$	$3$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+(1+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$
1540.2.q.f	$1540$	$2$	1540.q	7.c	$3$	$12$	$6$	$12.297$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1540.2.q.f	$2$	$0$	$0$	$-3$	$6$	$-3$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}+\beta _{6}-\beta _{10})q^{3}+\beta _{6}q^{5}-\beta _{1}q^{7}+\cdots$
1540.2.q.g	$1540$	$2$	1540.q	7.c	$3$	$12$	$6$	$12.297$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1540.2.q.g	$2$	$0$	$0$	$2$	$-6$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{3}q^{7}+(\beta _{3}+2\beta _{5}+\cdots)q^{9}+\cdots$
1540.2.q.h	$1540$	$2$	1540.q	7.c	$3$	$16$	$8$	$12.297$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		1540.2.q.h	$2$	$0$	$0$	$-3$	$-8$	$-1$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{11}q^{3}+\beta _{1}q^{5}+\beta _{12}q^{7}+(\beta _{1}-\beta _{4}+\cdots)q^{9}+\cdots$
1540.2.v.a	$1540$	$2$	1540.v	35.f	$4$	$4$	$2$	$12.297$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1540.2.v.a	$2$	$0$	$0$	$-4$	$4$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{3}+(1+2\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
1540.2.v.b	$1540$	$2$	1540.v	35.f	$4$	$4$	$2$	$12.297$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1540.2.v.a	$2$	$0$	$0$	$4$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{3}+(-1-2\beta _{1})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1540.2.v.c	$1540$	$2$	1540.v	35.f	$4$	$32$	$16$	$12.297$		$_{}$	None	None		✓			1540.2.v.c	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1540.2.v.d	$1540$	$2$	1540.v	35.f	$4$	$40$	$20$	$12.297$		$_{}$	None	None		✓	✓		1540.2.v.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1540.2.y.a	$1540$	$2$	1540.y	55.e	$4$	$72$	$36$	$12.297$		$_{}$	None	None		✓	✓	✓	1540.2.y.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1540.2.z.a	$1540$	$2$	1540.z	11.c	$5$	$20$	$5$	$12.297$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1540.2.z.a	$2$	$0$	$0$	$0$	$-5$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{11})q^{3}+\beta _{7}q^{5}+(1+\beta _{7}+\cdots)q^{7}+\cdots$
1540.2.z.b	$1540$	$2$	1540.z	11.c	$5$	$20$	$5$	$12.297$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1540.2.z.b	$2$	$0$	$0$	$0$	$5$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{7}-\beta _{8})q^{3}-\beta _{9}q^{5}+(-1-\beta _{8}+\cdots)q^{7}+\cdots$
1540.2.z.c	$1540$	$2$	1540.z	11.c	$5$	$28$	$7$	$12.297$		$_{}$	None	None		✓			1540.2.z.c	$2$	$0$	$0$	$-7$	$-7$	$-7$			$\mathrm{SU}(2)[C_{5}]$
1540.2.z.d	$1540$	$2$	1540.z	11.c	$5$	$28$	$7$	$12.297$		$_{}$	None	None		✓			1540.2.z.d	$2$	$0$	$0$	$-1$	$7$	$7$			$\mathrm{SU}(2)[C_{5}]$
1540.2.ba.a	$1540$	$2$	1540.ba	385.o	$6$	$96$	$48$	$12.297$		$_{}$	None	None		✓	✓	✓	1540.2.ba.a	$8$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
1540.2.bi.a	$1540$	$2$	1540.bi	35.j	$6$	$4$	$2$	$12.297$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1540.2.bi.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots$
1540.2.bi.b	$1540$	$2$	1540.bi	35.j	$6$	$36$	$18$	$12.297$		$_{}$	None	None		✓			1540.2.bi.b	$4$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{6}]$
1540.2.bi.c	$1540$	$2$	1540.bi	35.j	$6$	$40$	$20$	$12.297$		$_{}$	None	None		✓	✓		1540.2.bi.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1540.2.bl.a	$1540$	$2$	1540.bl	77.i	$6$	$64$	$32$	$12.297$		$_{}$	None	None		✓	✓	✓	1540.2.bl.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1540.3.c.a	$1540$	$3$	1540.c	7.b	$2$	$56$	$56$	$41.962$		$_{}$	None	None		✓	✓	✓	1540.3.c.a	$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{2}]$
1540.3.f.a	$1540$	$3$	1540.f	55.d	$2$	$72$	$72$	$41.962$		$_{}$	None	None		✓	✓	✓	1540.3.f.a	$4$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{2}]$
1540.3.j.a	$1540$	$3$	1540.j	11.b	$2$	$48$	$48$	$41.962$		$_{}$	None	None		✓	✓	✓	1540.3.j.a	$2$	$0$	$0$	$16$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1540.3.o.a	$1540$	$3$	1540.o	35.c	$2$	$80$	$80$	$41.962$		$_{}$	None	None		✓	✓	✓	1540.3.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1540.4.a.a	$1540$	$4$	1540.a	1.a	$1$	$1$	$1$	$90.863$	$\Q$	$_{}$	None	None	✓	✓			1540.4.a.a	$1$	$0$	$0$	$-8$	$5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+5q^{5}-7q^{7}+37q^{9}-11q^{11}+\cdots$
1540.4.a.b	$1540$	$4$	1540.a	1.a	$1$	$1$	$1$	$90.863$	$\Q$	$_{}$	None	None	✓	✓			1540.4.a.b	$1$	$1$	$0$	$-8$	$5$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+5q^{5}-7q^{7}+37q^{9}+11q^{11}+\cdots$

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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.