LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (1-50 of 78 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1188.1.d.a	$1188$	$1$	1188.d	132.d	$2$	$1$	$1$	$0.593$	$\Q$	$D_{3}$	$\Q(\sqrt{-33}) $	None	✓	✓	1188.1.d.a	$2$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+q^{14}+\cdots$
1188.1.d.b	$1188$	$1$	1188.d	132.d	$2$	$1$	$1$	$0.593$	$\Q$	$D_{3}$	$\Q(\sqrt{-33}) $	None	✓	✓	1188.1.d.a	$2$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-q^{14}+\cdots$
1188.1.d.c	$1188$	$1$	1188.d	132.d	$2$	$1$	$1$	$0.593$	$\Q$	$D_{3}$	$\Q(\sqrt{-33}) $	None	✓	✓	1188.1.d.a	$2$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}-q^{14}+\cdots$
1188.1.d.d	$1188$	$1$	1188.d	132.d	$2$	$1$	$1$	$0.593$	$\Q$	$D_{3}$	$\Q(\sqrt{-33}) $	None	✓	✓	1188.1.d.a	$2$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+q^{14}+\cdots$
1188.1.m.a	$1188$	$1$	1188.m	99.h	$6$	$2$	$1$	$0.593$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None			396.1.m.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+\zeta_{6}^{2}q^{23}+\zeta_{6}^{2}q^{31}+\cdots$
1188.1.m.b	$1188$	$1$	1188.m	99.h	$6$	$2$	$1$	$0.593$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None			396.1.m.b	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+\zeta_{6}^{2}q^{23}-3\zeta_{6}q^{25}+\cdots$
1188.1.v.a	$1188$	$1$	1188.v	33.h	$10$	$8$	$2$	$0.593$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	1188.1.v.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(\zeta_{20}^{3}-\zeta_{20}^{9})q^{5}+\zeta_{20}^{8}q^{7}+\zeta_{20}^{9}q^{11}+\cdots$
1188.1.bg.a	$1188$	$1$	1188.bg	297.q	$18$	$6$	$1$	$0.593$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		✓	1188.1.bg.a	$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q-\zeta_{18}q^{3}+(-\zeta_{18}^{3}+\zeta_{18}^{8})q^{5}+\zeta_{18}^{2}q^{9}+\cdots$
1188.1.bg.b	$1188$	$1$	1188.bg	297.q	$18$	$6$	$1$	$0.593$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		✓	1188.1.bg.b	$4$	$0$	$0$	$0$	$6$	$0$		$1$		$q+\zeta_{18}^{4}q^{3}+(1+\zeta_{18}^{2})q^{5}+\zeta_{18}^{8}q^{9}+\cdots$
1188.2.a.a	$1188$	$2$	1188.a	1.a	$1$	$1$	$1$	$9.486$	$\Q$	$_{}$	None	None	✓	✓	1188.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+q^{11}+3q^{13}-2q^{17}+\cdots$
1188.2.a.b	$1188$	$2$	1188.a	1.a	$1$	$1$	$1$	$9.486$	$\Q$	$_{}$	None	None	✓	✓	1188.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-q^{11}-4q^{13}+3q^{17}-4q^{19}+\cdots$
1188.2.a.c	$1188$	$2$	1188.a	1.a	$1$	$1$	$1$	$9.486$	$\Q$	$_{}$	None	None	✓	✓	1188.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+q^{11}-4q^{13}-3q^{17}-4q^{19}+\cdots$
1188.2.a.d	$1188$	$2$	1188.a	1.a	$1$	$1$	$1$	$9.486$	$\Q$	$_{}$	None	None	✓	✓	1188.2.a.a	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-q^{11}+3q^{13}+2q^{17}+\cdots$
1188.2.a.e	$1188$	$2$	1188.a	1.a	$1$	$2$	$2$	$9.486$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓	1188.2.a.e	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-\beta q^{7}-q^{11}-\beta q^{13}+\cdots$
1188.2.a.f	$1188$	$2$	1188.a	1.a	$1$	$2$	$2$	$9.486$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓	1188.2.a.e	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+\beta q^{7}+q^{11}+\beta q^{13}+\cdots$
1188.2.a.g	$1188$	$2$	1188.a	1.a	$1$	$3$	$3$	$9.486$	3.3.3124.1	$_{}$	None	None	✓	✓	1188.2.a.g	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{11}+(2-\beta _{1})q^{13}+\cdots$
1188.2.a.h	$1188$	$2$	1188.a	1.a	$1$	$3$	$3$	$9.486$	3.3.3124.1	$_{}$	None	None	✓	✓	1188.2.a.g	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+q^{11}+(2-\beta _{1})q^{13}+\cdots$
1188.2.b.a	$1188$	$2$	1188.b	33.d	$2$	$8$	$8$	$9.486$	8.0.3317760000.8	$_{}$	None	None		✓	1188.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{4})q^{5}-\beta _{5}q^{7}+(\beta _{4}-\beta _{6})q^{11}+\cdots$
1188.2.b.b	$1188$	$2$	1188.b	33.d	$2$	$8$	$8$	$9.486$	8.0.$\cdots$.15	$_{}$	None	None		✓	1188.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+\beta _{5}q^{7}+\beta _{4}q^{11}+(-2\beta _{2}+\cdots)q^{13}+\cdots$
1188.2.c.a	$1188$	$2$	1188.c	12.b	$2$	$20$	$20$	$9.486$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	1188.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{6}q^{4}+\beta _{16}q^{5}-\beta _{11}q^{7}+\cdots$
1188.2.c.b	$1188$	$2$	1188.c	12.b	$2$	$20$	$20$	$9.486$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	1188.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{15}q^{5}+\beta _{10}q^{7}+\cdots$
1188.2.c.c	$1188$	$2$	1188.c	12.b	$2$	$20$	$20$	$9.486$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	1188.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{13}q^{4}+\beta _{17}q^{5}-\beta _{3}q^{7}+\cdots$
1188.2.c.d	$1188$	$2$	1188.c	12.b	$2$	$20$	$20$	$9.486$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	1188.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{16}q^{5}-\beta _{4}q^{7}+\cdots$
1188.2.h.a	$1188$	$2$	1188.h	44.c	$2$	$8$	$8$	$9.486$	8.0.959512576.1	$_{}$	$\Q(\sqrt{-33}) $	None		✓	1188.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{2}-2q^{4}+\beta _{6}q^{7}-2\beta _{4}q^{8}+\cdots$
1188.2.h.b	$1188$	$2$	1188.h	44.c	$2$	$8$	$8$	$9.486$	8.0.40960000.1	$_{}$	None	None		✓	1188.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+2q^{4}-\beta _{4}q^{5}-\beta _{3}q^{7}+2\beta _{2}q^{8}+\cdots$
1188.2.h.c	$1188$	$2$	1188.h	44.c	$2$	$32$	$32$	$9.486$		$_{}$	None	None		✓	1188.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1188.2.h.d	$1188$	$2$	1188.h	44.c	$2$	$48$	$48$	$9.486$		$_{}$	None	None		✓	1188.2.h.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1188.2.i.a	$1188$	$2$	1188.i	9.c	$3$	$2$	$1$	$9.486$	$\Q(\sqrt{-3}) $	$_{}$	None	None			396.2.i.c	$2$	$0$	$0$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
1188.2.i.b	$1188$	$2$	1188.i	9.c	$3$	$2$	$1$	$9.486$	$\Q(\sqrt{-3}) $	$_{}$	None	None			396.2.i.b	$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
1188.2.i.c	$1188$	$2$	1188.i	9.c	$3$	$2$	$1$	$9.486$	$\Q(\sqrt{-3}) $	$_{}$	None	None			396.2.i.a	$2$	$0$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
1188.2.i.d	$1188$	$2$	1188.i	9.c	$3$	$6$	$3$	$9.486$	6.0.309123.1	$_{}$	None	None			396.2.i.d	$2$	$0$	$0$	$0$	$-5$	$5$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\beta _{4}-\beta _{5})q^{5}+(\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{7}+\cdots$
1188.2.i.e	$1188$	$2$	1188.i	9.c	$3$	$8$	$4$	$9.486$	8.0.5206055409.1	$_{}$	None	None			396.2.i.e	$2$	$0$	$0$	$0$	$4$	$1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{3})q^{5}+(-\beta _{2}-\beta _{3}+\beta _{4})q^{7}+\cdots$
1188.2.j.a	$1188$	$2$	1188.j	11.c	$5$	$16$	$4$	$9.486$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	1188.2.j.a	$2$	$0$	$0$	$0$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{5}-\beta _{10}q^{7}+(-\beta _{4}+\beta _{7}-\beta _{8}+\cdots)q^{11}+\cdots$
1188.2.j.b	$1188$	$2$	1188.j	11.c	$5$	$16$	$4$	$9.486$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	1188.2.j.b	$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{7}+\beta _{10})q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots$
1188.2.j.c	$1188$	$2$	1188.j	11.c	$5$	$16$	$4$	$9.486$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	1188.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{5}-\beta _{9}+\beta _{11})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
1188.2.j.d	$1188$	$2$	1188.j	11.c	$5$	$16$	$4$	$9.486$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	1188.2.j.a	$2$	$0$	$0$	$0$	$5$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{5}-\beta _{10}q^{7}+(\beta _{4}-\beta _{7}+\beta _{8}+\cdots)q^{11}+\cdots$
1188.2.q.a	$1188$	$2$	1188.q	99.g	$6$	$4$	$2$	$9.486$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None			396.2.q.a	$4$	$1$	$0$	$0$	$-9$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+\beta _{1}-\beta _{2})q^{5}+(-\beta _{2}-2\beta _{3})q^{11}+\cdots$
1188.2.q.b	$1188$	$2$	1188.q	99.g	$6$	$4$	$2$	$9.486$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None			396.2.q.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1+2\beta _{1}+\beta _{2})q^{5}+(\beta _{2}+2\beta _{3})q^{11}+\cdots$
1188.2.q.c	$1188$	$2$	1188.q	99.g	$6$	$16$	$8$	$9.486$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			396.2.q.c	$4$	$0$	$0$	$0$	$12$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{9})q^{5}-\beta _{12}q^{7}+\cdots$
1188.2.y.a	$1188$	$2$	1188.y	33.f	$10$	$32$	$8$	$9.486$		$_{}$	None	None		✓	1188.2.y.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1188.2.y.b	$1188$	$2$	1188.y	33.f	$10$	$32$	$8$	$9.486$		$_{}$	None	None		✓	1188.2.y.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1188.2.z.a	$1188$	$2$	1188.z	99.m	$15$	$96$	$12$	$9.486$		$_{}$	None	None			396.2.y.a	$4$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{15}]$
1188.2.bh.a	$1188$	$2$	1188.bh	99.p	$30$	$96$	$12$	$9.486$		$_{}$	None	None			396.2.z.a	$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{30}]$
1188.3.e.a	$1188$	$3$	1188.e	3.b	$2$	$2$	$2$	$32.371$	$\Q(\sqrt{-11}) $	$_{}$	None	None		✓	1188.3.e.a	$2$	$0$	$0$	$0$	$0$	$-22$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{5}-11q^{7}-\beta q^{11}+q^{13}+2\beta q^{17}+\cdots$
1188.3.e.b	$1188$	$3$	1188.e	3.b	$2$	$4$	$4$	$32.371$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	None	None		✓	1188.3.e.b	$2$	$0$	$0$	$0$	$0$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{3})q^{5}+2q^{7}+\beta _{3}q^{11}+(-5+\cdots)q^{13}+\cdots$
1188.3.e.c	$1188$	$3$	1188.e	3.b	$2$	$8$	$8$	$32.371$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	1188.3.e.c	$2$	$0$	$0$	$0$	$0$	$8$		$2^{4}\cdot 3^{2}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{5}+(1+\beta _{4})q^{7}-\beta _{1}q^{11}+(-2+\cdots)q^{13}+\cdots$
1188.3.e.d	$1188$	$3$	1188.e	3.b	$2$	$12$	$12$	$32.371$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	1188.3.e.d	$2$	$0$	$0$	$0$	$0$	$20$		$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(2+\beta _{2})q^{7}-\beta _{6}q^{11}+(-5+\cdots)q^{13}+\cdots$
1188.3.f.a	$1188$	$3$	1188.f	11.b	$2$	$16$	$16$	$32.371$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	1188.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{5}+\beta _{1}q^{7}+\beta _{12}q^{11}-\beta _{5}q^{13}+\cdots$
1188.3.f.b	$1188$	$3$	1188.f	11.b	$2$	$16$	$16$	$32.371$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	1188.3.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{5}+\beta _{13}q^{7}+\beta _{8}q^{11}-\beta _{14}q^{13}+\cdots$
1188.3.m.a	$1188$	$3$	1188.m	99.h	$6$	$4$	$2$	$32.371$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None			396.3.m.a	$4$	$0$	$0$	$0$	$-2$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{5}+(-11-11\beta _{1})q^{11}+(3+19\beta _{1}+\cdots)q^{23}+\cdots$

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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.