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 222 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
1152.1.b.a	$1152$	$1$	1152.b	8.d	$2$	$1$	$1$	$0.575$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓				128.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+2q^{17}+q^{25}-2q^{41}+q^{49}-2q^{73}+\cdots$
1152.1.b.b	$1152$	$1$	1152.b	8.d	$2$	$2$	$2$	$0.575$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{6}) $		✓	✓		1152.1.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-iq^{5}-3q^{25}-iq^{29}+q^{49}+iq^{53}+\cdots$
1152.1.h.a	$1152$	$1$	1152.h	24.h	$2$	$4$	$4$	$0.575$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1152.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}+\cdots)q^{17}+\cdots$
1152.1.n.a	$1152$	$1$	1152.n	72.j	$6$	$2$	$1$	$0.575$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1152.1.n.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
1152.1.n.b	$1152$	$1$	1152.n	72.j	$6$	$2$	$1$	$0.575$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1152.1.n.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
1152.1.t.a	$1152$	$1$	1152.t	72.p	$6$	$4$	$2$	$0.575$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	1152.1.t.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{11}+\cdots$
1152.2.a.a	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.a	$1$	$0$	$0$	$0$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots$
1152.2.a.b	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.a	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots$
1152.2.a.c	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				128.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}+2q^{11}+2q^{13}+2q^{17}+\cdots$
1152.2.a.d	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+4q^{11}-2q^{13}+4q^{17}+\cdots$
1152.2.a.e	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+4q^{11}+2q^{13}-4q^{17}+\cdots$
1152.2.a.f	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-4q^{11}-2q^{13}+4q^{17}+\cdots$
1152.2.a.g	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-4q^{11}+2q^{13}-4q^{17}+\cdots$
1152.2.a.h	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				128.2.a.a	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots$
1152.2.a.i	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-4q^{11}+6q^{13}-6q^{17}+4q^{23}+\cdots$
1152.2.a.j	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+4q^{11}-6q^{13}-6q^{17}+4q^{23}+\cdots$
1152.2.a.k	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.b	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-4q^{11}-6q^{13}-6q^{17}-4q^{23}+\cdots$
1152.2.a.l	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.b	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+4q^{11}+6q^{13}-6q^{17}-4q^{23}+\cdots$
1152.2.a.m	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				128.2.a.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots$
1152.2.a.n	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{11}-2q^{13}-4q^{17}+\cdots$
1152.2.a.o	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots$
1152.2.a.p	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+4q^{11}-2q^{13}-4q^{17}+\cdots$
1152.2.a.q	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓	✓			1152.2.a.d	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+4q^{11}+2q^{13}+4q^{17}+\cdots$
1152.2.a.r	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				128.2.a.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots$
1152.2.a.s	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.a	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-2q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots$
1152.2.a.t	$1152$	$2$	1152.a	1.a	$1$	$1$	$1$	$9.199$	$\Q$	$_{}$	None	None	✓				384.2.a.a	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots$
1152.2.c.a	$1152$	$2$	1152.c	12.b	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
1152.2.c.b	$1152$	$2$	1152.c	12.b	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots$
1152.2.c.c	$1152$	$2$	1152.c	12.b	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
1152.2.c.d	$1152$	$2$	1152.c	12.b	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots$
1152.2.d.a	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-1}) $	$_{}$	None	None					384.2.d.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots$
1152.2.d.b	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1152.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots$
1152.2.d.c	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None					128.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots$
1152.2.d.d	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					128.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots$
1152.2.d.e	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1152.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots$
1152.2.d.f	$1152$	$2$	1152.d	8.b	$2$	$2$	$2$	$9.199$	$\Q(\sqrt{-1}) $	$_{}$	None	None					384.2.d.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots$
1152.2.d.g	$1152$	$2$	1152.d	8.b	$2$	$4$	$4$	$9.199$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1152.2.d.g	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots$
1152.2.d.h	$1152$	$2$	1152.d	8.b	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None					384.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots$
1152.2.f.a	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}-\zeta_{8}q^{13}+\cdots$
1152.2.f.b	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1152.2.f.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}-3q^{25}+\cdots$
1152.2.f.c	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1152.2.f.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{13}-5\zeta_{8}^{2}q^{17}+13q^{25}+\cdots$
1152.2.f.d	$1152$	$2$	1152.f	24.f	$2$	$4$	$4$	$9.199$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1152.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}+\zeta_{8}q^{13}+\cdots$
1152.2.i.a	$1152$	$2$	1152.i	9.c	$3$	$2$	$1$	$9.199$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1152.2.i.a	$2$	$0$	$0$	$-3$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
1152.2.i.b	$1152$	$2$	1152.i	9.c	$3$	$2$	$1$	$9.199$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1152.2.i.a	$2$	$1$	$0$	$-3$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
1152.2.i.c	$1152$	$2$	1152.i	9.c	$3$	$2$	$1$	$9.199$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1152.2.i.a	$2$	$0$	$0$	$3$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
1152.2.i.d	$1152$	$2$	1152.i	9.c	$3$	$2$	$1$	$9.199$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1152.2.i.a	$2$	$0$	$0$	$3$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
1152.2.i.e	$1152$	$2$	1152.i	9.c	$3$	$10$	$5$	$9.199$	10.0.$\cdots$.1	$_{}$	None	None		✓			1152.2.i.e	$2$	$0$	$0$	$-1$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{5}-\beta _{7})q^{3}-\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
1152.2.i.f	$1152$	$2$	1152.i	9.c	$3$	$10$	$5$	$9.199$	10.0.$\cdots$.1	$_{}$	None	None		✓			1152.2.i.e	$2$	$0$	$0$	$-1$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{8}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
1152.2.i.g	$1152$	$2$	1152.i	9.c	$3$	$10$	$5$	$9.199$	10.0.$\cdots$.1	$_{}$	None	None		✓			1152.2.i.e	$2$	$0$	$0$	$1$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{5}+\beta _{7})q^{3}+\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
1152.2.i.h	$1152$	$2$	1152.i	9.c	$3$	$10$	$5$	$9.199$	10.0.$\cdots$.1	$_{}$	None	None		✓			1152.2.i.e	$2$	$0$	$0$	$1$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{5}+\beta _{7})q^{3}-\beta _{8}q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$

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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.