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 225 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
1280.1.e.a	$1280$	$1$	1280.e	40.e	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $			✓	✓	80.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}+q^{9}-q^{25}-2 i q^{29}+2 q^{41}+\cdots$
1280.1.h.a	$1280$	$1$	1280.h	20.d	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None	✓				640.1.e.c	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
1280.1.h.b	$1280$	$1$	1280.h	20.d	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{10}) $					640.1.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}-q^{9}-2 i q^{13}-q^{25}-2 i q^{37}+\cdots$
1280.1.h.c	$1280$	$1$	1280.h	20.d	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None	✓				640.1.e.c	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{3}+q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
1280.1.m.a	$1280$	$1$	1280.m	40.i	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					160.1.p.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}+i q^{9}+(i-1)q^{13}+(i-1)q^{17}+\cdots$
1280.1.m.b	$1280$	$1$	1280.m	40.i	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					160.1.p.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}+i q^{9}+(-i+1)q^{13}+(i-1)q^{17}+\cdots$
1280.1.p.a	$1280$	$1$	1280.p	5.c	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					640.1.m.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-i q^{9}+(i+1)q^{13}+(-i+1)q^{17}+\cdots$
1280.1.p.b	$1280$	$1$	1280.p	5.c	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					640.1.m.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-i q^{9}+(-i-1)q^{13}+(-i+1)q^{17}+\cdots$
1280.2.a.a	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				40.2.d.a	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.b	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				320.2.d.a	$1$	$0$	$0$	$-2$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+(3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.c	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				320.2.d.a	$1$	$1$	$0$	$-2$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+\cdots$
1280.2.a.d	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				40.2.d.a	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+\cdots$
1280.2.a.e	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.c	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}-2\beta q^{11}+\cdots$
1280.2.a.f	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.d	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots$
1280.2.a.g	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots$
1280.2.a.h	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓				640.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+\beta q^{7}+7q^{9}-6q^{13}+\cdots$
1280.2.a.i	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.b	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots$
1280.2.a.j	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.d	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots$
1280.2.a.k	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				640.2.d.c	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+\beta q^{7}-q^{9}-2\beta q^{11}+\cdots$
1280.2.a.l	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓				640.2.d.a	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-\beta q^{7}+7q^{9}+6q^{13}+\cdots$
1280.2.a.m	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				320.2.d.a	$1$	$1$	$0$	$2$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(-3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.n	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				40.2.d.a	$1$	$0$	$0$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.o	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				40.2.d.a	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1280.2.a.p	$1280$	$2$	1280.a	1.a	$1$	$2$	$2$	$10.221$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				320.2.d.a	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1280.2.c.a	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					640.2.f.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(i-2)q^{5}+3 q^{9}-6 i q^{13}+8 i q^{17}+\cdots$
1280.2.c.b	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-5}) $	$_{}$	$\Q(\sqrt{-10}) $	None					320.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots$
1280.2.c.c	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-5}) $	$_{}$	$\Q(\sqrt{-10}) $	None					320.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots$
1280.2.c.d	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					640.2.f.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(i+2)q^{5}+3 q^{9}-6 i q^{13}-8 i q^{17}+\cdots$
1280.2.c.e	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{6})$	$_{}$	None	None					640.2.f.c	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots$
1280.2.c.f	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5}) $	None					640.2.f.f	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots$
1280.2.c.g	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					320.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$
1280.2.c.h	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					320.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots$
1280.2.c.i	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					40.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
1280.2.c.j	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5}) $	None					640.2.f.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots$
1280.2.c.k	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					40.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots$
1280.2.c.l	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-10}) $	None					640.2.f.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots$
1280.2.c.m	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{6})$	$_{}$	None	None					640.2.f.c	$4$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots$
1280.2.d.a	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					40.2.a.a	$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}-4 q^{7}+3 q^{9}-4 i q^{11}+\cdots$
1280.2.d.b	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.a.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+i q^{5}-2 q^{7}-q^{9}-4 i q^{11}+\cdots$
1280.2.d.c	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.2.a.a	$2$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{5}-2 q^{7}-q^{9}-2 i q^{13}+\cdots$
1280.2.d.d	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					640.2.a.c	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{5}-2 q^{7}+3 q^{9}-6 i q^{11}+\cdots$
1280.2.d.e	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					640.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+i q^{5}-q^{9}-2 i q^{11}+\cdots$
1280.2.d.f	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					640.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{5}-q^{9}-2 i q^{11}+\cdots$
1280.2.d.g	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+i q^{5}+2 q^{7}-q^{9}+2 i q^{13}+\cdots$
1280.2.d.h	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{5}+2 q^{7}-q^{9}-4 i q^{11}+\cdots$
1280.2.d.i	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					640.2.a.c	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}+2 q^{7}+3 q^{9}-6 i q^{11}+\cdots$
1280.2.d.j	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1}) $	$_{}$	None	None					40.2.a.a	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}+4 q^{7}+3 q^{9}+4 i q^{11}+\cdots$
1280.2.d.k	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{5})$	$_{}$	None	None					640.2.a.i	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots$
1280.2.d.l	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	$\Q(\zeta_{8})$	$_{}$	None	None					160.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}+\beta_1 q^{5}-\beta_{3} q^{7}-5 q^{9}+\cdots$
1280.2.d.m	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{5})$	$_{}$	None	None					640.2.a.i	$2$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots$

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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.