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 127 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
1792.1.c.a	$1792$	$1$	1792.c	7.b	$2$	$1$	$1$	$0.894$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓				56.1.h.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots$
1792.1.c.b	$1792$	$1$	1792.c	7.b	$2$	$1$	$1$	$0.894$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓				56.1.h.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots$
1792.1.c.c	$1792$	$1$	1792.c	7.b	$2$	$2$	$2$	$0.894$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None					896.1.h.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots$
1792.1.c.d	$1792$	$1$	1792.c	7.b	$2$	$2$	$2$	$0.894$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None					896.1.h.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots$
1792.1.o.a	$1792$	$1$	1792.o	56.k	$6$	$4$	$2$	$0.894$	$\Q(\zeta_{12})$	$A_{4}$	None	None					224.1.r.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1792.1.o.b	$1792$	$1$	1792.o	56.k	$6$	$4$	$2$	$0.894$	$\Q(\zeta_{12})$	$A_{4}$	None	None					224.1.r.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
1792.1.v.a	$1792$	$1$	1792.v	224.v	$8$	$4$	$1$	$0.894$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None					224.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots$
1792.1.v.b	$1792$	$1$	1792.v	224.v	$8$	$4$	$1$	$0.894$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None					224.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1792.1.bf.a	$1792$	$1$	1792.bf	448.af	$16$	$8$	$1$	$0.894$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-7}) $	None			✓	✓	448.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots$
1792.1.bt.a	$1792$	$1$	1792.bt	1792.at	$64$	$32$	$1$	$0.894$	$\Q(\zeta_{64})$	$D_{64}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1792.1.bt.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots$
1792.2.a.a	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				448.2.b.a	$1$	$1$	$0$	$-2$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots$
1792.2.a.b	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				896.2.b.a	$1$	$1$	$0$	$-2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots$
1792.2.a.c	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				896.2.b.a	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots$
1792.2.a.d	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				448.2.b.a	$1$	$0$	$0$	$-2$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1792.2.a.e	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				448.2.b.a	$1$	$1$	$0$	$2$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
1792.2.a.f	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				896.2.b.a	$1$	$0$	$0$	$2$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots$
1792.2.a.g	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				896.2.b.a	$1$	$0$	$0$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots$
1792.2.a.h	$1792$	$2$	1792.a	1.a	$1$	$1$	$1$	$14.309$	$\Q$	$_{}$	None	None	✓				448.2.b.a	$1$	$0$	$0$	$2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots$
1792.2.a.i	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				448.2.b.c	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots$
1792.2.a.j	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				896.2.b.e	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots$
1792.2.a.k	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				448.2.b.c	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$
1792.2.a.l	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				896.2.b.e	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
1792.2.a.m	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				896.2.b.b	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots$
1792.2.a.n	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				56.2.b.a	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots$
1792.2.a.o	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				896.2.b.b	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots$
1792.2.a.p	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				56.2.b.a	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots$
1792.2.a.q	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				448.2.b.c	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$
1792.2.a.r	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				896.2.b.e	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
1792.2.a.s	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				448.2.b.c	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
1792.2.a.t	$1792$	$2$	1792.a	1.a	$1$	$2$	$2$	$14.309$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				896.2.b.e	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots$
1792.2.a.u	$1792$	$2$	1792.a	1.a	$1$	$4$	$4$	$14.309$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓		✓		896.2.b.f	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots$
1792.2.a.v	$1792$	$2$	1792.a	1.a	$1$	$4$	$4$	$14.309$	4.4.9248.1	$_{}$	None	None	✓		✓		56.2.b.b	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots$
1792.2.a.w	$1792$	$2$	1792.a	1.a	$1$	$4$	$4$	$14.309$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				896.2.b.f	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
1792.2.a.x	$1792$	$2$	1792.a	1.a	$1$	$4$	$4$	$14.309$	4.4.9248.1	$_{}$	None	None	✓				56.2.b.b	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots$
1792.2.b.a	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+2\beta q^{5}-q^{7}-q^{9}-8 q^{15}+\cdots$
1792.2.b.b	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					224.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-q^{7}-q^{9}-2\beta q^{11}-2\beta q^{13}+\cdots$
1792.2.b.c	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					14.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-q^{7}-q^{9}+2\beta q^{13}+6 q^{17}+\cdots$
1792.2.b.d	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}-q^{7}+3 q^{9}-2\beta q^{11}+\beta q^{13}+\cdots$
1792.2.b.e	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					896.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{7}+3 q^{9}-\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots$
1792.2.b.f	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					224.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{11}+2\beta q^{13}+\cdots$
1792.2.b.g	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					14.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{13}+6 q^{17}+\cdots$
1792.2.b.h	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.b	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2\beta q^{5}+q^{7}-q^{9}+8 q^{15}+\cdots$
1792.2.b.i	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+q^{7}+3 q^{9}+2\beta q^{11}+\beta q^{13}+\cdots$
1792.2.b.j	$1792$	$2$	1792.b	8.b	$2$	$2$	$2$	$14.309$	$\Q(\sqrt{-1}) $	$_{}$	None	None					896.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{7}+3 q^{9}+\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots$
1792.2.b.k	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	$\Q(i, \sqrt{5})$	$_{}$	None	None					224.2.a.c	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots$
1792.2.b.l	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	$\Q(\zeta_{12})$	$_{}$	None	None					896.2.a.e	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}-\beta_1 q^{5}-q^{7}+(\beta_{3}-1)q^{9}+\cdots$
1792.2.b.m	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	$\Q(i, \sqrt{5})$	$_{}$	None	None					224.2.a.c	$2$	$0$	$0$	$0$	$0$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots$
1792.2.b.n	$1792$	$2$	1792.b	8.b	$2$	$4$	$4$	$14.309$	$\Q(\zeta_{12})$	$_{}$	None	None					896.2.a.e	$2$	$0$	$0$	$0$	$0$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+\beta_1 q^{5}+q^{7}+(\beta_{3}-1)q^{9}+\cdots$
1792.2.b.o	$1792$	$2$	1792.b	8.b	$2$	$6$	$6$	$14.309$	6.0.399424.1	$_{}$	None	None					896.2.a.i	$2$	$0$	$0$	$0$	$0$	$-6$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots$
1792.2.b.p	$1792$	$2$	1792.b	8.b	$2$	$6$	$6$	$14.309$	6.0.399424.1	$_{}$	None	None					896.2.a.i	$2$	$0$	$0$	$0$	$0$	$6$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots$

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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.