Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

Sort order

Select

Results (1-50 of 38787 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1001.1.r.a	$1001$	$1$	1001.r	1001.r	$6$	$4$	$2$	$0.500$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
1001.1.y.a	$1001$	$1$	1001.y	1001.y	$6$	$2$	$1$	$0.500$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\)
1001.1.y.b	$1001$	$1$	1001.y	1001.y	$6$	$2$	$1$	$0.500$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1001.1.y.c	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.y.d	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.bo.a	$1001$	$1$	1001.bo	1001.ao	$6$	$4$	$2$	$0.500$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1003.1.b.a	$1003$	$1$	1003.b	1003.b	$2$	$1$	$1$	$0.501$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \)	\(\Q(\sqrt{17}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b	$1003$	$1$	1003.b	1003.b	$2$	$2$	$2$	$0.501$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
1003.1.f.a	$1003$	$1$	1003.f	1003.f	$4$	$2$	$1$	$0.501$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)	$1$		\(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b	$1003$	$1$	1003.f	1003.f	$4$	$4$	$2$	$0.501$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(2\)	\(2\)	\(2\)	$2$		\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
1003.1.h.a	$1003$	$1$	1003.h	1003.h	$8$	$4$	$1$	$0.501$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1003.1.h.b	$1003$	$1$	1003.h	1003.h	$8$	$8$	$2$	$0.501$	\(\Q(\zeta_{24})\)	$D_{24}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1004.1.d.a	$1004$	$1$	1004.d	251.b	$2$	$1$	$1$	$0.501$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-251}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots\)
1004.1.d.b	$1004$	$1$	1004.d	251.b	$2$	$6$	$6$	$0.501$	\(\Q(\zeta_{21})^+\)	$D_{21}$	\(\Q(\sqrt{-251}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)	$1$		\(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1005.1.p.a	$1005$	$1$	1005.p	1005.p	$6$	$4$	$2$	$0.502$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)
1005.1.p.b	$1005$	$1$	1005.p	1005.p	$6$	$4$	$2$	$0.502$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
1007.1.d.a	$1007$	$1$	1007.d	1007.d	$2$	$1$	$1$	$0.503$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)	$1$		\(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots\)
1007.1.d.b	$1007$	$1$	1007.d	1007.d	$2$	$1$	$1$	$0.503$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(2\)	$1$		\(q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots\)
1007.1.d.c	$1007$	$1$	1007.d	1007.d	$2$	$2$	$2$	$0.503$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.d	$1007$	$1$	1007.d	1007.d	$2$	$2$	$2$	$0.503$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.e	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1007.1.d.f	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)	$1$		\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1008.1.f.a	$1008$	$1$	1008.f	7.b	$2$	$1$	$1$	$0.503$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)
1008.1.u.a	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
1008.1.u.b	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
1008.1.u.c	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)
1008.1.y.a	$1008$	$1$	1008.y	336.v	$4$	$4$	$2$	$0.503$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1008.1.y.b	$1008$	$1$	1008.y	336.v	$4$	$4$	$2$	$0.503$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots\)
1008.1.bw.a	$1008$	$1$	1008.bw	252.u	$6$	$4$	$2$	$0.503$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1008.1.cd.a	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots\)
1008.1.cd.b	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots\)
1008.1.cg.a	$1008$	$1$	1008.cg	7.d	$6$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1008.1.dc.a	$1008$	$1$	1008.dc	21.h	$6$	$4$	$2$	$0.503$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
1008.1.dd.a	$1008$	$1$	1008.dd	252.al	$6$	$4$	$2$	$0.503$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
1008.1.dt.a	$1008$	$1$	1008.dt	112.u	$12$	$8$	$2$	$0.503$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)
1008.1.ed.a	$1008$	$1$	1008.ed	336.at	$12$	$8$	$2$	$0.503$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
1011.1.c.a	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1011}) \)	\(\Q(\sqrt{337}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$1$		\(q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots\)
1011.1.c.b	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1011}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1011.1.c.c	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1011}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1011.1.c.d	$1011$	$1$	1011.c	1011.c	$2$	$2$	$2$	$0.505$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1011}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$		\(q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots\)
1011.1.f.a	$1011$	$1$	1011.f	1011.f	$4$	$2$	$1$	$0.505$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots\)
1011.1.f.b	$1011$	$1$	1011.f	1011.f	$4$	$4$	$2$	$0.505$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
1011.1.l.a	$1011$	$1$	1011.l	1011.l	$8$	$4$	$1$	$0.505$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
1011.1.q.a	$1011$	$1$	1011.q	1011.q	$14$	$6$	$1$	$0.505$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots\)
1011.1.r.a	$1011$	$1$	1011.r	1011.r	$14$	$6$	$1$	$0.505$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
1011.1.y.a	$1011$	$1$	1011.y	1011.y	$28$	$12$	$1$	$0.505$	\(\Q(\zeta_{28})\)	$D_{28}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots\)
1011.1.bf.a	$1011$	$1$	1011.bf	1011.af	$56$	$24$	$1$	$0.505$	\(\Q(\zeta_{56})\)	$D_{56}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots\)
1012.1.r.a	$1012$	$1$	1012.r	253.k	$22$	$20$	$2$	$0.505$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$		\(q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots\)
1015.1.f.a	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \)	\(\Q(\sqrt{29}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots\)
1015.1.f.b	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \)	\(\Q(\sqrt{29}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(1\)	\(1\)	$1$		\(q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots\)