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
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Results (1-50 of 275 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.1.e.a	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$		\(q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots\)
1344.1.e.b	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots\)
1344.1.e.c	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots\)
1344.1.e.d	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$1$		\(q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots\)
1344.1.o.a	$1344$	$1$	1344.o	84.h	$2$	$1$	$1$	$0.671$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.o.b	$1344$	$1$	1344.o	84.h	$2$	$1$	$1$	$0.671$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$1$		\(q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.z.a	$1344$	$1$	1344.z	84.j	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.z.b	$1344$	$1$	1344.z	84.j	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$1$		\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.a	$1344$	$1$	1344.ba	168.s	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.b	$1344$	$1$	1344.ba	168.s	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.bm.a	$1344$	$1$	1344.bm	168.ae	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bm.b	$1344$	$1$	1344.bm	168.ae	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-q^{13}+\cdots\)
1344.1.bm.c	$1344$	$1$	1344.bm	168.ae	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+q^{13}+\cdots\)
1344.1.bm.d	$1344$	$1$	1344.bm	168.ae	$6$	$4$	$2$	$0.671$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$1$		\(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bn.a	$1344$	$1$	1344.bn	21.h	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$1$		\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.1.bn.b	$1344$	$1$	1344.bn	21.h	$6$	$2$	$1$	$0.671$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.2.a.a	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1344.2.a.b	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots\)
1344.2.a.c	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1344.2.a.d	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1344.2.a.e	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.f	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1344.2.a.g	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
1344.2.a.h	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1344.2.a.i	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1344.2.a.j	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.k	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1344.2.a.l	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
1344.2.a.m	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1344.2.a.n	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
1344.2.a.o	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1344.2.a.p	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.q	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1344.2.a.r	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
1344.2.a.s	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1344.2.a.t	$1344$	$2$	1344.a	1.a	$1$	$1$	$1$	$10.732$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.u	$1344$	$2$	1344.a	1.a	$1$	$2$	$2$	$10.732$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1344.2.a.v	$1344$	$2$	1344.a	1.a	$1$	$2$	$2$	$10.732$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
1344.2.b.a	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-6}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
1344.2.b.c	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
1344.2.b.d	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-6}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e	$1344$	$2$	1344.b	28.d	$2$	$4$	$4$	$10.732$	4.0.2312.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f	$1344$	$2$	1344.b	28.d	$2$	$4$	$4$	$10.732$	4.0.2312.1	$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(2\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g	$1344$	$2$	1344.b	28.d	$2$	$8$	$8$	$10.732$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(4\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h	$1344$	$2$	1344.b	28.d	$2$	$8$	$8$	$10.732$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(-4\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)
1344.2.c.a	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.b	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.c	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.d	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)