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 165 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2736.1.b.a	$2736$	$1$	2736.b	228.b	$2$	$4$	$4$	$1.365$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-19}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
2736.1.b.b	$2736$	$1$	2736.b	228.b	$2$	$8$	$8$	$1.365$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-19}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$		\(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2736.1.o.a	$2736$	$1$	2736.o	19.b	$2$	$1$	$1$	$1.365$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{57}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$		\(q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots\)
2736.1.o.b	$2736$	$1$	2736.o	19.b	$2$	$1$	$1$	$1.365$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$1$		\(q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots\)
2736.1.o.c	$2736$	$1$	2736.o	19.b	$2$	$2$	$2$	$1.365$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$		\(q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots\)
2736.1.bk.a	$2736$	$1$	2736.bk	76.g	$6$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}-q^{19}+\cdots\)
2736.1.bk.b	$2736$	$1$	2736.bk	76.g	$6$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)
2736.1.bs.a	$2736$	$1$	2736.bs	171.o	$6$	$4$	$2$	$1.365$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$1$		\(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots\)
2736.1.cd.a	$2736$	$1$	2736.cd	19.d	$6$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$		\(q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)
2736.1.fg.a	$2736$	$1$	2736.fg	19.f	$18$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.1.ga.a	$2736$	$1$	2736.ga	76.l	$18$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.1.ga.b	$2736$	$1$	2736.ga	76.l	$18$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.2.a.a	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots\)
2736.2.a.b	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots\)
2736.2.a.c	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.d	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots\)
2736.2.a.e	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots\)
2736.2.a.f	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots\)
2736.2.a.g	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots\)
2736.2.a.h	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots\)
2736.2.a.i	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots\)
2736.2.a.j	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.k	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots\)
2736.2.a.l	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.m	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots\)
2736.2.a.n	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots\)
2736.2.a.o	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots\)
2736.2.a.p	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots\)
2736.2.a.q	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.r	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots\)
2736.2.a.s	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots\)
2736.2.a.t	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots\)
2736.2.a.u	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots\)
2736.2.a.v	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots\)
2736.2.a.w	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
2736.2.a.x	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots\)
2736.2.a.y	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{33}) \)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots\)
2736.2.a.z	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots\)
2736.2.a.ba	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{7}) \)	$_{}$	None	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots\)
2736.2.a.bb	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{41}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots\)
2736.2.a.bc	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2736.2.a.bd	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.961.1	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.a.be	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots\)
2736.2.a.bf	$2736$	$2$	2736.a	1.a	$1$	$4$	$4$	$21.847$	4.4.13068.1	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)
2736.2.d.a	$2736$	$2$	2736.d	12.b	$2$	$12$	$12$	$21.847$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{9})q^{5}+(\beta _{1}+\beta _{3}-\beta _{8})q^{7}+\cdots\)
2736.2.d.b	$2736$	$2$	2736.d	12.b	$2$	$24$	$24$	$21.847$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
2736.2.f.a	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.b	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.c	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.f.d	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots\)