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 189 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.1.ba.a	$672$	$1$	672.ba	168.s	$6$	$2$	$1$	$0.335$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.1.ba.b	$672$	$1$	672.ba	168.s	$6$	$2$	$1$	$0.335$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$1$		\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.2.a.a	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.b	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
672.2.a.c	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.d	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
672.2.a.e	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.f	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
672.2.a.g	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.h	$672$	$2$	672.a	1.a	$1$	$1$	$1$	$5.366$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
672.2.a.i	$672$	$2$	672.a	1.a	$1$	$2$	$2$	$5.366$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
672.2.a.j	$672$	$2$	672.a	1.a	$1$	$2$	$2$	$5.366$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
672.2.b.a	$672$	$2$	672.b	28.d	$2$	$8$	$8$	$5.366$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(-4\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.b.b	$672$	$2$	672.b	28.d	$2$	$8$	$8$	$5.366$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(4\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.c.a	$672$	$2$	672.c	8.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)
672.2.c.b	$672$	$2$	672.c	8.b	$2$	$8$	$8$	$5.366$	8.0.386672896.3	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.h.a	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.b	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.c	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.d	$672$	$2$	672.h	12.b	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.e	$672$	$2$	672.h	12.b	$2$	$8$	$8$	$5.366$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)
672.2.i.a	$672$	$2$	672.i	168.i	$2$	$4$	$4$	$5.366$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.b	$672$	$2$	672.i	168.i	$2$	$4$	$4$	$5.366$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
672.2.i.c	$672$	$2$	672.i	168.i	$2$	$4$	$4$	$5.366$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(8\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.d	$672$	$2$	672.i	168.i	$2$	$8$	$8$	$5.366$	8.0.3317760000.1	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
672.2.i.e	$672$	$2$	672.i	168.i	$2$	$8$	$8$	$5.366$	8.0.\(\cdots\).11	$_{}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
672.2.j.a	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.j.b	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(i, \sqrt{5})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
672.2.j.c	$672$	$2$	672.j	24.f	$2$	$4$	$4$	$5.366$	\(\Q(i, \sqrt{5})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
672.2.j.d	$672$	$2$	672.j	24.f	$2$	$12$	$12$	$5.366$	12.0.\(\cdots\).2	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)
672.2.k.a	$672$	$2$	672.k	21.c	$2$	$8$	$8$	$5.366$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.b	$672$	$2$	672.k	21.c	$2$	$8$	$8$	$5.366$	8.0.49787136.1	$_{}$	\(\Q(\sqrt{-21}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.k.c	$672$	$2$	672.k	21.c	$2$	$8$	$8$	$5.366$	8.0.40960000.1	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.d	$672$	$2$	672.k	21.c	$2$	$8$	$8$	$5.366$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
672.2.p.a	$672$	$2$	672.p	56.e	$2$	$16$	$16$	$5.366$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{7}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.q.a	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
672.2.q.b	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
672.2.q.c	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.d	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.e	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(4\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
672.2.q.f	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
672.2.q.g	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
672.2.q.h	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.i	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.j	$672$	$2$	672.q	7.c	$3$	$2$	$1$	$5.366$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
672.2.q.k	$672$	$2$	672.q	7.c	$3$	$6$	$3$	$5.366$	6.0.1156923.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-3\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.q.l	$672$	$2$	672.q	7.c	$3$	$6$	$3$	$5.366$	6.0.1156923.1	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.bb.a	$672$	$2$	672.bb	56.m	$6$	$32$	$16$	$5.366$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
672.2.bc.a	$672$	$2$	672.bc	21.g	$6$	$4$	$2$	$5.366$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
672.2.bc.b	$672$	$2$	672.bc	21.g	$6$	$4$	$2$	$5.366$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots\)