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 309 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.2.a.a	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.b	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
350.2.a.c	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
350.2.a.d	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.e	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
350.2.a.f	$350$	$2$	350.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.g	$350$	$2$	350.a	1.a	$1$	$2$	$2$	$2.795$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.h	$350$	$2$	350.a	1.a	$1$	$2$	$2$	$2.795$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
350.2.c.a	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots\)
350.2.c.b	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
350.2.c.c	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
350.2.c.d	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
350.2.e.a	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-2\)	\(0\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.b	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.c	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
350.2.e.d	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
350.2.e.e	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.f	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(3\)	\(0\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.g	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-3\)	\(0\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.h	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-2\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.i	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
350.2.e.j	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
350.2.e.k	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(2\)	\(0\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.l	$350$	$2$	350.e	7.c	$3$	$2$	$1$	$2.795$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(0\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.g.a	$350$	$2$	350.g	35.f	$4$	$8$	$4$	$2.795$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{3}q^{4}+(\zeta_{16}^{4}+\cdots)q^{6}+\cdots\)
350.2.g.b	$350$	$2$	350.g	35.f	$4$	$16$	$8$	$2.795$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{10}q^{4}+\beta _{15}q^{6}+\cdots\)
350.2.h.a	$350$	$2$	350.h	25.d	$5$	$8$	$2$	$2.795$	\(\Q(\zeta_{15})\)	None		$2$	$0$	\(-2\)	\(3\)	\(0\)	\(8\)		$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{15}^{4}q^{2}+(-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{6}+\cdots)q^{3}+\cdots\)
350.2.h.b	$350$	$2$	350.h	25.d	$5$	$12$	$3$	$2.795$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(3\)	\(1\)	\(-5\)	\(-12\)		$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots\)
350.2.h.c	$350$	$2$	350.h	25.d	$5$	$16$	$4$	$2.795$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-4\)	\(1\)	\(-4\)	\(-16\)		$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
350.2.h.d	$350$	$2$	350.h	25.d	$5$	$20$	$5$	$2.795$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(5\)	\(3\)	\(-5\)	\(20\)		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots\)
350.2.j.a	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
350.2.j.b	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.c	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
350.2.j.d	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.e	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.f	$350$	$2$	350.j	35.j	$6$	$4$	$2$	$2.795$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.m.a	$350$	$2$	350.m	25.e	$10$	$24$	$6$	$2.795$		None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
350.2.m.b	$350$	$2$	350.m	25.e	$10$	$40$	$10$	$2.795$		None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
350.2.o.a	$350$	$2$	350.o	35.k	$12$	$8$	$2$	$2.795$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.b	$350$	$2$	350.o	35.k	$12$	$8$	$2$	$2.795$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.c	$350$	$2$	350.o	35.k	$12$	$16$	$4$	$2.795$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{13}q^{2}+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(\beta _{11}+\cdots)q^{4}+\cdots\)
350.2.o.d	$350$	$2$	350.o	35.k	$12$	$16$	$4$	$2.795$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{5}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
350.2.q.a	$350$	$2$	350.q	175.q	$15$	$8$	$1$	$2.795$	\(\Q(\zeta_{15})\)	None		$4$	$0$	\(-1\)	\(-3\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{15}]$	\(q-\zeta_{15}q^{2}+(1-\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
350.2.q.b	$350$	$2$	350.q	175.q	$15$	$72$	$9$	$2.795$		None		$4$	$0$	\(-9\)	\(1\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{15}]$
350.2.q.c	$350$	$2$	350.q	175.q	$15$	$80$	$10$	$2.795$		None		$4$	$0$	\(10\)	\(2\)	\(-2\)	\(4\)			$\mathrm{SU}(2)[C_{15}]$
350.2.r.a	$350$	$2$	350.r	175.s	$20$	$160$	$20$	$2.795$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{20}]$
350.2.u.a	$350$	$2$	350.u	175.t	$30$	$160$	$20$	$2.795$		None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{30}]$
350.2.x.a	$350$	$2$	350.x	175.x	$60$	$320$	$20$	$2.795$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(-8\)			$\mathrm{SU}(2)[C_{60}]$
350.3.b.a	$350$	$3$	350.b	7.b	$2$	$4$	$4$	$9.537$	4.0.7168.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots\)
350.3.b.b	$350$	$3$	350.b	7.b	$2$	$4$	$4$	$9.537$	4.0.7168.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)