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 30552 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6001.2.a.a	$6001$	$2$	6001.a	1.a	$1$	$113$	$113$	$47.918$		None	✓	$1$	$1$	\(-11\)	\(-11\)	\(-19\)	\(11\)	$+$		$\mathrm{SU}(2)$
6001.2.a.b	$6001$	$2$	6001.a	1.a	$1$	$114$	$114$	$47.918$		None	✓	$1$	$1$	\(-8\)	\(-23\)	\(-27\)	\(-53\)	$+$		$\mathrm{SU}(2)$
6001.2.a.c	$6001$	$2$	6001.a	1.a	$1$	$121$	$121$	$47.918$		None	✓	$1$	$0$	\(9\)	\(13\)	\(21\)	\(-13\)	$-$		$\mathrm{SU}(2)$
6001.2.a.d	$6001$	$2$	6001.a	1.a	$1$	$121$	$121$	$47.918$		None	✓	$1$	$0$	\(9\)	\(21\)	\(27\)	\(39\)	$-$		$\mathrm{SU}(2)$
6002.2.a.a	$6002$	$2$	6002.a	1.a	$1$	$47$	$47$	$47.926$		None	✓	$1$	$1$	\(47\)	\(-13\)	\(-14\)	\(-17\)	$+$		$\mathrm{SU}(2)$
6002.2.a.b	$6002$	$2$	6002.a	1.a	$1$	$56$	$56$	$47.926$		None	✓	$1$	$1$	\(-56\)	\(-11\)	\(0\)	\(-21\)	$+$		$\mathrm{SU}(2)$
6002.2.a.c	$6002$	$2$	6002.a	1.a	$1$	$69$	$69$	$47.926$		None	✓	$1$	$0$	\(-69\)	\(11\)	\(-2\)	\(23\)	$-$		$\mathrm{SU}(2)$
6002.2.a.d	$6002$	$2$	6002.a	1.a	$1$	$79$	$79$	$47.926$		None	✓	$1$	$0$	\(79\)	\(17\)	\(18\)	\(19\)	$-$		$\mathrm{SU}(2)$
6003.2.a.a	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}-4q^{7}-4q^{11}-5q^{13}+\cdots\)
6003.2.a.b	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{11}+3q^{13}+4q^{16}-3q^{17}+\cdots\)
6003.2.a.c	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{5}-3q^{8}-3q^{10}+\cdots\)
6003.2.a.d	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+(1+\beta )q^{5}+3q^{8}+(-1+\cdots)q^{10}+\cdots\)
6003.2.a.e	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+\beta q^{5}+(-2+\beta )q^{7}+q^{13}+\cdots\)
6003.2.a.f	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(4\)	\(0\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
6003.2.a.g	$6003$	$2$	6003.a	1.a	$1$	$4$	$4$	$47.934$	4.4.5744.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{4}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
6003.2.a.h	$6003$	$2$	6003.a	1.a	$1$	$5$	$5$	$47.934$	5.5.312617.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-5\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(2-\beta _{1})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
6003.2.a.i	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
6003.2.a.j	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(3\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
6003.2.a.k	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-6\)	\(3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(2+\beta _{6})q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6003.2.a.l	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(10\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots\)
6003.2.a.m	$6003$	$2$	6003.a	1.a	$1$	$11$	$11$	$47.934$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(3\)	$+$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
6003.2.a.n	$6003$	$2$	6003.a	1.a	$1$	$12$	$12$	$47.934$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(16\)	\(-7\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{6}+\beta _{8})q^{4}+(1+\cdots)q^{5}+\cdots\)
6003.2.a.o	$6003$	$2$	6003.a	1.a	$1$	$13$	$13$	$47.934$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-16\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
6003.2.a.p	$6003$	$2$	6003.a	1.a	$1$	$14$	$14$	$47.934$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-3\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
6003.2.a.q	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-16\)	\(1\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
6003.2.a.r	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(13\)	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+(1-\beta _{10}+\cdots)q^{7}+\cdots\)
6003.2.a.s	$6003$	$2$	6003.a	1.a	$1$	$20$	$20$	$47.934$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(9\)	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{14}q^{7}+\cdots\)
6003.2.a.t	$6003$	$2$	6003.a	1.a	$1$	$22$	$22$	$47.934$		None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-6\)	$+$		$\mathrm{SU}(2)$
6003.2.a.u	$6003$	$2$	6003.a	1.a	$1$	$22$	$22$	$47.934$		None	✓	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-6\)	$+$		$\mathrm{SU}(2)$
6003.2.a.v	$6003$	$2$	6003.a	1.a	$1$	$30$	$30$	$47.934$		None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(10\)	$-$		$\mathrm{SU}(2)$
6003.2.a.w	$6003$	$2$	6003.a	1.a	$1$	$30$	$30$	$47.934$		None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(10\)	$-$		$\mathrm{SU}(2)$
6004.2.a.a	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-5q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
6004.2.a.b	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+2q^{11}-4q^{13}+\cdots\)
6004.2.a.c	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}-2q^{9}+5q^{13}+\cdots\)
6004.2.a.d	$6004$	$2$	6004.a	1.a	$1$	$8$	$8$	$47.942$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{4}q^{7}-3q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6004.2.a.e	$6004$	$2$	6004.a	1.a	$1$	$24$	$24$	$47.942$		None	✓	$1$	$0$	\(0\)	\(1\)	\(9\)	\(2\)	$-$		$\mathrm{SU}(2)$
6004.2.a.f	$6004$	$2$	6004.a	1.a	$1$	$25$	$25$	$47.942$		None	✓	$1$	$1$	\(0\)	\(4\)	\(-8\)	\(2\)	$+$		$\mathrm{SU}(2)$
6004.2.a.g	$6004$	$2$	6004.a	1.a	$1$	$27$	$27$	$47.942$		None	✓	$1$	$1$	\(0\)	\(-4\)	\(-10\)	\(-8\)	$+$		$\mathrm{SU}(2)$
6004.2.a.h	$6004$	$2$	6004.a	1.a	$1$	$31$	$31$	$47.942$		None	✓	$1$	$0$	\(0\)	\(-4\)	\(10\)	\(11\)	$-$		$\mathrm{SU}(2)$
6005.2.a.a	$6005$	$2$	6005.a	1.a	$1$	$1$	$1$	$47.950$	\(\Q\)	None	✓	$1$	$2$	\(-2\)	\(-2\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\)
6005.2.a.b	$6005$	$2$	6005.a	1.a	$1$	$1$	$1$	$47.950$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
6005.2.a.c	$6005$	$2$	6005.a	1.a	$1$	$4$	$4$	$47.950$	4.4.2777.1	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-4\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
6005.2.a.d	$6005$	$2$	6005.a	1.a	$1$	$83$	$83$	$47.950$		None	✓	$1$	$1$	\(1\)	\(-4\)	\(-83\)	\(2\)	$+$		$\mathrm{SU}(2)$
6005.2.a.e	$6005$	$2$	6005.a	1.a	$1$	$88$	$88$	$47.950$		None	✓	$1$	$1$	\(-14\)	\(-34\)	\(88\)	\(-35\)	$+$		$\mathrm{SU}(2)$
6005.2.a.f	$6005$	$2$	6005.a	1.a	$1$	$111$	$111$	$47.950$		None	✓	$1$	$0$	\(20\)	\(40\)	\(111\)	\(39\)	$-$		$\mathrm{SU}(2)$
6005.2.a.g	$6005$	$2$	6005.a	1.a	$1$	$113$	$113$	$47.950$		None	✓	$1$	$0$	\(-3\)	\(6\)	\(-113\)	\(7\)	$-$		$\mathrm{SU}(2)$
6006.2.a.a	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.b	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.c	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.d	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)