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 198 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.1.e.a	$304$	$1$	304.e	19.b	$2$	$1$	$1$	$0.152$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$1$		\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
304.2.a.a	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
304.2.a.b	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
304.2.a.c	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
304.2.a.d	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
304.2.a.e	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
304.2.a.f	$304$	$2$	304.a	1.a	$1$	$1$	$1$	$2.427$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
304.2.a.g	$304$	$2$	304.a	1.a	$1$	$3$	$3$	$2.427$	3.3.961.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
304.2.h.a	$304$	$2$	304.h	76.d	$2$	$2$	$2$	$2.427$	\(\Q(\sqrt{-19}) \)	$_{}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b	$304$	$2$	304.h	76.d	$2$	$4$	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c	$304$	$2$	304.h	76.d	$2$	$4$	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	$_{}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
304.2.i.a	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e	$304$	$2$	304.i	19.c	$3$	$4$	$2$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f	$304$	$2$	304.i	19.c	$3$	$6$	$3$	$2.427$	6.0.2696112.1	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
304.2.k.a	$304$	$2$	304.k	16.e	$4$	$4$	$2$	$2.427$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$2$	$1$	\(0\)	\(-4\)	\(-8\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b	$304$	$2$	304.k	16.e	$4$	$68$	$34$	$2.427$		$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
304.2.m.a	$304$	$2$	304.m	304.m	$4$	$76$	$38$	$2.427$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)			$\mathrm{SU}(2)[C_{4}]$
304.2.n.a	$304$	$2$	304.n	76.f	$6$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b	$304$	$2$	304.n	76.f	$6$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c	$304$	$2$	304.n	76.f	$6$	$4$	$2$	$2.427$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d	$304$	$2$	304.n	76.f	$6$	$6$	$3$	$2.427$	6.0.31726512.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e	$304$	$2$	304.n	76.f	$6$	$6$	$3$	$2.427$	6.0.31726512.1	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
304.2.u.a	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$1$	\(0\)	\(-9\)	\(-6\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(6\)	\(6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e	$304$	$2$	304.u	19.e	$9$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f	$304$	$2$	304.u	19.e	$9$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(9\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
304.2.v.a	$304$	$2$	304.v	304.v	$12$	$152$	$38$	$2.427$		$_{}$	None	None		$4$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
304.2.x.a	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(2\)	\(4\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c	$304$	$2$	304.x	304.x	$12$	$144$	$36$	$2.427$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-12\)	\(2\)	\(-8\)			$\mathrm{SU}(2)[C_{12}]$
304.2.be.a	$304$	$2$	304.be	76.k	$18$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b	$304$	$2$	304.be	76.k	$18$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c	$304$	$2$	304.be	76.k	$18$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d	$304$	$2$	304.be	76.k	$18$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(9\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.bg.a	$304$	$2$	304.bg	304.ag	$36$	$456$	$38$	$2.427$		$_{}$	None	None		$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
304.2.bi.a	$304$	$2$	304.bi	304.ai	$36$	$456$	$38$	$2.427$		$_{}$	None	None		$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
304.3.d.a	$304$	$3$	304.d	4.b	$2$	$6$	$6$	$8.283$	6.0.210056875.1	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
304.3.d.b	$304$	$3$	304.d	4.b	$2$	$12$	$12$	$8.283$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
304.3.e.a	$304$	$3$	304.e	19.b	$2$	$1$	$1$	$8.283$	\(\Q\)	$_{}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(5\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b	$304$	$3$	304.e	19.b	$2$	$2$	$2$	$8.283$	\(\Q(\sqrt{-29}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c	$304$	$3$	304.e	19.b	$2$	$2$	$2$	$8.283$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-10\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d	$304$	$3$	304.e	19.b	$2$	$2$	$2$	$8.283$	\(\Q(\sqrt{-13}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e	$304$	$3$	304.e	19.b	$2$	$2$	$2$	$8.283$	\(\Q(\sqrt{57}) \)	$_{}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(9\)	\(-5\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f	$304$	$3$	304.e	19.b	$2$	$2$	$2$	$8.283$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(-22\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g	$304$	$3$	304.e	19.b	$2$	$8$	$8$	$8.283$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(6\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)