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 110 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$1$		\(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
76.2.a.a	$76$	$2$	76.a	1.a	$1$	$1$	$1$	$0.607$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
76.2.d.a	$76$	$2$	76.d	76.d	$2$	$8$	$8$	$0.607$	8.0.\(\cdots\).1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
76.2.e.a	$76$	$2$	76.e	19.c	$3$	$2$	$1$	$0.607$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
76.2.f.a	$76$	$2$	76.f	76.f	$6$	$16$	$8$	$0.607$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)
76.2.i.a	$76$	$2$	76.i	19.e	$9$	$12$	$2$	$0.607$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)
76.2.k.a	$76$	$2$	76.k	76.k	$18$	$48$	$8$	$0.607$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.3.b.a	$76$	$3$	76.b	4.b	$2$	$4$	$4$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b	$76$	$3$	76.b	4.b	$2$	$14$	$14$	$2.071$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)
76.3.c.a	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	\(\Q(\sqrt{-29}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	\(\Q(\sqrt{57}) \)	$_{}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(9\)	\(5\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)
76.3.g.a	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(6\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	$_{}$	None	None		$2$	$0$	\(8\)	\(-6\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c	$76$	$3$	76.g	76.g	$6$	$28$	$14$	$2.071$		$_{}$	None	None		$4$	$0$	\(-5\)	\(0\)	\(6\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
76.3.h.a	$76$	$3$	76.h	19.d	$6$	$8$	$4$	$2.071$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(6\)	\(-1\)	\(-12\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
76.3.j.a	$76$	$3$	76.j	19.f	$18$	$18$	$3$	$2.071$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(9\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots\)
76.3.l.a	$76$	$3$	76.l	76.l	$18$	$108$	$18$	$2.071$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.4.a.a	$76$	$4$	76.a	1.a	$1$	$2$	$2$	$4.484$	\(\Q(\sqrt{33}) \)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-30\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b	$76$	$4$	76.a	1.a	$1$	$3$	$3$	$4.484$	3.3.35529.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(9\)	\(44\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)
76.4.d.a	$76$	$4$	76.d	76.d	$2$	$28$	$28$	$4.484$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
76.4.e.a	$76$	$4$	76.e	19.c	$3$	$10$	$5$	$4.484$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(7\)	\(-4\)	\(-20\)		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.4.f.a	$76$	$4$	76.f	76.f	$6$	$56$	$28$	$4.484$		$_{}$	None	None		$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
76.4.i.a	$76$	$4$	76.i	19.e	$9$	$30$	$5$	$4.484$		$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(6\)			$\mathrm{SU}(2)[C_{9}]$
76.4.k.a	$76$	$4$	76.k	76.k	$18$	$168$	$28$	$4.484$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.5.b.a	$76$	$5$	76.b	4.b	$2$	$36$	$36$	$7.856$		$_{}$	None	None		$2$	$0$	\(6\)	\(0\)	\(24\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
76.5.c.a	$76$	$5$	76.c	19.b	$2$	$2$	$2$	$7.856$	\(\Q(\sqrt{57}) \)	$_{}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-31\)	\(73\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots\)
76.5.c.b	$76$	$5$	76.c	19.b	$2$	$4$	$4$	$7.856$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(22\)	\(24\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots\)
76.5.g.a	$76$	$5$	76.g	76.g	$6$	$76$	$38$	$7.856$		$_{}$	None	None		$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
76.5.h.a	$76$	$5$	76.h	19.d	$6$	$12$	$6$	$7.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-12\)	\(9\)	\(-52\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
76.5.j.a	$76$	$5$	76.j	19.f	$18$	$42$	$7$	$7.856$		$_{}$	None	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(-45\)			$\mathrm{SU}(2)[C_{18}]$
76.5.l.a	$76$	$5$	76.l	76.l	$18$	$228$	$38$	$7.856$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.6.a.a	$76$	$6$	76.a	1.a	$1$	$3$	$3$	$12.189$	3.3.272193.1	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-8\)	\(-9\)	\(-13\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b	$76$	$6$	76.a	1.a	$1$	$4$	$4$	$12.189$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(10\)	\(-110\)	\(30\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)
76.6.d.a	$76$	$6$	76.d	76.d	$2$	$48$	$48$	$12.189$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
76.6.e.a	$76$	$6$	76.e	19.c	$3$	$18$	$9$	$12.189$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-11\)	\(11\)	\(336\)		$2^{16}\cdot 3^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.6.f.a	$76$	$6$	76.f	76.f	$6$	$96$	$48$	$12.189$		$_{}$	None	None		$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
76.6.i.a	$76$	$6$	76.i	19.e	$9$	$48$	$8$	$12.189$		$_{}$	None	None		$2$	$0$	\(0\)	\(33\)	\(0\)	\(-177\)			$\mathrm{SU}(2)[C_{9}]$
76.6.k.a	$76$	$6$	76.k	76.k	$18$	$288$	$48$	$12.189$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.7.b.a	$76$	$7$	76.b	4.b	$2$	$54$	$54$	$17.484$		$_{}$	None	None		$2$	$0$	\(-10\)	\(0\)	\(-44\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
76.7.c.a	$76$	$7$	76.c	19.b	$2$	$2$	$2$	$17.484$	\(\Q(\sqrt{57}) \)	$_{}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(54\)	\(-610\)		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b	$76$	$7$	76.c	19.b	$2$	$8$	$8$	$17.484$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(362\)		$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
76.7.g.a	$76$	$7$	76.g	76.g	$6$	$116$	$58$	$17.484$		$_{}$	None	None		$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
76.7.h.a	$76$	$7$	76.h	19.d	$6$	$20$	$10$	$17.484$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-30\)	\(-56\)	\(464\)		$2^{22}\cdot 3^{8}\cdot 19^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots\)
76.7.j.a	$76$	$7$	76.j	19.f	$18$	$60$	$10$	$17.484$		$_{}$	None	None		$2$	$0$	\(0\)	\(30\)	\(0\)	\(-216\)			$\mathrm{SU}(2)[C_{18}]$
76.7.l.a	$76$	$7$	76.l	76.l	$18$	$348$	$58$	$17.484$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
76.8.a.a	$76$	$8$	76.a	1.a	$1$	$5$	$5$	$23.741$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-14\)	\(-280\)	\(414\)	$-$	$2^{3}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
76.8.a.b	$76$	$8$	76.a	1.a	$1$	$6$	$6$	$23.741$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(40\)	\(279\)	\(-1565\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots\)
76.8.d.a	$76$	$8$	76.d	76.d	$2$	$68$	$68$	$23.741$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
76.8.e.a	$76$	$8$	76.e	19.c	$3$	$22$	$11$	$23.741$		$_{}$	None	None		$2$	$0$	\(0\)	\(13\)	\(1\)	\(560\)			$\mathrm{SU}(2)[C_{3}]$
76.8.f.a	$76$	$8$	76.f	76.f	$6$	$136$	$68$	$23.741$		$_{}$	None	None		$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$