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 227 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a	$24$	$2$	24.f	24.f	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
24.3.b.a	$24$	$3$	24.b	8.d	$2$	$4$	$4$	$0.654$	4.0.4752.1	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
24.3.e.a	$24$	$3$	24.e	3.b	$2$	$2$	$2$	$0.654$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-12\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
24.3.h.a	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-2\)	\(3\)	\(2\)	\(-10\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(2\)	\(-3\)	\(-2\)	\(-10\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c	$24$	$3$	24.h	24.h	$2$	$4$	$4$	$0.654$	\(\Q(\sqrt{2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
24.4.a.a	$24$	$4$	24.a	1.a	$1$	$1$	$1$	$1.416$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(14\)	\(-24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)
24.4.d.a	$24$	$4$	24.d	8.b	$2$	$6$	$6$	$1.416$	6.0.8248384.1	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(28\)		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
24.4.f.a	$24$	$4$	24.f	24.f	$2$	$2$	$2$	$1.416$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(10\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b	$24$	$4$	24.f	24.f	$2$	$8$	$8$	$1.416$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
24.5.b.a	$24$	$5$	24.b	8.d	$2$	$8$	$8$	$2.481$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$2^{9}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.5.e.a	$24$	$5$	24.e	3.b	$2$	$4$	$4$	$2.481$	\(\Q(\sqrt{-2}, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(24\)		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
24.5.h.a	$24$	$5$	24.h	24.h	$2$	$1$	$1$	$2.481$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-4\)	\(-9\)	\(46\)	\(2\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.b	$24$	$5$	24.h	24.h	$2$	$1$	$1$	$2.481$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(4\)	\(9\)	\(-46\)	\(2\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.c	$24$	$5$	24.h	24.h	$2$	$12$	$12$	$2.481$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{17}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
24.6.a.a	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(-34\)	\(-240\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(94\)	\(144\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(38\)	\(120\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)
24.6.d.a	$24$	$6$	24.d	8.b	$2$	$10$	$10$	$3.849$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-196\)		$2^{17}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
24.6.f.a	$24$	$6$	24.f	24.f	$2$	$2$	$2$	$3.849$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots\)
24.6.f.b	$24$	$6$	24.f	24.f	$2$	$16$	$16$	$3.849$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{32}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(3+\beta _{2}+\cdots)q^{4}+\cdots\)
24.7.b.a	$24$	$7$	24.b	8.d	$2$	$12$	$12$	$5.521$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(10\)	\(0\)	\(0\)	\(0\)		$2^{26}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
24.7.e.a	$24$	$7$	24.e	3.b	$2$	$6$	$6$	$5.521$	6.0.1173604352.2	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(156\)		$2^{22}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3^{3}+\cdots)q^{7}+\cdots\)
24.7.h.a	$24$	$7$	24.h	24.h	$2$	$1$	$1$	$5.521$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-8\)	\(27\)	\(-142\)	\(470\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-142q^{5}+\cdots\)
24.7.h.b	$24$	$7$	24.h	24.h	$2$	$1$	$1$	$5.521$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(8\)	\(-27\)	\(142\)	\(470\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+142q^{5}+\cdots\)
24.7.h.c	$24$	$7$	24.h	24.h	$2$	$20$	$20$	$5.521$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-944\)		$2^{49}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-10+\beta _{3})q^{4}+\cdots\)
24.8.a.a	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-27\)	\(-26\)	\(1056\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.b	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(27\)	\(-530\)	\(120\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.c	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(27\)	\(110\)	\(504\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\)
24.8.d.a	$24$	$8$	24.d	8.b	$2$	$14$	$14$	$7.497$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-14\)	\(0\)	\(0\)	\(1372\)		$2^{37}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)
24.8.f.a	$24$	$8$	24.f	24.f	$2$	$2$	$2$	$7.497$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-86\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots\)
24.8.f.b	$24$	$8$	24.f	24.f	$2$	$4$	$4$	$7.497$	\(\Q(\sqrt{6}, \sqrt{-26})\)	None		$4$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots\)
24.8.f.c	$24$	$8$	24.f	24.f	$2$	$20$	$20$	$7.497$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(120\)	\(0\)	\(0\)		$2^{52}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.9.b.a	$24$	$9$	24.b	8.d	$2$	$16$	$16$	$9.777$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$2^{49}\cdot 3^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(26-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
24.9.e.a	$24$	$9$	24.e	3.b	$2$	$8$	$8$	$9.777$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(56\)	\(0\)	\(1584\)		$2^{42}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)
24.9.h.a	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-16\)	\(-81\)	\(-866\)	\(-4798\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots\)
24.9.h.b	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(16\)	\(81\)	\(866\)	\(-4798\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots\)
24.9.h.c	$24$	$9$	24.h	24.h	$2$	$28$	$28$	$9.777$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(9592\)			$\mathrm{SU}(2)[C_{2}]$
24.10.a.a	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-81\)	\(830\)	\(672\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(81\)	\(-794\)	\(-5880\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(81\)	\(614\)	\(2184\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d	$24$	$10$	24.a	1.a	$1$	$2$	$2$	$12.361$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(-162\)	\(-772\)	\(-2880\)	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)
24.10.d.a	$24$	$10$	24.d	8.b	$2$	$18$	$18$	$12.361$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(34\)	\(0\)	\(0\)	\(-9604\)		$2^{65}\cdot 3^{28}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(29-2\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
24.10.f.a	$24$	$10$	24.f	24.f	$2$	$2$	$2$	$12.361$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(190\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}\beta q^{2}+(95-73\beta )q^{3}-2^{9}q^{4}+\cdots\)
24.10.f.b	$24$	$10$	24.f	24.f	$2$	$32$	$32$	$12.361$		None		$4$	$0$	\(0\)	\(-192\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
24.11.b.a	$24$	$11$	24.b	8.d	$2$	$20$	$20$	$15.249$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-22\)	\(0\)	\(0\)	\(0\)		$2^{82}\cdot 3^{38}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(-93-\beta _{1}+\cdots)q^{4}+\cdots\)
24.11.e.a	$24$	$11$	24.e	3.b	$2$	$10$	$10$	$15.249$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-22\)	\(0\)	\(-5436\)		$2^{72}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-545+\cdots)q^{7}+\cdots\)
24.11.h.a	$24$	$11$	24.h	24.h	$2$	$1$	$1$	$15.249$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-32\)	\(243\)	\(5282\)	\(24950\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+5282q^{5}+\cdots\)