Newform search results

Results (48 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
83.1.b.a	$83$	$1$	83.b	83.b	$2$	$1$	$1$	$0.041$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
83.2.a.a	$83$	$2$	83.a	1.a	$1$	$1$	$1$	$0.663$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
83.2.a.b	$83$	$2$	83.a	1.a	$1$	$6$	$6$	$0.663$	6.6.9059636.1	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(1\)	\(2\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
83.2.c.a	$83$	$2$	83.c	83.c	$41$	$240$	$6$	$0.663$		$_{}$	None	None		$2$	$0$	\(-38\)	\(-37\)	\(-35\)	\(-33\)			$\mathrm{SU}(2)[C_{41}]$
83.3.b.a	$83$	$3$	83.b	83.b	$2$	$3$	$3$	$2.262$	3.3.2241.1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-3\beta _{1}-2\beta _{2})q^{7}+\cdots\)
83.3.b.b	$83$	$3$	83.b	83.b	$2$	$10$	$10$	$2.262$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(12\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-3+\beta _{7}+\cdots)q^{4}+\cdots\)
83.3.d.a	$83$	$3$	83.d	83.d	$82$	$520$	$13$	$2.262$		$_{}$	None	None		$2$	$0$	\(-41\)	\(-35\)	\(-41\)	\(-53\)			$\mathrm{SU}(2)[C_{82}]$
83.4.a.a	$83$	$4$	83.a	1.a	$1$	$7$	$7$	$4.897$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-5\)	\(-11\)	\(-17\)	\(-46\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots\)
83.4.a.b	$83$	$4$	83.a	1.a	$1$	$13$	$13$	$4.897$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(5\)	\(7\)	\(33\)	\(52\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
83.4.c.a	$83$	$4$	83.c	83.c	$41$	$800$	$20$	$4.897$		$_{}$	None	None		$2$	$0$	\(-41\)	\(-37\)	\(-57\)	\(-47\)			$\mathrm{SU}(2)[C_{41}]$
83.5.b.a	$83$	$5$	83.b	83.b	$2$	$3$	$3$	$8.580$	3.3.2241.1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(21\beta _{1}-11\beta _{2})q^{7}+\cdots\)
83.5.b.b	$83$	$5$	83.b	83.b	$2$	$24$	$24$	$8.580$		$_{}$	None	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-112\)			$\mathrm{SU}(2)[C_{2}]$
83.5.d.a	$83$	$5$	83.d	83.d	$82$	$1080$	$27$	$8.580$		$_{}$	None	None		$2$	$0$	\(-41\)	\(-47\)	\(-41\)	\(71\)			$\mathrm{SU}(2)[C_{82}]$
83.6.a.a	$83$	$6$	83.a	1.a	$1$	$14$	$14$	$13.312$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-13\)	\(-17\)	\(-162\)	\(-247\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(10+\cdots)q^{4}+\cdots\)
83.6.a.b	$83$	$6$	83.a	1.a	$1$	$20$	$20$	$13.312$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(7\)	\(37\)	\(88\)	\(439\)	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{5})q^{3}+(19+\beta _{2})q^{4}+\cdots\)
83.6.c.a	$83$	$6$	83.c	83.c	$41$	$1360$	$34$	$13.312$		$_{}$	None	None		$2$	$0$	\(-35\)	\(-61\)	\(33\)	\(-233\)			$\mathrm{SU}(2)[C_{41}]$
83.7.b.a	$83$	$7$	83.b	83.b	$2$	$1$	$1$	$19.094$	\(\Q\)	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(-29\)	\(0\)	\(-61\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots\)
83.7.b.b	$83$	$7$	83.b	83.b	$2$	$2$	$2$	$19.094$	\(\Q(\sqrt{249}) \)	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(29\)	\(0\)	\(61\)		$5$	$\mathrm{U}(1)[D_{2}]$	\(q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots\)
83.7.b.c	$83$	$7$	83.b	83.b	$2$	$38$	$38$	$19.094$		$_{}$	None	None		$2$	$0$	\(0\)	\(18\)	\(0\)	\(262\)			$\mathrm{SU}(2)[C_{2}]$
83.7.d.a	$83$	$7$	83.d	83.d	$82$	$1640$	$41$	$19.094$		$_{}$	None	None		$2$	$0$	\(-41\)	\(-59\)	\(-41\)	\(-303\)			$\mathrm{SU}(2)[C_{82}]$
83.8.a.a	$83$	$8$	83.a	1.a	$1$	$21$	$21$	$25.928$		$_{}$	None	None	✓	$1$	$1$	\(-17\)	\(-95\)	\(-502\)	\(-3273\)	$-$		$\mathrm{SU}(2)$
83.8.a.b	$83$	$8$	83.a	1.a	$1$	$27$	$27$	$25.928$		$_{}$	None	None	✓	$1$	$0$	\(23\)	\(67\)	\(748\)	\(1529\)	$+$		$\mathrm{SU}(2)$
83.8.c.a	$83$	$8$	83.c	83.c	$41$	$1920$	$48$	$25.928$		$_{}$	None	None		$2$	$0$	\(-47\)	\(-13\)	\(-287\)	\(1703\)			$\mathrm{SU}(2)[C_{41}]$
83.9.b.a	$83$	$9$	83.b	83.b	$2$	$3$	$3$	$33.812$	3.3.2241.1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-47\beta _{1}-2\beta _{2})q^{3}+2^{8}q^{4}+(-846\beta _{1}+\cdots)q^{7}+\cdots\)
83.9.b.b	$83$	$9$	83.b	83.b	$2$	$52$	$52$	$33.812$		$_{}$	None	None		$2$	$0$	\(0\)	\(-114\)	\(0\)	\(2028\)			$\mathrm{SU}(2)[C_{2}]$
83.9.d.a	$83$	$9$	83.d	83.d	$82$	$2200$	$55$	$33.812$		$_{}$	None	None		$2$	$0$	\(-41\)	\(73\)	\(-41\)	\(-2069\)			$\mathrm{SU}(2)[C_{82}]$
83.10.a.a	$83$	$10$	83.a	1.a	$1$	$28$	$28$	$42.748$		$_{}$	None	None	✓	$1$	$1$	\(-49\)	\(-317\)	\(-3467\)	\(-13836\)	$+$		$\mathrm{SU}(2)$
83.10.a.b	$83$	$10$	83.a	1.a	$1$	$34$	$34$	$42.748$		$_{}$	None	None	✓	$1$	$0$	\(31\)	\(169\)	\(2783\)	\(19778\)	$-$		$\mathrm{SU}(2)$
83.10.c.a	$83$	$10$	83.c	83.c	$41$	$2480$	$62$	$42.748$		$_{}$	None	None		$2$	$0$	\(-23\)	\(107\)	\(643\)	\(-5983\)			$\mathrm{SU}(2)[C_{41}]$
83.11.b.a	$83$	$11$	83.b	83.b	$2$	$3$	$3$	$52.735$	3.3.2241.1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-139\beta _{1}+6\beta _{2})q^{3}+2^{10}q^{4}+(5922\beta _{1}+\cdots)q^{7}+\cdots\)
83.11.b.b	$83$	$11$	83.b	83.b	$2$	$66$	$66$	$52.735$		$_{}$	None	None		$2$	$0$	\(0\)	\(42\)	\(0\)	\(-22288\)			$\mathrm{SU}(2)[C_{2}]$
83.11.d.a	$83$	$11$	83.d	83.d	$82$	$2760$	$69$	$52.735$		$_{}$	None	None		$2$	$0$	\(-41\)	\(-83\)	\(-41\)	\(22247\)			$\mathrm{SU}(2)[C_{82}]$
83.12.a.a	$83$	$12$	83.a	1.a	$1$	$34$	$34$	$63.772$		$_{}$	None	None	✓	$1$	$1$	\(-41\)	\(-719\)	\(-19862\)	\(-97477\)	$-$		$\mathrm{SU}(2)$
83.12.a.b	$83$	$12$	83.a	1.a	$1$	$40$	$40$	$63.772$		$_{}$	None	None	✓	$1$	$0$	\(119\)	\(739\)	\(11388\)	\(137821\)	$+$		$\mathrm{SU}(2)$
83.12.c.a	$83$	$12$	83.c	83.c	$41$	$3040$	$76$	$63.772$		$_{}$	None	None		$2$	$0$	\(-71\)	\(-565\)	\(-1227\)	\(-6897\)			$\mathrm{SU}(2)[C_{41}]$
83.13.b.a	$83$	$13$	83.b	83.b	$2$	$1$	$1$	$75.861$	\(\Q\)	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(-617\)	\(0\)	\(-231577\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-617q^{3}+2^{12}q^{4}-231577q^{7}+\cdots\)
83.13.b.b	$83$	$13$	83.b	83.b	$2$	$2$	$2$	$75.861$	\(\Q(\sqrt{249}) \)	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(617\)	\(0\)	\(231577\)		$5$	$\mathrm{U}(1)[D_{2}]$	\(q+(294-29\beta )q^{3}+2^{12}q^{4}+(116246+\cdots)q^{7}+\cdots\)
83.13.b.c	$83$	$13$	83.b	83.b	$2$	$80$	$80$	$75.861$		$_{}$	None	None		$2$	$0$	\(0\)	\(918\)	\(0\)	\(103918\)			$\mathrm{SU}(2)[C_{2}]$
83.14.a.a	$83$	$14$	83.a	1.a	$1$	$42$	$42$	$89.002$		$_{}$	None	None	✓	$1$	$1$	\(-193\)	\(-2057\)	\(-78072\)	\(-907547\)	$+$		$\mathrm{SU}(2)$
83.14.a.b	$83$	$14$	83.a	1.a	$1$	$48$	$48$	$89.002$		$_{}$	None	None	✓	$1$	$0$	\(127\)	\(2317\)	\(78178\)	\(739539\)	$-$		$\mathrm{SU}(2)$
83.15.b.a	$83$	$15$	83.b	83.b	$2$	$3$	$3$	$103.193$	3.3.2241.1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$13$	$\mathrm{U}(1)[D_{2}]$	\(q+(-63\beta _{1}+152\beta _{2})q^{3}+2^{14}q^{4}+\cdots\)
83.15.b.b	$83$	$15$	83.b	83.b	$2$	$94$	$94$	$103.193$		$_{}$	None	None		$2$	$0$	\(0\)	\(-2238\)	\(0\)	\(-386388\)			$\mathrm{SU}(2)[C_{2}]$
83.16.a.a	$83$	$16$	83.a	1.a	$1$	$48$	$48$	$118.436$		$_{}$	None	None	✓	$1$	$1$	\(-473\)	\(-5843\)	\(-442447\)	\(-7927854\)	$-$		$\mathrm{SU}(2)$
83.16.a.b	$83$	$16$	83.a	1.a	$1$	$54$	$54$	$118.436$		$_{}$	None	None	✓	$1$	$0$	\(167\)	\(7279\)	\(338803\)	\(3601748\)	$+$		$\mathrm{SU}(2)$
83.18.a.a	$83$	$18$	83.a	1.a	$1$	$55$	$55$	$152.074$		$_{}$	None	None	✓	$1$	$1$	\(-241\)	\(-11321\)	\(-1009352\)	\(-50694303\)	$+$		$\mathrm{SU}(2)$
83.18.a.b	$83$	$18$	83.a	1.a	$1$	$61$	$61$	$152.074$		$_{}$	None	None	✓	$1$	$0$	\(1039\)	\(28045\)	\(2896898\)	\(30012911\)	$-$		$\mathrm{SU}(2)$
83.20.a.a	$83$	$20$	83.a	1.a	$1$	$62$	$62$	$189.918$		$_{}$	None	None	✓	$1$	$1$	\(-1481\)	\(-94199\)	\(-6266132\)	\(-202919777\)	$-$		$\mathrm{SU}(2)$
83.20.a.b	$83$	$20$	83.a	1.a	$1$	$68$	$68$	$189.918$		$_{}$	None	None	✓	$1$	$0$	\(1079\)	\(23899\)	\(13265118\)	\(362030721\)	$+$		$\mathrm{SU}(2)$