LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 107 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
578.2.a.a	$578$	$2$	578.a	1.a	$1$	$1$	$1$	$4.615$	$\Q$	None	✓				34.2.a.a	$1$	$0$	$1$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+4q^{7}+q^{8}+\cdots$
578.2.a.b	$578$	$2$	578.a	1.a	$1$	$2$	$2$	$4.615$	$\Q(\sqrt{2}) $	None	✓				34.2.c.b	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-3q^{9}-\beta q^{10}+\cdots$
578.2.a.c	$578$	$2$	578.a	1.a	$1$	$2$	$2$	$4.615$	$\Q(\sqrt{2}) $	None	✓				34.2.c.a	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}+\beta q^{6}+\cdots$
578.2.a.d	$578$	$2$	578.a	1.a	$1$	$2$	$2$	$4.615$	$\Q(\sqrt{2}) $	None	✓				34.2.b.a	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{8}+\cdots$
578.2.a.e	$578$	$2$	578.a	1.a	$1$	$3$	$3$	$4.615$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		578.2.a.e	$1$	$1$	$-3$	$-3$	$0$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+q^{4}+\cdots$
578.2.a.f	$578$	$2$	578.a	1.a	$1$	$3$	$3$	$4.615$	$\Q(\zeta_{18})^+$	None	✓	✓			578.2.a.e	$1$	$0$	$-3$	$3$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
578.2.a.g	$578$	$2$	578.a	1.a	$1$	$3$	$3$	$4.615$	$\Q(\zeta_{18})^+$	None	✓	✓	✓	✓	578.2.a.g	$1$	$1$	$3$	$-3$	$-6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
578.2.a.h	$578$	$2$	578.a	1.a	$1$	$3$	$3$	$4.615$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		578.2.a.g	$1$	$0$	$3$	$3$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$
578.2.a.i	$578$	$2$	578.a	1.a	$1$	$4$	$4$	$4.615$	$\Q(\zeta_{16})^+$	None	✓		✓		34.2.d.a	$2$	$0$	$-4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
578.2.b.a	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	$\Q(\sqrt{-1}) $	None					34.2.a.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-2\beta q^{7}+\cdots$
578.2.b.b	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	$\Q(\sqrt{-2}) $	None					34.2.c.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots$
578.2.b.c	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	$\Q(\sqrt{-2}) $	None					34.2.c.b	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+3q^{9}+\beta q^{10}+\cdots$
578.2.b.d	$578$	$2$	578.b	17.b	$2$	$4$	$4$	$4.615$	4.0.2048.2	None					34.2.d.a	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots$
578.2.b.e	$578$	$2$	578.b	17.b	$2$	$6$	$6$	$4.615$	6.0.419904.1	None		✓			578.2.a.g	$2$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
578.2.b.f	$578$	$2$	578.b	17.b	$2$	$6$	$6$	$4.615$	6.0.419904.1	None		✓			578.2.a.e	$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
578.2.c.a	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	$\Q(\sqrt{-1}) $	None					34.2.b.a	$2$	$1$	$0$	$-4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(-2 i-2)q^{3}-q^{4}+(-2 i-2)q^{5}+\cdots$
578.2.c.b	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	$\Q(\sqrt{-1}) $	None					34.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}-q^{4}+(i+1)q^{5}-i q^{8}+\cdots$
578.2.c.c	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	$\Q(\sqrt{-1}) $	None					34.2.c.a	$2$	$0$	$0$	$2$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(i+1)q^{3}-q^{4}+(-2 i-2)q^{5}+\cdots$
578.2.c.d	$578$	$2$	578.c	17.c	$4$	$2$	$1$	$4.615$	$\Q(\sqrt{-1}) $	None					34.2.b.a	$2$	$0$	$0$	$4$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(2 i+2)q^{3}-q^{4}+(2 i+2)q^{5}+\cdots$
578.2.c.e	$578$	$2$	578.c	17.c	$4$	$4$	$2$	$4.615$	$\Q(\zeta_{8})$	None					34.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_{2} q^{2}+\beta_1 q^{3}-q^{4}-\beta_{3} q^{6}+\cdots$
578.2.c.f	$578$	$2$	578.c	17.c	$4$	$8$	$4$	$4.615$	$\Q(\zeta_{16})$	None					34.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{2}+\beta_{7} q^{3}-q^{4}-2\beta_{7} q^{5}+\cdots$
578.2.c.g	$578$	$2$	578.c	17.c	$4$	$12$	$6$	$4.615$	12.0.$\cdots$.1	None		✓			578.2.a.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{3}+2\beta _{5})q^{3}-q^{4}+\cdots$
578.2.c.h	$578$	$2$	578.c	17.c	$4$	$12$	$6$	$4.615$	12.0.$\cdots$.1	None		✓			578.2.a.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+(-\beta _{8}+\beta _{10})q^{3}-q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots$
578.2.d.a	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	$\Q(\zeta_{8})$	None					34.2.d.a	$2$	$0$	$0$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
578.2.d.b	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	$\Q(\zeta_{8})$	None					34.2.d.a	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
578.2.d.c	$578$	$2$	578.d	17.d	$8$	$4$	$1$	$4.615$	$\Q(\zeta_{8})$	None					34.2.d.a	$2$	$0$	$0$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
578.2.d.d	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	$\Q(\zeta_{16})$	None					34.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta_1 q^{2}+\beta_{6} q^{3}+\beta_{2} q^{4}-2\beta_{3} q^{5}+\cdots$
578.2.d.e	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	$\Q(\zeta_{16})$	None					34.2.a.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta_{6} q^{2}+\beta_{5} q^{3}-\beta_{4} q^{4}-\beta_{3} q^{6}+\cdots$
578.2.d.f	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	$\Q(\zeta_{16})$	None					34.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta_1 q^{2}+\beta_{2} q^{4}+\beta_{3} q^{5}-\beta_{4} q^{8}+\cdots$
578.2.d.g	$578$	$2$	578.d	17.d	$8$	$8$	$2$	$4.615$	$\Q(\zeta_{16})$	None					34.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta_1 q^{2}+\beta_{6} q^{3}+\beta_{2} q^{4}+\beta_{3} q^{5}+\cdots$
578.2.d.h	$578$	$2$	578.d	17.d	$8$	$24$	$6$	$4.615$		None		✓			578.2.a.e	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
578.2.d.i	$578$	$2$	578.d	17.d	$8$	$24$	$6$	$4.615$		None		✓			578.2.a.g	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
578.2.f.a	$578$	$2$	578.f	289.f	$17$	$192$	$12$	$4.615$		None		✓			578.2.f.a	$2$	$0$	$12$	$0$	$-17$	$0$			$\mathrm{SU}(2)[C_{17}]$
578.2.f.b	$578$	$2$	578.f	289.f	$17$	$224$	$14$	$4.615$		None		✓	✓		578.2.f.b	$2$	$0$	$-14$	$-2$	$28$	$-4$			$\mathrm{SU}(2)[C_{17}]$
578.2.g.a	$578$	$2$	578.g	289.g	$34$	$192$	$12$	$4.615$		None		✓			578.2.g.a	$2$	$0$	$-12$	$0$	$17$	$0$			$\mathrm{SU}(2)[C_{34}]$
578.2.g.b	$578$	$2$	578.g	289.g	$34$	$224$	$14$	$4.615$		None		✓	✓		578.2.g.b	$2$	$0$	$14$	$0$	$-34$	$0$			$\mathrm{SU}(2)[C_{34}]$
578.2.h.a	$578$	$2$	578.h	289.h	$68$	$416$	$13$	$4.615$		None		✓			578.2.h.a	$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{68}]$
578.2.h.b	$578$	$2$	578.h	289.h	$68$	$416$	$13$	$4.615$		None		✓			578.2.h.b	$2$	$0$	$0$	$2$	$-4$	$4$			$\mathrm{SU}(2)[C_{68}]$
578.2.i.a	$578$	$2$	578.i	289.i	$136$	$768$	$12$	$4.615$		None		✓			578.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{136}]$
578.2.i.b	$578$	$2$	578.i	289.i	$136$	$832$	$13$	$4.615$		None		✓	✓		578.2.i.b	$2$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{136}]$
578.4.a.a	$578$	$4$	578.a	1.a	$1$	$1$	$1$	$34.103$	$\Q$	None	✓				34.4.a.b	$1$	$0$	$-2$	$2$	$-16$	$-24$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}-2^{4}q^{5}-4q^{6}+\cdots$
578.4.a.b	$578$	$4$	578.a	1.a	$1$	$1$	$1$	$34.103$	$\Q$	None	✓				34.4.a.a	$1$	$0$	$-2$	$2$	$18$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots$
578.4.a.c	$578$	$4$	578.a	1.a	$1$	$1$	$1$	$34.103$	$\Q$	None	✓				34.4.b.a	$1$	$1$	$2$	$-2$	$-8$	$34$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+4q^{4}-8q^{5}-4q^{6}+\cdots$
578.4.a.d	$578$	$4$	578.a	1.a	$1$	$1$	$1$	$34.103$	$\Q$	None	✓				34.4.b.a	$1$	$1$	$2$	$2$	$8$	$-34$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+4q^{4}+8q^{5}+4q^{6}+\cdots$
578.4.a.e	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{13}) $	None	✓	✓			578.4.a.e	$1$	$1$	$-4$	$-7$	$1$	$-19$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-3\beta )q^{3}+4q^{4}+(1-\beta )q^{5}+\cdots$
578.4.a.f	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{2}) $	None	✓				34.4.b.b	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+2\beta q^{3}+4q^{4}+\beta q^{5}-4\beta q^{6}+\cdots$
578.4.a.g	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{13}) $	None	✓	✓			578.4.a.e	$1$	$0$	$-4$	$7$	$-1$	$19$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(2+3\beta )q^{3}+4q^{4}+(-1+\beta )q^{5}+\cdots$
578.4.a.h	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{13}) $	None	✓				34.4.a.c	$1$	$1$	$4$	$-6$	$4$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(-3-\beta )q^{3}+4q^{4}+(2+4\beta )q^{5}+\cdots$
578.4.a.i	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{205}) $	None	✓	✓			578.4.a.i	$1$	$0$	$4$	$-3$	$17$	$33$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta )q^{3}+4q^{4}+(8+\beta )q^{5}+\cdots$
578.4.a.j	$578$	$4$	578.a	1.a	$1$	$2$	$2$	$34.103$	$\Q(\sqrt{2}) $	None	✓				34.4.c.a	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3\beta q^{3}+4q^{4}-7\beta q^{5}+6\beta q^{6}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.