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 155 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
507.1.c.a	$507$	$1$	507.c	3.b	$2$	$1$	$1$	$0.253$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓		✓	✓	39.1.d.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
507.1.h.a	$507$	$1$	507.h	39.h	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $			✓	✓	39.1.d.a	$8$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$
507.1.i.a	$507$	$1$	507.i	39.i	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $			✓	✓	39.1.d.a	$8$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$
507.1.n.a	$507$	$1$	507.n	507.n	$26$	$12$	$1$	$0.253$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	507.1.n.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{26}^{7}q^{3}-\zeta_{26}^{2}q^{4}+(\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$
507.1.o.a	$507$	$1$	507.o	507.o	$26$	$12$	$1$	$0.253$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	507.1.o.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{2}q^{4}+(-\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$
507.2.a.a	$507$	$2$	507.a	1.a	$1$	$1$	$1$	$4.048$	$\Q$	$_{}$	None	None	✓				39.2.a.a	$1$	$1$	$-1$	$-1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots$
507.2.a.b	$507$	$2$	507.a	1.a	$1$	$1$	$1$	$4.048$	$\Q$	$_{}$	None	None	✓				39.2.e.a	$1$	$1$	$-1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
507.2.a.c	$507$	$2$	507.a	1.a	$1$	$1$	$1$	$4.048$	$\Q$	$_{}$	None	None	✓				39.2.e.a	$1$	$1$	$1$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
507.2.a.d	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				39.2.e.b	$1$	$0$	$-1$	$2$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(2-\beta )q^{5}+\cdots$
507.2.a.e	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				39.2.j.a	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2\beta q^{5}+\beta q^{7}+q^{9}+\cdots$
507.2.a.f	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				39.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots$
507.2.a.g	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				39.2.e.b	$1$	$0$	$1$	$2$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
507.2.a.h	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				39.2.a.b	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$
507.2.a.i	$507$	$2$	507.a	1.a	$1$	$3$	$3$	$4.048$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓		507.2.a.i	$1$	$1$	$-3$	$-3$	$-6$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
507.2.a.j	$507$	$2$	507.a	1.a	$1$	$3$	$3$	$4.048$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓	✓	507.2.a.j	$1$	$1$	$-1$	$3$	$-4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
507.2.a.k	$507$	$2$	507.a	1.a	$1$	$3$	$3$	$4.048$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓		507.2.a.j	$1$	$0$	$1$	$3$	$4$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$
507.2.a.l	$507$	$2$	507.a	1.a	$1$	$3$	$3$	$4.048$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓		507.2.a.i	$1$	$0$	$3$	$-3$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(4-\beta _{1})q^{4}+\cdots$
507.2.b.a	$507$	$2$	507.b	13.b	$2$	$2$	$2$	$4.048$	$\Q(\sqrt{-1}) $	$_{}$	None	None					39.2.a.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}+q^{4}+2 i q^{5}-i q^{6}+\cdots$
507.2.b.b	$507$	$2$	507.b	13.b	$2$	$2$	$2$	$4.048$	$\Q(\sqrt{-1}) $	$_{}$	None	None					39.2.e.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}+q^{4}-i q^{5}-i q^{6}+\cdots$
507.2.b.c	$507$	$2$	507.b	13.b	$2$	$2$	$2$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.j.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2 q^{4}+2\beta q^{5}-\beta q^{7}+q^{9}+\cdots$
507.2.b.d	$507$	$2$	507.b	13.b	$2$	$4$	$4$	$4.048$	$\Q(i, \sqrt{17})$	$_{}$	None	None					39.2.e.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
507.2.b.e	$507$	$2$	507.b	13.b	$2$	$4$	$4$	$4.048$	$\Q(\zeta_{8})$	$_{}$	None	None					39.2.a.b	$2$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+q^{3}+(-\beta_{3}-1)q^{4}+\cdots$
507.2.b.f	$507$	$2$	507.b	13.b	$2$	$6$	$6$	$4.048$	6.0.153664.1	$_{}$	None	None		✓			507.2.a.i	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-3-\beta _{2}+\cdots)q^{4}+\cdots$
507.2.b.g	$507$	$2$	507.b	13.b	$2$	$6$	$6$	$4.048$	6.0.153664.1	$_{}$	None	None		✓			507.2.a.j	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots$
507.2.e.a	$507$	$2$	507.e	13.c	$3$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.a.a	$2$	$0$	$-1$	$1$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
507.2.e.b	$507$	$2$	507.e	13.c	$3$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.a.a	$2$	$0$	$1$	$1$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
507.2.e.c	$507$	$2$	507.e	13.c	$3$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.e.a	$2$	$0$	$1$	$1$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
507.2.e.d	$507$	$2$	507.e	13.c	$3$	$4$	$2$	$4.048$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					39.2.a.b	$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots$
507.2.e.e	$507$	$2$	507.e	13.c	$3$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	None	None					39.2.b.a	$4$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots$
507.2.e.f	$507$	$2$	507.e	13.c	$3$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	None	None					39.2.j.a	$4$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{3}+(-2\beta_1+2)q^{4}-2\beta_{3} q^{5}+\cdots$
507.2.e.g	$507$	$2$	507.e	13.c	$3$	$4$	$2$	$4.048$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None					39.2.e.b	$2$	$0$	$1$	$-2$	$6$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
507.2.e.h	$507$	$2$	507.e	13.c	$3$	$4$	$2$	$4.048$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					39.2.a.b	$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots$
507.2.e.i	$507$	$2$	507.e	13.c	$3$	$6$	$3$	$4.048$	6.0.64827.1	$_{}$	None	None		✓			507.2.a.i	$2$	$0$	$-3$	$3$	$12$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\beta _{1}+\beta _{4}+2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots$
507.2.e.j	$507$	$2$	507.e	13.c	$3$	$6$	$3$	$4.048$	6.0.64827.1	$_{}$	None	None		✓			507.2.a.j	$2$	$0$	$-1$	$-3$	$8$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
507.2.e.k	$507$	$2$	507.e	13.c	$3$	$6$	$3$	$4.048$	6.0.64827.1	$_{}$	None	None		✓			507.2.a.j	$2$	$0$	$1$	$-3$	$-8$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
507.2.e.l	$507$	$2$	507.e	13.c	$3$	$6$	$3$	$4.048$	6.0.64827.1	$_{}$	None	None		✓			507.2.a.i	$2$	$0$	$3$	$3$	$-12$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{1}-\beta _{4}-2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots$
507.2.f.a	$507$	$2$	507.f	39.f	$4$	$4$	$2$	$4.048$	$\Q(\zeta_{8})$	$_{}$	None	None					39.2.f.a	$4$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
507.2.f.b	$507$	$2$	507.f	39.f	$4$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None					39.2.k.a	$4$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+2\beta_{2} q^{4}+\cdots$
507.2.f.c	$507$	$2$	507.f	39.f	$4$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None					39.2.k.a	$4$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+2\beta_{2} q^{4}+\cdots$
507.2.f.d	$507$	$2$	507.f	39.f	$4$	$8$	$4$	$4.048$	8.0.56070144.2	$_{}$	$\Q(\sqrt{-39}) $	None		✓			507.2.f.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-2\beta _{2}-\beta _{5})q^{4}+\cdots$
507.2.f.e	$507$	$2$	507.f	39.f	$4$	$8$	$4$	$4.048$	8.0.56070144.2	$_{}$	None	None					39.2.k.b	$4$	$0$	$0$	$4$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(\beta _{4}+\beta _{5})q^{3}+\cdots$
507.2.f.f	$507$	$2$	507.f	39.f	$4$	$8$	$4$	$4.048$	8.0.56070144.2	$_{}$	None	None					39.2.k.b	$4$	$0$	$0$	$4$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
507.2.f.g	$507$	$2$	507.f	39.f	$4$	$48$	$24$	$4.048$		$_{}$	None	None		✓	✓		507.2.f.g	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
507.2.j.a	$507$	$2$	507.j	13.e	$6$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.b.a	$2$	$0$	$-3$	$1$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
507.2.j.b	$507$	$2$	507.j	13.e	$6$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.j.a	$2$	$0$	$0$	$1$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots$
507.2.j.c	$507$	$2$	507.j	13.e	$6$	$2$	$1$	$4.048$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.b.a	$2$	$0$	$3$	$1$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
507.2.j.d	$507$	$2$	507.j	13.e	$6$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	None	None					39.2.e.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
507.2.j.e	$507$	$2$	507.j	13.e	$6$	$4$	$2$	$4.048$	$\Q(\zeta_{12})$	$_{}$	None	None					39.2.a.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
507.2.j.f	$507$	$2$	507.j	13.e	$6$	$8$	$4$	$4.048$	$\Q(\zeta_{24})$	$_{}$	None	None					39.2.a.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_{3} q^{2}-\beta_1 q^{3}+(\beta_{6}-\beta_{4}-\beta_1+1)q^{4}+\cdots$
507.2.j.g	$507$	$2$	507.j	13.e	$6$	$8$	$4$	$4.048$	8.0.1731891456.1	$_{}$	None	None					39.2.e.b	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+3\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$

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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.