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 214 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
270.2.a.a	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	$\Q$	None	✓	✓	✓	✓	270.2.a.a	$1$	$0$	$-1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
270.2.a.b	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	$\Q$	None	✓	✓	✓	✓	270.2.a.b	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
270.2.a.c	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	$\Q$	None	✓	✓	✓	✓	270.2.a.b	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
270.2.a.d	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	$\Q$	None	✓	✓	✓	✓	270.2.a.a	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
270.2.c.a	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	$\Q(\sqrt{-1}) $	None		✓			270.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots$
270.2.c.b	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	$\Q(\sqrt{-1}) $	None		✓			270.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots$
270.2.c.c	$270$	$2$	270.c	5.b	$2$	$4$	$4$	$2.156$	$\Q(i, \sqrt{19})$	None		✓	✓		270.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots$
270.2.e.a	$270$	$2$	270.e	9.c	$3$	$2$	$1$	$2.156$	$\Q(\sqrt{-3}) $	None					90.2.e.b	$2$	$0$	$-1$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
270.2.e.b	$270$	$2$	270.e	9.c	$3$	$2$	$1$	$2.156$	$\Q(\sqrt{-3}) $	None					90.2.e.a	$2$	$0$	$1$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
270.2.e.c	$270$	$2$	270.e	9.c	$3$	$4$	$2$	$2.156$	$\Q(\sqrt{-3}, \sqrt{-11})$	None			✓		90.2.e.c	$2$	$0$	$-2$	$0$	$-2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
270.2.f.a	$270$	$2$	270.f	15.e	$4$	$8$	$4$	$2.156$	$\Q(\zeta_{24})$	None		✓			270.2.f.a	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots$
270.2.f.b	$270$	$2$	270.f	15.e	$4$	$8$	$4$	$2.156$	$\Q(\zeta_{24})$	None		✓			270.2.f.b	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots$
270.2.i.a	$270$	$2$	270.i	45.j	$6$	$4$	$2$	$2.156$	$\Q(\zeta_{12})$	None					90.2.i.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
270.2.i.b	$270$	$2$	270.i	45.j	$6$	$8$	$4$	$2.156$	$\Q(\zeta_{24})$	None			✓		90.2.i.b	$4$	$0$	$0$	$0$	$4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots$
270.2.k.a	$270$	$2$	270.k	27.e	$9$	$6$	$1$	$2.156$	$\Q(\zeta_{18})$	None		✓			270.2.k.a	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
270.2.k.b	$270$	$2$	270.k	27.e	$9$	$12$	$2$	$2.156$	12.0.$\cdots$.1	None		✓			270.2.k.b	$2$	$0$	$0$	$3$	$0$	$-12$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots$
270.2.k.c	$270$	$2$	270.k	27.e	$9$	$12$	$2$	$2.156$	12.0.$\cdots$.1	None		✓			270.2.k.c	$2$	$0$	$0$	$3$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots$
270.2.k.d	$270$	$2$	270.k	27.e	$9$	$18$	$3$	$2.156$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			270.2.k.d	$2$	$0$	$0$	$-3$	$0$	$-3$		$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots$
270.2.k.e	$270$	$2$	270.k	27.e	$9$	$24$	$4$	$2.156$		None		✓	✓		270.2.k.e	$2$	$0$	$0$	$-3$	$0$	$3$			$\mathrm{SU}(2)[C_{9}]$
270.2.m.a	$270$	$2$	270.m	45.l	$12$	$8$	$2$	$2.156$	$\Q(\zeta_{24})$	None					90.2.l.a	$4$	$0$	$0$	$0$	$-12$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots$
270.2.m.b	$270$	$2$	270.m	45.l	$12$	$16$	$4$	$2.156$	16.0.$\cdots$.9	None			✓		90.2.l.b	$4$	$0$	$0$	$0$	$12$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
270.2.p.a	$270$	$2$	270.p	135.p	$18$	$108$	$18$	$2.156$		None		✓	✓	✓	270.2.p.a	$4$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{18}]$
270.2.r.a	$270$	$2$	270.r	135.q	$36$	$216$	$18$	$2.156$		None		✓	✓	✓	270.2.r.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{36}]$
270.3.b.a	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	4.0.31744.1	None		✓			270.3.b.a	$2$	$0$	$0$	$0$	$-12$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots$
270.3.b.b	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	$\Q(\zeta_{8})$	None		✓			270.3.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots$
270.3.b.c	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	$\Q(\zeta_{8})$	None		✓			270.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots$
270.3.b.d	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	4.0.31744.1	None		✓			270.3.b.a	$2$	$0$	$0$	$0$	$12$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots$
270.3.d.a	$270$	$3$	270.d	3.b	$2$	$4$	$4$	$7.357$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			270.3.d.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots$
270.3.d.b	$270$	$3$	270.d	3.b	$2$	$8$	$8$	$7.357$	8.0.40960000.1	None		✓	✓		270.3.d.b	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots$
270.3.g.a	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	$\Q(i, \sqrt{6})$	None		✓			270.3.g.a	$2$	$0$	$-4$	$0$	$-12$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.b	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	$\Q(i, \sqrt{6})$	None		✓			270.3.g.b	$2$	$0$	$-4$	$0$	$12$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.c	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	$\Q(i, \sqrt{6})$	None		✓			270.3.g.b	$2$	$0$	$4$	$0$	$-12$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.d	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	$\Q(i, \sqrt{6})$	None		✓			270.3.g.a	$2$	$0$	$4$	$0$	$12$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
270.3.g.e	$270$	$3$	270.g	5.c	$4$	$8$	$4$	$7.357$	8.0.$\cdots$.38	None		✓			270.3.g.e	$2$	$0$	$-8$	$0$	$12$	$-8$		$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
270.3.g.f	$270$	$3$	270.g	5.c	$4$	$8$	$4$	$7.357$	8.0.$\cdots$.38	None		✓			270.3.g.e	$2$	$0$	$8$	$0$	$-12$	$-8$		$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
270.3.h.a	$270$	$3$	270.h	9.d	$6$	$16$	$8$	$7.357$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None			✓	✓	90.3.h.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
270.3.j.a	$270$	$3$	270.j	45.h	$6$	$8$	$4$	$7.357$	$\Q(\zeta_{24})$	None					90.3.j.a	$4$	$0$	$0$	$0$	$12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots$
270.3.j.b	$270$	$3$	270.j	45.h	$6$	$16$	$8$	$7.357$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			✓		90.3.j.b	$4$	$0$	$0$	$0$	$-30$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$
270.3.l.a	$270$	$3$	270.l	45.k	$12$	$24$	$6$	$7.357$		None					90.3.k.b	$4$	$0$	$-12$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{12}]$
270.3.l.b	$270$	$3$	270.l	45.k	$12$	$24$	$6$	$7.357$		None					90.3.k.a	$4$	$0$	$12$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{12}]$
270.3.n.a	$270$	$3$	270.n	135.n	$18$	$216$	$36$	$7.357$		None		✓	✓	✓	270.3.n.a	$4$	$0$	$0$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{18}]$
270.3.o.a	$270$	$3$	270.o	27.f	$18$	$144$	$24$	$7.357$		None		✓	✓	✓	270.3.o.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
270.3.q.a	$270$	$3$	270.q	135.r	$36$	$216$	$18$	$7.357$		None		✓			270.3.q.a	$4$	$0$	$0$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{36}]$
270.3.q.b	$270$	$3$	270.q	135.r	$36$	$216$	$18$	$7.357$		None		✓			270.3.q.b	$4$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{36}]$
270.4.a.a	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓			270.4.a.a	$1$	$0$	$-2$	$0$	$-5$	$-34$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots$
270.4.a.b	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓	✓	✓	270.4.a.b	$1$	$1$	$-2$	$0$	$-5$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots$
270.4.a.c	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓			270.4.a.c	$1$	$0$	$-2$	$0$	$5$	$-22$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots$
270.4.a.d	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓			270.4.a.d	$1$	$1$	$-2$	$0$	$5$	$-13$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots$
270.4.a.e	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓			270.4.a.e	$1$	$1$	$-2$	$0$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots$
270.4.a.f	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	$\Q$	None	✓	✓			270.4.a.f	$1$	$0$	$-2$	$0$	$5$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots$

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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.