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 212 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
490.2.a.a	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.d	$1$	$0$	$-1$	$-2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots$
490.2.a.b	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓		✓	✓	70.2.e.c	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
490.2.a.c	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.c	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
490.2.a.d	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓		✓	✓	70.2.e.d	$1$	$0$	$-1$	$2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots$
490.2.a.e	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.a	$1$	$0$	$1$	$-3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{8}+\cdots$
490.2.a.f	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓	✓	✓	✓	490.2.a.f	$1$	$1$	$1$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots$
490.2.a.g	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.b	$1$	$0$	$1$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots$
490.2.a.h	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
490.2.a.i	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓	✓			490.2.a.f	$1$	$0$	$1$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots$
490.2.a.j	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.b	$1$	$0$	$1$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots$
490.2.a.k	$490$	$2$	490.a	1.a	$1$	$1$	$1$	$3.913$	$\Q$	None	✓				70.2.e.a	$1$	$0$	$1$	$3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+q^{8}+\cdots$
490.2.a.l	$490$	$2$	490.a	1.a	$1$	$2$	$2$	$3.913$	$\Q(\sqrt{2}) $	None	✓	✓	✓		490.2.a.l	$1$	$1$	$-2$	$-4$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots$
490.2.a.m	$490$	$2$	490.a	1.a	$1$	$2$	$2$	$3.913$	$\Q(\sqrt{2}) $	None	✓	✓	✓		490.2.a.l	$1$	$0$	$-2$	$4$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots$
490.2.c.a	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	$\Q(\sqrt{-1}) $	None					70.2.i.b	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(-2-i)q^{5}-iq^{8}+\cdots$
490.2.c.b	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	$\Q(\sqrt{-1}) $	None					70.2.i.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-3iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$
490.2.c.c	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	$\Q(\sqrt{-1}) $	None					70.2.i.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+3iq^{3}-q^{4}+(1+2i)q^{5}+\cdots$
490.2.c.d	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	$\Q(\sqrt{-1}) $	None					70.2.i.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(2+i)q^{5}-iq^{8}+3q^{9}+\cdots$
490.2.c.e	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	$\Q(i, \sqrt{6})$	None					70.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
490.2.c.f	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	$\Q(\zeta_{8})$	None		✓			490.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots$
490.2.c.g	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	$\Q(\zeta_{8})$	None		✓			490.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
490.2.e.a	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.e.b	$2$	$1$	$-1$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.b	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None		✓			490.2.a.f	$2$	$0$	$-1$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.c	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.a.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots$
490.2.e.d	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.a.a	$2$	$0$	$-1$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{8}+\cdots$
490.2.e.e	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None		✓			490.2.a.f	$2$	$0$	$-1$	$2$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.f	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.e.a	$2$	$0$	$-1$	$3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.g	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.e.d	$2$	$0$	$1$	$-2$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.h	$490$	$2$	490.e	7.c	$3$	$2$	$1$	$3.913$	$\Q(\sqrt{-3}) $	None					70.2.e.c	$2$	$0$	$1$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
490.2.e.i	$490$	$2$	490.e	7.c	$3$	$4$	$2$	$3.913$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			490.2.a.l	$2$	$0$	$2$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}+\cdots$
490.2.e.j	$490$	$2$	490.e	7.c	$3$	$4$	$2$	$3.913$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			490.2.a.l	$2$	$0$	$2$	$4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(2+\beta _{1}+2\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
490.2.g.a	$490$	$2$	490.g	35.f	$4$	$8$	$4$	$3.913$	$\Q(\zeta_{16})$	None		✓			490.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{16}^{2}q^{2}+(-\zeta_{16}-\zeta_{16}^{3}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots$
490.2.g.b	$490$	$2$	490.g	35.f	$4$	$16$	$8$	$3.913$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			490.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{9}q^{2}+(-\beta _{11}-\beta _{12}+\beta _{13})q^{3}+\cdots$
490.2.g.c	$490$	$2$	490.g	35.f	$4$	$16$	$8$	$3.913$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					70.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}+(-\beta _{8}+\beta _{14})q^{3}-\beta _{9}q^{4}+\cdots$
490.2.i.a	$490$	$2$	490.i	35.j	$6$	$4$	$2$	$3.913$	$\Q(\zeta_{12})$	None					70.2.i.b	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}+\cdots)q^{5}+\cdots$
490.2.i.b	$490$	$2$	490.i	35.j	$6$	$4$	$2$	$3.913$	$\Q(\zeta_{12})$	None					70.2.i.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
490.2.i.c	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	$\Q(\zeta_{24})$	None					70.2.c.a	$4$	$0$	$0$	$0$	$-4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
490.2.i.d	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	$\Q(\zeta_{24})$	None		✓			490.2.c.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
490.2.i.e	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	$\Q(\zeta_{24})$	None		✓			490.2.c.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
490.2.i.f	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	$\Q(\zeta_{24})$	None					70.2.c.a	$4$	$0$	$0$	$0$	$4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
490.2.k.a	$490$	$2$	490.k	49.e	$7$	$6$	$1$	$3.913$	$\Q(\zeta_{14})$	None		✓			490.2.k.a	$2$	$0$	$-1$	$0$	$-1$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
490.2.k.b	$490$	$2$	490.k	49.e	$7$	$6$	$1$	$3.913$	$\Q(\zeta_{14})$	None		✓			490.2.k.b	$2$	$0$	$1$	$-1$	$1$	$-7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
490.2.k.c	$490$	$2$	490.k	49.e	$7$	$6$	$1$	$3.913$	$\Q(\zeta_{14})$	None		✓			490.2.k.c	$2$	$0$	$1$	$6$	$1$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
490.2.k.d	$490$	$2$	490.k	49.e	$7$	$12$	$2$	$3.913$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			490.2.k.d	$2$	$0$	$-2$	$-4$	$-2$	$0$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{6}q^{2}+(-1-\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{3}+\cdots$
490.2.k.e	$490$	$2$	490.k	49.e	$7$	$12$	$2$	$3.913$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			490.2.k.e	$2$	$0$	$2$	$-4$	$2$	$0$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{6})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
490.2.k.f	$490$	$2$	490.k	49.e	$7$	$24$	$4$	$3.913$		None		✓			490.2.k.f	$2$	$0$	$4$	$6$	$-4$	$0$			$\mathrm{SU}(2)[C_{7}]$
490.2.k.g	$490$	$2$	490.k	49.e	$7$	$30$	$5$	$3.913$		None		✓	✓		490.2.k.g	$2$	$0$	$-5$	$1$	$5$	$1$			$\mathrm{SU}(2)[C_{7}]$
490.2.l.a	$490$	$2$	490.l	35.k	$12$	$16$	$4$	$3.913$	$\Q(\zeta_{48})$	None					70.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\zeta_{48}^{10}q^{2}+(-\zeta_{48}^{5}-\zeta_{48}^{7}+\zeta_{48}^{15})q^{3}+\cdots$
490.2.l.b	$490$	$2$	490.l	35.k	$12$	$16$	$4$	$3.913$	$\Q(\zeta_{48})$	None		✓			490.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{48}^{14}q^{2}+(-\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{7}+\cdots)q^{3}+\cdots$
490.2.l.c	$490$	$2$	490.l	35.k	$12$	$16$	$4$	$3.913$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					70.2.k.a	$4$	$0$	$0$	$0$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{7}-\beta _{15})q^{2}+(\beta _{4}-\beta _{13})q^{3}+\cdots$
490.2.l.d	$490$	$2$	490.l	35.k	$12$	$32$	$8$	$3.913$		None		✓	✓		490.2.g.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$

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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.