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 82 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
1305.1.b.a	$1305$	$1$	1305.b	435.b	$2$	$4$	$4$	$0.651$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1305.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
1305.1.b.b	$1305$	$1$	1305.b	435.b	$2$	$4$	$4$	$0.651$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1305.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
1305.1.l.a	$1305$	$1$	1305.l	145.f	$4$	$2$	$1$	$0.651$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $			✓	✓	145.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{4}-i q^{5}+(-i+1)q^{11}-q^{16}+\cdots$
1305.1.o.a	$1305$	$1$	1305.o	145.h	$4$	$2$	$1$	$0.651$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $			✓	✓	145.1.h.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-i q^{4}+i q^{5}+(i-1)q^{7}+(i+1)q^{13}+\cdots$
1305.2.a.a	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓	✓			1305.2.a.a	$1$	$1$	$-2$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-2q^{7}-2q^{10}+\cdots$
1305.2.a.b	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓				435.2.a.d	$1$	$0$	$-1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
1305.2.a.c	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓				435.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-2q^{7}-q^{11}+6q^{13}+\cdots$
1305.2.a.d	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓				435.2.a.c	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+2q^{7}-3q^{11}+2q^{13}+\cdots$
1305.2.a.e	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓				435.2.a.a	$1$	$0$	$1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-4q^{7}-3q^{8}-q^{10}+\cdots$
1305.2.a.f	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓				145.2.a.a	$1$	$0$	$1$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
1305.2.a.g	$1305$	$2$	1305.a	1.a	$1$	$1$	$1$	$10.420$	$\Q$	$_{}$	None	None	✓	✓			1305.2.a.a	$1$	$1$	$2$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots$
1305.2.a.h	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1305.2.a.h	$1$	$1$	$-1$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots$
1305.2.a.i	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				435.2.a.h	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots$
1305.2.a.j	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				435.2.a.g	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}+q^{5}+2q^{7}-\beta q^{8}+\cdots$
1305.2.a.k	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				435.2.a.e	$1$	$1$	$1$	$0$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-3q^{7}+\cdots$
1305.2.a.l	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1305.2.a.h	$1$	$1$	$1$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1-2\beta )q^{7}+\cdots$
1305.2.a.m	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓				435.2.a.f	$1$	$0$	$1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3+\beta )q^{4}-q^{5}+q^{7}+(5+2\beta )q^{8}+\cdots$
1305.2.a.n	$1305$	$2$	1305.a	1.a	$1$	$2$	$2$	$10.420$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				145.2.a.b	$1$	$0$	$2$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots$
1305.2.a.o	$1305$	$2$	1305.a	1.a	$1$	$3$	$3$	$10.420$	3.3.148.1	$_{}$	None	None	✓		✓		145.2.a.d	$1$	$1$	$-3$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1305.2.a.p	$1305$	$2$	1305.a	1.a	$1$	$3$	$3$	$10.420$	3.3.148.1	$_{}$	None	None	✓				145.2.a.c	$1$	$1$	$-1$	$0$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
1305.2.a.q	$1305$	$2$	1305.a	1.a	$1$	$3$	$3$	$10.420$	3.3.469.1	$_{}$	None	None	✓				435.2.a.i	$1$	$1$	$-1$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
1305.2.a.r	$1305$	$2$	1305.a	1.a	$1$	$4$	$4$	$10.420$	4.4.2225.1	$_{}$	None	None	✓		✓		435.2.a.j	$1$	$0$	$3$	$0$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
1305.2.a.s	$1305$	$2$	1305.a	1.a	$1$	$7$	$7$	$10.420$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1305.2.a.s	$1$	$0$	$-1$	$0$	$-7$	$10$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
1305.2.a.t	$1305$	$2$	1305.a	1.a	$1$	$7$	$7$	$10.420$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1305.2.a.s	$1$	$0$	$1$	$0$	$7$	$10$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
1305.2.c.a	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}+(-i+2)q^{5}-2 i q^{7}+\cdots$
1305.2.c.b	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(-2 i-1)q^{5}+2 i q^{7}+\cdots$
1305.2.c.c	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-5}) $	$_{}$	None	None		✓			1305.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+\beta q^{5}-2\beta q^{7}-5q^{11}-2\beta q^{13}+\cdots$
1305.2.c.d	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-5}) $	$_{}$	None	None		✓			1305.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}-\beta q^{5}-2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots$
1305.2.c.e	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					145.2.b.a	$2$	$0$	$0$	$0$	$3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
1305.2.c.f	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					145.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
1305.2.c.g	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	$\Q(\zeta_{8})$	$_{}$	None	None					435.2.c.c	$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+q^{4}+(2\beta_1+1)q^{5}+\beta_{2} q^{7}+\cdots$
1305.2.c.h	$1305$	$2$	1305.c	5.b	$2$	$6$	$6$	$10.420$	6.0.84345856.2	$_{}$	None	None					145.2.b.c	$2$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-3+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$
1305.2.c.i	$1305$	$2$	1305.c	5.b	$2$	$10$	$10$	$10.420$	10.0.$\cdots$.1	$_{}$	None	None					435.2.c.d	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1305.2.c.j	$1305$	$2$	1305.c	5.b	$2$	$10$	$10$	$10.420$	10.0.$\cdots$.1	$_{}$	None	None					435.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{4}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
1305.2.c.k	$1305$	$2$	1305.c	5.b	$2$	$12$	$12$	$10.420$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1305.2.c.k	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
1305.2.c.l	$1305$	$2$	1305.c	5.b	$2$	$12$	$12$	$10.420$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1305.2.c.k	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\beta _{3}q^{7}+\cdots$
1305.2.d.a	$1305$	$2$	1305.d	29.b	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					145.2.c.a	$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$
1305.2.d.b	$1305$	$2$	1305.d	29.b	$2$	$6$	$6$	$10.420$	6.0.16516096.1	$_{}$	None	None					145.2.c.b	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots$
1305.2.d.c	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	10.0.$\cdots$.1	$_{}$	None	None					435.2.d.b	$2$	$0$	$0$	$0$	$-10$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
1305.2.d.d	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	10.0.$\cdots$.1	$_{}$	None	None					435.2.d.a	$2$	$0$	$0$	$0$	$10$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}-\beta _{5}q^{7}+\cdots$
1305.2.d.e	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			1305.2.d.e	$2$	$0$	$0$	$0$	$-10$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+\beta _{7}q^{7}+\cdots$
1305.2.d.f	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			1305.2.d.e	$2$	$0$	$0$	$0$	$10$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots$
1305.2.f.a	$1305$	$2$	1305.f	145.d	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.f.a	$2$	$1$	$-4$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{2}+2 q^{4}+(-i-2)q^{5}+4 i q^{7}+\cdots$
1305.2.f.b	$1305$	$2$	1305.f	145.d	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.f.b	$2$	$0$	$-2$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}+(-\beta+1)q^{5}+\beta q^{7}+\cdots$
1305.2.f.c	$1305$	$2$	1305.f	145.d	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.f.b	$2$	$0$	$2$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}+(-\beta+1)q^{5}+\beta q^{7}+\cdots$
1305.2.f.d	$1305$	$2$	1305.f	145.d	$2$	$2$	$2$	$10.420$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.f.a	$2$	$0$	$4$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{2}+2 q^{4}+(-i-2)q^{5}+4 i q^{7}+\cdots$
1305.2.f.e	$1305$	$2$	1305.f	145.d	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None					145.2.d.a	$2$	$0$	$-4$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+\cdots$
1305.2.f.f	$1305$	$2$	1305.f	145.d	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{5}, \sqrt{-6})$	$_{}$	None	None		✓			1305.2.f.f	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}+3q^{8}+\cdots$
1305.2.f.g	$1305$	$2$	1305.f	145.d	$2$	$4$	$4$	$10.420$	$\Q(\sqrt{-5}, \sqrt{-29})$	$_{}$	$\Q(\sqrt{-435}) $	None		✓			1305.2.f.g	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{1}q^{5}-\beta _{2}q^{11}+4q^{16}+\cdots$
1305.2.f.h	$1305$	$2$	1305.f	145.d	$2$	$4$	$4$	$10.420$	$\Q(i, \sqrt{5})$	$_{}$	None	None					145.2.d.b	$4$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+3q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots$

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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.