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 187 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
735.1.f.a	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	✓			735.1.f.a	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots$
735.1.f.b	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	✓			735.1.f.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots$
735.1.f.c	$735$	$1$	735.f	15.d	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None	✓	✓			735.1.f.c	$4$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots$
735.1.f.d	$735$	$1$	735.f	15.d	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None	✓	✓			735.1.f.c	$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots$
735.1.o.a	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		✓			735.1.f.a	$8$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
735.1.o.b	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		✓			735.1.f.a	$8$	$0$	$0$	$1$	$1$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
735.1.o.c	$735$	$1$	735.o	105.o	$6$	$4$	$2$	$0.367$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			735.1.f.c	$8$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
735.1.o.d	$735$	$1$	735.o	105.o	$6$	$4$	$2$	$0.367$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			735.1.f.c	$8$	$0$	$0$	$2$	$-2$	$0$		$1$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
735.2.a.a	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓				105.2.i.b	$1$	$0$	$-2$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots$
735.2.a.b	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓		✓	✓	105.2.i.b	$1$	$1$	$-2$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots$
735.2.a.c	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots$
735.2.a.d	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓		✓	✓	105.2.i.a	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+q^{9}+2q^{12}+q^{13}+\cdots$
735.2.a.e	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓				105.2.i.a	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{9}-2q^{12}-q^{13}+\cdots$
735.2.a.f	$735$	$2$	735.a	1.a	$1$	$1$	$1$	$5.869$	$\Q$	$_{}$	None	None	✓				105.2.a.a	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots$
735.2.a.g	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				105.2.i.d	$1$	$0$	$-2$	$-2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots$
735.2.a.h	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		105.2.i.d	$1$	$1$	$-2$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots$
735.2.a.i	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓	✓	105.2.i.c	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots$
735.2.a.j	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				105.2.i.c	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots$
735.2.a.k	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				105.2.a.b	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
735.2.a.l	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓		735.2.a.l	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
735.2.a.m	$735$	$2$	735.a	1.a	$1$	$2$	$2$	$5.869$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			735.2.a.l	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$
735.2.a.n	$735$	$2$	735.a	1.a	$1$	$4$	$4$	$5.869$	4.4.4352.1	$_{}$	None	None	✓	✓	✓		735.2.a.n	$1$	$0$	$4$	$-4$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{3})q^{2}-q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
735.2.a.o	$735$	$2$	735.a	1.a	$1$	$4$	$4$	$5.869$	4.4.4352.1	$_{}$	None	None	✓	✓	✓		735.2.a.n	$1$	$0$	$4$	$4$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{3})q^{2}+q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
735.2.b.a	$735$	$2$	735.b	21.c	$2$	$2$	$2$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.s.a	$2$	$0$	$0$	$-3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-q^{4}+\cdots$
735.2.b.b	$735$	$2$	735.b	21.c	$2$	$2$	$2$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.s.a	$2$	$0$	$0$	$3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-q^{4}+q^{5}+\cdots$
735.2.b.c	$735$	$2$	735.b	21.c	$2$	$8$	$8$	$5.869$	8.0.856615824.2	$_{}$	None	None					105.2.s.c	$2$	$0$	$0$	$-1$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots$
735.2.b.d	$735$	$2$	735.b	21.c	$2$	$8$	$8$	$5.869$	8.0.856615824.2	$_{}$	None	None					105.2.s.c	$2$	$0$	$0$	$1$	$-8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$
735.2.b.e	$735$	$2$	735.b	21.c	$2$	$16$	$16$	$5.869$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			735.2.b.e	$2$	$0$	$0$	$-4$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
735.2.b.f	$735$	$2$	735.b	21.c	$2$	$16$	$16$	$5.869$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			735.2.b.e	$2$	$0$	$0$	$4$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
735.2.d.a	$735$	$2$	735.d	5.b	$2$	$2$	$2$	$5.869$	$\Q(\sqrt{-1}) $	$_{}$	None	None					105.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}+q^{4}+(2 i-1)q^{5}+\cdots$
735.2.d.b	$735$	$2$	735.d	5.b	$2$	$6$	$6$	$5.869$	6.0.350464.1	$_{}$	None	None					105.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots$
735.2.d.c	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.309760000.3	$_{}$	None	None		✓			735.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{6}-\beta _{7})q^{4}+\cdots$
735.2.d.d	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.2058981376.2	$_{}$	None	None					105.2.q.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
735.2.d.e	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.2058981376.2	$_{}$	None	None					105.2.q.a	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
735.2.d.f	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			735.2.d.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{4} q^{2}+\beta_1 q^{3}+\beta_{3} q^{4}+(\beta_{6}+\beta_{5}-\beta_{2})q^{5}+\cdots$
735.2.g.a	$735$	$2$	735.g	105.g	$2$	$16$	$16$	$5.869$	16.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-15}) $	None		✓			735.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 7^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+\beta _{5}q^{3}+(2-\beta _{8})q^{4}+\beta _{11}q^{5}+\cdots$
735.2.g.b	$735$	$2$	735.g	105.g	$2$	$24$	$24$	$5.869$		$_{}$	None	None					105.2.p.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
735.2.g.c	$735$	$2$	735.g	105.g	$2$	$32$	$32$	$5.869$		$_{}$	None	None		✓	✓		735.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
735.2.i.a	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.a.a	$2$	$1$	$-1$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
735.2.i.b	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.a.a	$2$	$0$	$-1$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
735.2.i.c	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
735.2.i.d	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					15.2.a.a	$2$	$0$	$1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
735.2.i.e	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					15.2.a.a	$2$	$0$	$1$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
735.2.i.f	$735$	$2$	735.i	7.c	$3$	$2$	$1$	$5.869$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.b	$2$	$0$	$2$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
735.2.i.g	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			735.2.a.l	$2$	$0$	$-2$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
735.2.i.h	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			735.2.a.l	$2$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
735.2.i.i	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					105.2.a.b	$2$	$0$	$0$	$-2$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+3\beta _{1}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
735.2.i.j	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					105.2.i.c	$2$	$0$	$0$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{3}q^{6}+\cdots$
735.2.i.k	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					105.2.a.b	$2$	$0$	$0$	$2$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+3\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
735.2.i.l	$735$	$2$	735.i	7.c	$3$	$4$	$2$	$5.869$	$\Q(\zeta_{12})$	$_{}$	None	None					105.2.i.d	$2$	$0$	$2$	$-2$	$2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{2}+\beta_1)q^{2}+(\beta_1-1)q^{3}+\cdots$

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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.