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 142 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
1014.2.a.a	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓		✓	✓	78.2.e.b	$1$	$1$	$-1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
1014.2.a.b	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓				78.2.b.a	$1$	$1$	$-1$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
1014.2.a.c	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓				78.2.e.a	$1$	$0$	$-1$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots$
1014.2.a.d	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓				78.2.a.a	$1$	$0$	$1$	$-1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-4q^{7}+\cdots$
1014.2.a.e	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓				78.2.e.b	$1$	$0$	$1$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
1014.2.a.f	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓		✓	✓	78.2.e.a	$1$	$1$	$1$	$1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-2q^{7}+\cdots$
1014.2.a.g	$1014$	$2$	1014.a	1.a	$1$	$1$	$1$	$8.097$	$\Q$	None	✓				78.2.b.a	$1$	$0$	$1$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots$
1014.2.a.h	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	$\Q(\sqrt{3})$	None	✓				78.2.i.b	$1$	$0$	$-2$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+(3-\beta )q^{7}+\cdots$
1014.2.a.i	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	$\Q(\sqrt{3})$	None	✓		✓		78.2.i.a	$1$	$1$	$-2$	$2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots$
1014.2.a.j	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	$\Q(\sqrt{3})$	None	✓		✓	✓	78.2.i.b	$1$	$1$	$2$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots$
1014.2.a.k	$1014$	$2$	1014.a	1.a	$1$	$2$	$2$	$8.097$	$\Q(\sqrt{3})$	None	✓				78.2.i.a	$1$	$0$	$2$	$2$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots$
1014.2.a.l	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		1014.2.a.l	$1$	$0$	$-3$	$-3$	$-1$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+\cdots$
1014.2.a.m	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		1014.2.a.m	$1$	$0$	$-3$	$3$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$
1014.2.a.n	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		1014.2.a.l	$1$	$0$	$3$	$-3$	$1$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots$
1014.2.a.o	$1014$	$2$	1014.a	1.a	$1$	$3$	$3$	$8.097$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		1014.2.a.m	$1$	$0$	$3$	$3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$
1014.2.b.a	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	$\Q(\sqrt{-1})$	None					78.2.e.b	$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots$
1014.2.b.b	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	$\Q(\sqrt{-1})$	None					78.2.a.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{3}-q^{4}+2 i q^{5}+i q^{6}+\cdots$
1014.2.b.c	$1014$	$2$	1014.b	13.b	$2$	$2$	$2$	$8.097$	$\Q(\sqrt{-1})$	None					78.2.e.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+q^{3}-q^{4}+3 i q^{5}-i q^{6}+\cdots$
1014.2.b.d	$1014$	$2$	1014.b	13.b	$2$	$4$	$4$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-q^{3}-q^{4}-\beta_{2} q^{5}-\beta_1 q^{6}+\cdots$
1014.2.b.e	$1014$	$2$	1014.b	13.b	$2$	$4$	$4$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+q^{3}-q^{4}+(\beta_{2}+2\beta_1)q^{5}+\cdots$
1014.2.b.f	$1014$	$2$	1014.b	13.b	$2$	$6$	$6$	$8.097$	6.0.153664.1	None		✓			1014.2.a.l	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-q^{3}-q^{4}+(-2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1014.2.b.g	$1014$	$2$	1014.b	13.b	$2$	$6$	$6$	$8.097$	6.0.153664.1	None		✓			1014.2.a.m	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+q^{3}-q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+\cdots$
1014.2.e.a	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.e.a	$2$	$0$	$-1$	$-1$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.b	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.b.a	$2$	$0$	$-1$	$-1$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.c	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.a.a	$2$	$0$	$-1$	$1$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.d	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.e.b	$2$	$0$	$-1$	$1$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.e	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.b.a	$2$	$0$	$1$	$-1$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.f	$1014$	$2$	1014.e	13.c	$3$	$2$	$1$	$8.097$	$\Q(\sqrt{-3})$	None					78.2.a.a	$2$	$0$	$1$	$1$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
1014.2.e.g	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$-2$	$-2$	$8$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_1-1)q^{2}+(\beta_1-1)q^{3}-\beta_1 q^{4}+\cdots$
1014.2.e.h	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$-2$	$2$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_1 q^{2}+\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots$
1014.2.e.i	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$2$	$-2$	$-8$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}-\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots$
1014.2.e.j	$1014$	$2$	1014.e	13.c	$3$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$2$	$2$	$0$	$-6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}+\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots$
1014.2.e.k	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.m	$2$	$0$	$-3$	$-3$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5})q^{2}+(-1+\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots$
1014.2.e.l	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.l	$2$	$0$	$-3$	$3$	$2$	$-9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5})q^{2}+(1-\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots$
1014.2.e.m	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.m	$2$	$0$	$3$	$-3$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}-\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
1014.2.e.n	$1014$	$2$	1014.e	13.c	$3$	$6$	$3$	$8.097$	6.0.64827.1	None		✓			1014.2.a.l	$2$	$0$	$3$	$3$	$-2$	$9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$
1014.2.g.a	$1014$	$2$	1014.g	39.f	$4$	$8$	$4$	$8.097$	8.0.959512576.1	None		✓			1014.2.g.a	$8$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{2}+(1+\beta _{2})q^{3}+\beta _{4}q^{4}+\beta _{5}q^{5}+\cdots$
1014.2.g.b	$1014$	$2$	1014.g	39.f	$4$	$12$	$6$	$8.097$	12.0. $\cdots$ .52	None					78.2.g.a	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{8}q^{4}+(\beta _{5}-\beta _{9}+\cdots)q^{5}+\cdots$
1014.2.g.c	$1014$	$2$	1014.g	39.f	$4$	$16$	$8$	$8.097$	16.0. $\cdots$ .9	None					78.2.k.a	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{11}q^{2}-\beta _{15}q^{3}+\beta _{12}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
1014.2.g.d	$1014$	$2$	1014.g	39.f	$4$	$16$	$8$	$8.097$	16.0. $\cdots$ .9	None					78.2.k.a	$4$	$0$	$0$	$0$	$0$	$16$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{11}q^{2}+(-\beta _{2}-\beta _{5}-\beta _{6}+\beta _{15})q^{3}+\cdots$
1014.2.g.e	$1014$	$2$	1014.g	39.f	$4$	$48$	$24$	$8.097$		None		✓	✓		1014.2.g.e	$8$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1014.2.i.a	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$0$	$-2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
1014.2.i.b	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.e.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$
1014.2.i.c	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.b.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
1014.2.i.d	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.a.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$
1014.2.i.e	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.e.b	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
1014.2.i.f	$1014$	$2$	1014.i	13.e	$6$	$4$	$2$	$8.097$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$0$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$
1014.2.i.g	$1014$	$2$	1014.i	13.e	$6$	$12$	$6$	$8.097$	12.0. $\cdots$ .1	None		✓			1014.2.a.m	$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{2}-\beta _{7}q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
1014.2.i.h	$1014$	$2$	1014.i	13.e	$6$	$12$	$6$	$8.097$	12.0. $\cdots$ .1	None		✓			1014.2.a.l	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(1-\beta _{7})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
1014.3.f.a	$1014$	$3$	1014.f	13.d	$4$	$4$	$2$	$27.629$	$\Q(\zeta_{12})$	None					78.3.f.a	$2$	$0$	$-4$	$0$	$-12$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1-1)q^{2}+\beta_{3} q^{3}-2\beta_1 q^{4}+\cdots$

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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.