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 51 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
2944.1.e.a	$2944$	$1$	2944.e	184.e	$2$	$2$	$2$	$1.469$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	✓			2944.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}-q^{23}+\cdots$
2944.1.e.b	$2944$	$1$	2944.e	184.e	$2$	$2$	$2$	$1.469$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	✓			2944.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}+q^{23}+\cdots$
2944.1.k.a	$2944$	$1$	2944.k	368.k	$4$	$2$	$1$	$1.469$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None					368.1.k.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(i-1)q^{3}-i q^{9}+(-i+1)q^{13}+\cdots$
2944.1.k.b	$2944$	$1$	2944.k	368.k	$4$	$2$	$1$	$1.469$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None					368.1.k.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-i+1)q^{3}-i q^{9}+(-i+1)q^{13}+\cdots$
2944.1.k.c	$2944$	$1$	2944.k	368.k	$4$	$4$	$2$	$1.469$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None					368.1.k.b	$4$	$0$	$0$	$-2$	$0$	$0$		$2$		$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{9}+\cdots$
2944.1.k.d	$2944$	$1$	2944.k	368.k	$4$	$4$	$2$	$1.469$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None					368.1.k.b	$4$	$0$	$0$	$2$	$0$	$0$		$2$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{9}+\cdots$
2944.1.p.a	$2944$	$1$	2944.p	736.p	$8$	$4$	$1$	$1.469$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-23}) $	None					736.1.p.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+(1+\zeta_{8}^{3})q^{3}+(1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots$
2944.1.p.b	$2944$	$1$	2944.p	736.p	$8$	$8$	$2$	$1.469$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-23}) $	None			✓		736.1.p.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2$		$q+(-\zeta_{24}^{7}+\zeta_{24}^{8})q^{3}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{9}+\cdots$
2944.1.bf.a	$2944$	$1$	2944.bf	2944.af	$32$	$16$	$1$	$1.469$	$\Q(\zeta_{32})$	$D_{32}$	$\Q(\sqrt{-23}) $	None		✓			2944.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{32}^{11}q^{2}+(-\zeta_{32}^{4}-\zeta_{32}^{11})q^{3}+\cdots$
2944.1.bf.b	$2944$	$1$	2944.bf	2944.af	$32$	$32$	$2$	$1.469$	$\Q(\zeta_{96})$	$D_{96}$	$\Q(\sqrt{-23}) $	None		✓	✓		2944.1.bf.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{96}^{5}q^{2}+(-\zeta_{96}^{37}+\zeta_{96}^{44})q^{3}+\cdots$
2944.2.a.a	$2944$	$2$	2944.a	1.a	$1$	$1$	$1$	$23.508$	$\Q$	$_{}$	None	None	✓	✓			2944.2.a.a	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
2944.2.a.b	$2944$	$2$	2944.a	1.a	$1$	$1$	$1$	$23.508$	$\Q$	$_{}$	None	None	✓	✓			2944.2.a.a	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
2944.2.a.c	$2944$	$2$	2944.a	1.a	$1$	$1$	$1$	$23.508$	$\Q$	$_{}$	None	None	✓	✓			2944.2.a.a	$1$	$0$	$0$	$2$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
2944.2.a.d	$2944$	$2$	2944.a	1.a	$1$	$1$	$1$	$23.508$	$\Q$	$_{}$	None	None	✓	✓			2944.2.a.a	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
2944.2.a.e	$2944$	$2$	2944.a	1.a	$1$	$4$	$4$	$23.508$	4.4.6224.1	$_{}$	None	None	✓	✓			2944.2.a.e	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
2944.2.a.f	$2944$	$2$	2944.a	1.a	$1$	$4$	$4$	$23.508$	4.4.6224.1	$_{}$	None	None	✓	✓			2944.2.a.e	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+\cdots$
2944.2.a.g	$2944$	$2$	2944.a	1.a	$1$	$4$	$4$	$23.508$	4.4.6224.1	$_{}$	None	None	✓	✓			2944.2.a.e	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-1-\beta _{1})q^{7}+\cdots$
2944.2.a.h	$2944$	$2$	2944.a	1.a	$1$	$4$	$4$	$23.508$	4.4.6224.1	$_{}$	None	None	✓	✓			2944.2.a.e	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+\cdots$
2944.2.a.i	$2944$	$2$	2944.a	1.a	$1$	$5$	$5$	$23.508$	5.5.719440.1	$_{}$	None	None	✓	✓			2944.2.a.i	$1$	$1$	$0$	$-2$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
2944.2.a.j	$2944$	$2$	2944.a	1.a	$1$	$5$	$5$	$23.508$	5.5.719440.1	$_{}$	None	None	✓	✓			2944.2.a.i	$1$	$1$	$0$	$-2$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
2944.2.a.k	$2944$	$2$	2944.a	1.a	$1$	$5$	$5$	$23.508$	5.5.719440.1	$_{}$	None	None	✓	✓			2944.2.a.i	$1$	$1$	$0$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
2944.2.a.l	$2944$	$2$	2944.a	1.a	$1$	$5$	$5$	$23.508$	5.5.719440.1	$_{}$	None	None	✓	✓			2944.2.a.i	$1$	$0$	$0$	$2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
2944.2.a.m	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.269055680.1	$_{}$	None	None	✓	✓	✓		2944.2.a.m	$1$	$1$	$0$	$-4$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$
2944.2.a.n	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.269055680.1	$_{}$	None	None	✓	✓			2944.2.a.m	$1$	$0$	$0$	$-4$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{5})q^{5}+\beta _{4}q^{7}+\cdots$
2944.2.a.o	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.353444288.1	$_{}$	None	None	✓	✓	✓		2944.2.a.o	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{5})q^{7}+\cdots$
2944.2.a.p	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.353444288.1	$_{}$	None	None	✓	✓			2944.2.a.o	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{7}+\cdots$
2944.2.a.q	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.353444288.1	$_{}$	None	None	✓	✓			2944.2.a.o	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{7}+\cdots$
2944.2.a.r	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.353444288.1	$_{}$	None	None	✓	✓			2944.2.a.o	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{5})q^{7}+\cdots$
2944.2.a.s	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.269055680.1	$_{}$	None	None	✓	✓			2944.2.a.m	$1$	$0$	$0$	$4$	$-6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{5})q^{5}+\beta _{4}q^{7}+\cdots$
2944.2.a.t	$2944$	$2$	2944.a	1.a	$1$	$6$	$6$	$23.508$	6.6.269055680.1	$_{}$	None	None	✓	✓			2944.2.a.m	$1$	$0$	$0$	$4$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$
2944.2.b.a	$2944$	$2$	2944.b	8.b	$2$	$2$	$2$	$23.508$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			2944.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}-5q^{9}-8q^{15}-2q^{17}+\cdots$
2944.2.b.b	$2944$	$2$	2944.b	8.b	$2$	$2$	$2$	$23.508$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			2944.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}-5q^{9}+8q^{15}-2q^{17}+\cdots$
2944.2.b.c	$2944$	$2$	2944.b	8.b	$2$	$2$	$2$	$23.508$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2944.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+3 q^{9}-3\beta q^{11}+2\beta q^{13}+\cdots$
2944.2.b.d	$2944$	$2$	2944.b	8.b	$2$	$2$	$2$	$23.508$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2944.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+3 q^{9}-3\beta q^{11}-2\beta q^{13}+\cdots$
2944.2.b.e	$2944$	$2$	2944.b	8.b	$2$	$8$	$8$	$23.508$	8.0.3588489216.5	$_{}$	None	None		✓			2944.2.b.e	$2$	$0$	$0$	$0$	$0$	$-16$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots$
2944.2.b.f	$2944$	$2$	2944.b	8.b	$2$	$8$	$8$	$23.508$	$\Q(\zeta_{16})$	$_{}$	None	None		✓			2944.2.b.f	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{4}+\beta_{3}+\beta_1)q^{3}+(\beta_{3}-\beta_{2})q^{5}+\cdots$
2944.2.b.g	$2944$	$2$	2944.b	8.b	$2$	$8$	$8$	$23.508$	$\Q(\zeta_{16})$	$_{}$	None	None		✓			2944.2.b.f	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{4}+\beta_{3}+\beta_1)q^{3}+(-\beta_{3}+\beta_{2})q^{5}+\cdots$
2944.2.b.h	$2944$	$2$	2944.b	8.b	$2$	$8$	$8$	$23.508$	8.0.3588489216.5	$_{}$	None	None		✓			2944.2.b.e	$2$	$0$	$0$	$0$	$0$	$16$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{4})q^{5}+(2+\beta _{2}+\cdots)q^{7}+\cdots$
2944.2.b.i	$2944$	$2$	2944.b	8.b	$2$	$12$	$12$	$23.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2944.2.b.i	$2$	$0$	$0$	$0$	$0$	$-16$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{9}q^{5}+(-1-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots$
2944.2.b.j	$2944$	$2$	2944.b	8.b	$2$	$12$	$12$	$23.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2944.2.b.j	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{3}q^{5}-\beta _{8}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots$
2944.2.b.k	$2944$	$2$	2944.b	8.b	$2$	$12$	$12$	$23.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2944.2.b.j	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{3}q^{5}+\beta _{8}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots$
2944.2.b.l	$2944$	$2$	2944.b	8.b	$2$	$12$	$12$	$23.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2944.2.b.i	$2$	$0$	$0$	$0$	$0$	$16$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{9}q^{5}+(1+\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots$
2944.2.c.a	$2944$	$2$	2944.c	92.b	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2944.2.c.b	$2944$	$2$	2944.c	92.b	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2944.2.c.c	$2944$	$2$	2944.c	92.b	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2944.2.c.d	$2944$	$2$	2944.c	92.b	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2944.2.h.a	$2944$	$2$	2944.h	184.h	$2$	$8$	$8$	$23.508$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-46}) $	None		✓			2944.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{5}-3q^{9}-\beta _{5}q^{11}-\beta _{2}q^{19}+\cdots$
2944.2.h.b	$2944$	$2$	2944.h	184.h	$2$	$16$	$16$	$23.508$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2944.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{11}\cdot 23^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{6}q^{5}+\beta _{3}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
2944.2.h.c	$2944$	$2$	2944.h	184.h	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.h.c	$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2944.2.h.d	$2944$	$2$	2944.h	184.h	$2$	$24$	$24$	$23.508$		$_{}$	None	None		✓			2944.2.h.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.