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 80 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
3042.2.a.a	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.a.a	$1$	$0$	$-1$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots$
3042.2.a.b	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				234.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots$
3042.2.a.c	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.b.a	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots$
3042.2.a.d	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.e.b	$1$	$0$	$-1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
3042.2.a.e	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.c.a	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
3042.2.a.f	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.a.a	$1$	$0$	$-1$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-4q^{7}-q^{8}-2q^{10}+\cdots$
3042.2.a.g	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.b.a	$1$	$1$	$-1$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots$
3042.2.a.h	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.e.a	$1$	$0$	$-1$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{10}+\cdots$
3042.2.a.i	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.e.a	$1$	$1$	$1$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots$
3042.2.a.j	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.b.a	$1$	$0$	$1$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{10}+\cdots$
3042.2.a.k	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.c.a	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
3042.2.a.l	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				26.2.a.b	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
3042.2.a.m	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.e.b	$1$	$1$	$1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
3042.2.a.n	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				78.2.b.a	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
3042.2.a.o	$3042$	$2$	3042.a	1.a	$1$	$1$	$1$	$24.290$	$\Q$	None	✓				234.2.a.a	$1$	$0$	$1$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots$
3042.2.a.p	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				78.2.i.a	$1$	$1$	$-2$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
3042.2.a.q	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{10}) $	None	✓				234.2.h.d	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta )q^{5}+\beta q^{7}-q^{8}+\cdots$
3042.2.a.r	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{10}) $	None	✓				234.2.h.d	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta )q^{5}-\beta q^{7}-q^{8}+\cdots$
3042.2.a.s	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				78.2.i.b	$1$	$1$	$-2$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(-3+\beta )q^{7}-q^{8}+\cdots$
3042.2.a.t	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				234.2.l.b	$2$	$0$	$-2$	$0$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{16}+\cdots$
3042.2.a.u	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				234.2.l.b	$2$	$1$	$2$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{16}+\cdots$
3042.2.a.v	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				78.2.i.b	$1$	$0$	$2$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+(3+\beta )q^{7}+q^{8}+\cdots$
3042.2.a.w	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{10}) $	None	✓				234.2.h.d	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+\beta q^{7}+q^{8}+\cdots$
3042.2.a.x	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{10}) $	None	✓				234.2.h.d	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots$
3042.2.a.y	$3042$	$2$	3042.a	1.a	$1$	$2$	$2$	$24.290$	$\Q(\sqrt{3}) $	None	✓				78.2.i.a	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots$
3042.2.a.z	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓				338.2.a.g	$1$	$0$	$-3$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2\beta _{1}q^{5}+(-2\beta _{1}+2\beta _{2})q^{7}+\cdots$
3042.2.a.ba	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.l	$1$	$0$	$-3$	$0$	$-1$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots$
3042.2.a.bb	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		3042.2.a.bb	$1$	$1$	$-3$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+\cdots$
3042.2.a.bc	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		3042.2.a.bb	$1$	$0$	$-3$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots$
3042.2.a.bd	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓		✓		1014.2.a.m	$1$	$1$	$-3$	$0$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
3042.2.a.be	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓		✓		1014.2.a.m	$1$	$1$	$3$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
3042.2.a.bf	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		3042.2.a.bb	$1$	$0$	$3$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+\cdots$
3042.2.a.bg	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		3042.2.a.bb	$1$	$1$	$3$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots$
3042.2.a.bh	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.l	$1$	$0$	$3$	$0$	$1$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
3042.2.a.bi	$3042$	$2$	3042.a	1.a	$1$	$3$	$3$	$24.290$	$\Q(\zeta_{14})^+$	None	✓				338.2.a.g	$1$	$0$	$3$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+(2\beta _{1}-2\beta _{2})q^{7}+\cdots$
3042.2.b.a	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					26.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+3 i q^{5}+i q^{7}-i q^{8}+\cdots$
3042.2.b.b	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					234.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots$
3042.2.b.c	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					234.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}-2 i q^{7}-i q^{8}+\cdots$
3042.2.b.d	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					78.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+i q^{5}+2 i q^{7}-i q^{8}+\cdots$
3042.2.b.e	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					26.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{5}-4 i q^{7}+i q^{8}+\cdots$
3042.2.b.f	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					26.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{5}-i q^{7}+i q^{8}+\cdots$
3042.2.b.g	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					78.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+2 i q^{5}+4 i q^{7}+i q^{8}+\cdots$
3042.2.b.h	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	$\Q(\sqrt{-1}) $	None					78.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+3 i q^{5}+2 i q^{7}+i q^{8}+\cdots$
3042.2.b.i	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-q^{4}+(\beta_{2}+2\beta_1)q^{5}+\cdots$
3042.2.b.j	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	$\Q(i, \sqrt{10})$	None					234.2.h.d	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots$
3042.2.b.k	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	$\Q(i, \sqrt{10})$	None					234.2.h.d	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$
3042.2.b.l	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-q^{4}-\beta_{2} q^{5}+(\beta_{2}-3\beta_1)q^{7}+\cdots$
3042.2.b.m	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	$\Q(\zeta_{12})$	None					234.2.l.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}-q^{4}+3\beta_1 q^{5}+\beta_1 q^{8}+\cdots$
3042.2.b.n	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None					338.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-q^{4}+2\beta _{1}q^{5}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots$
3042.2.b.o	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None					1014.2.a.l	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$

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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.