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 57 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
6084.2.a.a	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				468.2.a.a	$1$	$0$	$0$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}+4q^{11}-8q^{23}+11q^{25}+\cdots$
6084.2.a.b	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.a.a	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}-4q^{11}-2q^{17}+2q^{19}+\cdots$
6084.2.a.c	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				52.2.e.b	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}-3q^{17}-2q^{19}+6q^{23}+\cdots$
6084.2.a.d	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.b.b	$1$	$2$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-6q^{11}-2q^{17}-8q^{23}+\cdots$
6084.2.a.e	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.i.a	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-2q^{11}+4q^{17}+4q^{19}+\cdots$
6084.2.a.f	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				52.2.e.a	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+5q^{11}-3q^{17}-3q^{19}+\cdots$
6084.2.a.g	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	$\Q(\sqrt{-3}) $	✓				468.2.l.c	$2$	$0$	$0$	$0$	$0$	$-5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}-8q^{19}-5q^{25}-11q^{31}+\cdots$
6084.2.a.h	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+6q^{17}-2q^{19}-5q^{25}+6q^{29}+\cdots$
6084.2.a.i	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	$\Q(\sqrt{-3}) $	✓				36.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}-8q^{19}-5q^{25}+4q^{31}+10q^{37}+\cdots$
6084.2.a.j	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	$\Q(\sqrt{-3}) $	✓				468.2.l.c	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$1$	$N(\mathrm{U}(1))$	$q+5q^{7}+8q^{19}-5q^{25}+11q^{31}+\cdots$
6084.2.a.k	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				52.2.e.a	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-5q^{11}-3q^{17}+3q^{19}+\cdots$
6084.2.a.l	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.i.a	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+2q^{11}+4q^{17}-4q^{19}+\cdots$
6084.2.a.m	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				52.2.a.a	$1$	$1$	$0$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-2q^{11}-6q^{17}+6q^{19}+\cdots$
6084.2.a.n	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				156.2.b.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+6q^{11}-2q^{17}-8q^{23}+\cdots$
6084.2.a.o	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				52.2.e.b	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-3q^{17}+2q^{19}+6q^{23}+\cdots$
6084.2.a.p	$6084$	$2$	6084.a	1.a	$1$	$1$	$1$	$48.581$	$\Q$	None	✓				468.2.a.a	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-4q^{7}-4q^{11}+8q^{23}+11q^{25}+\cdots$
6084.2.a.q	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{7}) $	None	✓				468.2.l.e	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{7}+2\beta q^{11}+3\beta q^{17}+\cdots$
6084.2.a.r	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓				468.2.b.b	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q-\beta q^{7}+\beta q^{19}-5q^{25}+3\beta q^{31}+\cdots$
6084.2.a.s	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓				468.2.t.b	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{7}-2\beta q^{19}-5q^{25}+\beta q^{31}+\cdots$
6084.2.a.t	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{3}) $	None	✓				52.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}+3\beta q^{11}+3q^{17}+3\beta q^{19}+\cdots$
6084.2.a.u	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{3}) $	None	✓				156.2.q.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+2\beta q^{7}+2\beta q^{11}+3q^{17}+\cdots$
6084.2.a.v	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{3}) $	None	✓				156.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{11}+6q^{17}+2\beta q^{19}+\cdots$
6084.2.a.w	$6084$	$2$	6084.a	1.a	$1$	$2$	$2$	$48.581$	$\Q(\sqrt{7}) $	None	✓				468.2.l.e	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+2q^{7}+2\beta q^{11}-3\beta q^{17}+\cdots$
6084.2.a.x	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				676.2.a.g	$1$	$1$	$0$	$0$	$-8$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-3-\beta _{2})q^{5}+(-2+2\beta _{1}-3\beta _{2})q^{7}+\cdots$
6084.2.a.y	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.i	$1$	$0$	$0$	$0$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(-1-2\beta _{1}+\beta _{2})q^{7}+\cdots$
6084.2.a.z	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.k	$1$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots$
6084.2.a.ba	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.k	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\beta _{2})q^{7}+\cdots$
6084.2.a.bb	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.i	$1$	$1$	$0$	$0$	$2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+(-2+\cdots)q^{11}+\cdots$
6084.2.a.bc	$6084$	$2$	6084.a	1.a	$1$	$3$	$3$	$48.581$	$\Q(\zeta_{14})^+$	None	✓				676.2.a.g	$1$	$0$	$0$	$0$	$8$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta _{1})q^{5}+(-\beta _{1}-2\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots$
6084.2.a.bd	$6084$	$2$	6084.a	1.a	$1$	$4$	$4$	$48.581$	$\Q(\sqrt{3}, \sqrt{43})$	None	✓		✓		156.2.q.b	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}-2\beta _{2}q^{11}+\cdots$
6084.2.a.be	$6084$	$2$	6084.a	1.a	$1$	$6$	$6$	$48.581$	6.6.25969216.1	None	✓	✓	✓		6084.2.a.be	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{5}+(-1-\beta _{2})q^{7}+(\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$
6084.2.a.bf	$6084$	$2$	6084.a	1.a	$1$	$6$	$6$	$48.581$	6.6.25969216.1	None	✓	✓	✓		6084.2.a.be	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{5}+(1+\beta _{2})q^{7}+(\beta _{1}-\beta _{4})q^{11}+\cdots$
6084.2.b.a	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					156.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{7}-6 q^{17}+\beta q^{19}+5 q^{25}+\cdots$
6084.2.b.b	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					156.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{5}+i q^{7}-2 i q^{11}-4 q^{17}+\cdots$
6084.2.b.c	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-3}) $	None					156.2.q.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+2\beta q^{7}+2\beta q^{11}-3 q^{17}+\cdots$
6084.2.b.d	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-3}) $	None					52.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{7}-3\beta q^{11}-3 q^{17}+3\beta q^{19}+\cdots$
6084.2.b.e	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					468.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+2\beta q^{7}+2\beta q^{11}-8 q^{23}+\cdots$
6084.2.b.f	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $					36.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2\beta q^{7}-4\beta q^{19}+5 q^{25}+2\beta q^{31}+\cdots$
6084.2.b.g	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $					468.2.l.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5 i q^{7}-8 i q^{19}+5 q^{25}-11 i q^{31}+\cdots$
6084.2.b.h	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					468.2.t.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{7}+2\beta q^{19}+5 q^{25}-\beta q^{31}+\cdots$
6084.2.b.i	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					468.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-2\beta q^{7}+2\beta q^{11}+8 q^{23}+\cdots$
6084.2.b.j	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					156.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+\beta q^{7}-2\beta q^{11}+2 q^{17}+\cdots$
6084.2.b.k	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					52.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{5}+4 i q^{7}+3 q^{17}+2 i q^{19}+\cdots$
6084.2.b.l	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					52.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{5}+i q^{7}+5 i q^{11}+3 q^{17}+\cdots$
6084.2.b.m	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	$\Q(\sqrt{-1}) $	None					52.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{7}+\beta q^{11}+6 q^{17}+3\beta q^{19}+\cdots$
6084.2.b.n	$6084$	$2$	6084.b	13.b	$2$	$4$	$4$	$48.581$	$\Q(i, \sqrt{7})$	None					468.2.l.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}-2\beta _{1}q^{7}+2\beta _{3}q^{11}-3\beta _{2}q^{17}+\cdots$
6084.2.b.o	$6084$	$2$	6084.b	13.b	$2$	$4$	$4$	$48.581$	$\Q(\sqrt{-3}, \sqrt{-43})$	None					156.2.q.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{11}+\cdots$
6084.2.b.p	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None					676.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-3\beta _{5})q^{5}+(-3\beta _{1}+2\beta _{3}+2\beta _{5})q^{7}+\cdots$
6084.2.b.q	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None					2028.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3}+2\beta _{5})q^{7}+\cdots$
6084.2.b.r	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None					2028.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}-\beta _{3}-3\beta _{5})q^{7}+\cdots$

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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.