LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (49 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6900.2.a.a	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
6900.2.a.b	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{13}+3q^{17}+\cdots$
6900.2.a.c	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
6900.2.a.d	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+q^{11}-q^{13}-5q^{19}+\cdots$
6900.2.a.e	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-2q^{13}-6q^{17}+\cdots$
6900.2.a.f	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+q^{11}+q^{13}-5q^{19}+\cdots$
6900.2.a.g	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+6q^{13}-2q^{17}+6q^{19}+\cdots$
6900.2.a.h	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-5q^{11}+q^{13}+\cdots$
6900.2.a.i	$6900$	$2$	6900.a	1.a	$1$	$1$	$1$	$55.097$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+5q^{7}+q^{9}-4q^{13}+3q^{17}+\cdots$
6900.2.a.j	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{15}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots$
6900.2.a.k	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
6900.2.a.l	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2-\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
6900.2.a.m	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{7}+q^{9}+4\beta q^{11}-4\beta q^{13}+\cdots$
6900.2.a.n	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{73}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+(-1+\beta )q^{11}+q^{13}+\cdots$
6900.2.a.o	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
6900.2.a.p	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{7}+q^{9}-4q^{13}+\cdots$
6900.2.a.q	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
6900.2.a.r	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+(-2-\beta )q^{11}-\beta q^{13}+\cdots$
6900.2.a.s	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+2\beta )q^{7}+q^{9}+(-1+3\beta )q^{11}+\cdots$
6900.2.a.t	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{73}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+(-1+\beta )q^{11}-q^{13}+\cdots$
6900.2.a.u	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{7}+q^{9}+2\beta q^{11}-2q^{13}+\cdots$
6900.2.a.v	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(3-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
6900.2.a.w	$6900$	$2$	6900.a	1.a	$1$	$2$	$2$	$55.097$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(3-\beta )q^{7}+q^{9}+(3-\beta )q^{11}+\cdots$
6900.2.a.x	$6900$	$2$	6900.a	1.a	$1$	$3$	$3$	$55.097$	3.3.3144.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
6900.2.a.y	$6900$	$2$	6900.a	1.a	$1$	$3$	$3$	$55.097$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-\beta _{2}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots$
6900.2.a.z	$6900$	$2$	6900.a	1.a	$1$	$3$	$3$	$55.097$	3.3.148.1	None	✓	$1$	$1$	$0$	$3$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-\beta _{2}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots$
6900.2.a.ba	$6900$	$2$	6900.a	1.a	$1$	$4$	$4$	$55.097$	4.4.175557.1	None	✓	$1$	$0$	$0$	$-4$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots$
6900.2.a.bb	$6900$	$2$	6900.a	1.a	$1$	$4$	$4$	$55.097$	4.4.175557.1	None	✓	$1$	$1$	$0$	$4$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1}+\beta _{3})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots$
6900.2.a.bc	$6900$	$2$	6900.a	1.a	$1$	$7$	$7$	$55.097$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-7$	$0$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{7}+q^{9}+(\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
6900.2.a.bd	$6900$	$2$	6900.a	1.a	$1$	$7$	$7$	$55.097$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$0$	$-1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{7}+q^{9}+(\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
6900.2.f.a	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+3iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots$
6900.2.f.b	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-2iq^{13}+\cdots$
6900.2.f.c	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{9}+6iq^{13}+2iq^{17}-6q^{19}+\cdots$
6900.2.f.d	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+4iq^{7}-q^{9}+2iq^{13}-6iq^{17}+\cdots$
6900.2.f.e	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}-q^{9}-4iq^{13}+3iq^{17}+\cdots$
6900.2.f.f	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+5iq^{7}-q^{9}+4iq^{13}+3iq^{17}+\cdots$
6900.2.f.g	$6900$	$2$	6900.f	5.b	$2$	$2$	$2$	$55.097$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+3iq^{7}-q^{9}+q^{11}+iq^{13}+\cdots$
6900.2.f.h	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{1}q^{7}-q^{9}+(-2+\beta _{3})q^{11}+\cdots$
6900.2.f.i	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{3}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}-q^{9}+\cdots$
6900.2.f.j	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{73})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{2}q^{7}-q^{9}+(-1+\beta _{3})q^{11}+\cdots$
6900.2.f.k	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{10})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{7}-q^{9}-4\beta _{1}q^{13}+\cdots$
6900.2.f.l	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{7}-q^{9}-4\zeta_{8}^{3}q^{11}+\cdots$
6900.2.f.m	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}+3\beta _{2})q^{7}-q^{9}+\beta _{3}q^{11}+\cdots$
6900.2.f.n	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+\beta _{3}q^{11}+\cdots$
6900.2.f.o	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{15})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+3\beta _{1}q^{7}-q^{9}+(1+\beta _{2})q^{11}+\cdots$
6900.2.f.p	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{17})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(2-2\beta _{3})q^{11}+\cdots$
6900.2.f.q	$6900$	$2$	6900.f	5.b	$2$	$4$	$4$	$55.097$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}+3\beta _{2})q^{7}-q^{9}+(2+\beta _{3})q^{11}+\cdots$
6900.2.f.r	$6900$	$2$	6900.f	5.b	$2$	$6$	$6$	$55.097$	6.0.158155776.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$
6900.2.f.s	$6900$	$2$	6900.f	5.b	$2$	$8$	$8$	$55.097$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(-\beta _{4}+\beta _{5})q^{7}-q^{9}+\beta _{2}q^{11}+\cdots$

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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.