Newform search results

The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

Results (45 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	11
8624.2.a.b	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				154.2.e.a	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+6q^{9}+q^{11}-7q^{13}+\cdots\)
8624.2.a.c	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				88.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+3q^{5}+6q^{9}+q^{11}-9q^{15}+\cdots\)
8624.2.a.e	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
8624.2.a.f	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				4312.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots\)
8624.2.a.g	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				1078.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
8624.2.a.i	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots\)
8624.2.a.j	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-q^{11}-4q^{13}+\cdots\)
8624.2.a.k	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				154.2.e.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}+q^{11}-q^{13}-6q^{17}+\cdots\)
8624.2.a.l	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				154.2.e.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}+q^{11}+5q^{13}+6q^{17}+\cdots\)
8624.2.a.n	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				308.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-q^{11}+4q^{13}+\cdots\)
8624.2.a.p	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}+q^{11}+6q^{13}-2q^{19}-4q^{23}+\cdots\)
8624.2.a.q	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots\)
8624.2.a.y	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				1078.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
8624.2.a.z	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				154.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
8624.2.a.ba	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.a.e	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{15}+\cdots\)
8624.2.a.bb	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				4312.2.a.c	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+q^{11}+2q^{13}-2q^{17}+\cdots\)
8624.2.a.bc	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				77.2.a.c	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
8624.2.a.bd	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				154.2.e.d	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-4q^{5}+6q^{9}+q^{11}-q^{13}+\cdots\)
8624.2.a.bf	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{5}) \)	None	✓				154.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+(3+2\beta )q^{9}+\cdots\)
8624.2.a.bg	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				616.2.q.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}-2\beta q^{9}-q^{11}+\cdots\)
8624.2.a.bh	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				154.2.e.e	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2+\beta )q^{5}-2\beta q^{9}+\cdots\)
8624.2.a.bk	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{7}) \)	None	✓				154.2.e.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+4q^{9}-q^{11}+\cdots\)
8624.2.a.bn	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				4312.2.a.p	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{5}-3q^{9}-q^{11}-\beta q^{13}+2\beta q^{17}+\cdots\)
8624.2.a.bo	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				1078.2.a.o	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-3q^{9}-q^{11}-2\beta q^{13}-\beta q^{17}+\cdots\)
8624.2.a.bp	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				4312.2.a.o	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-3q^{9}+q^{11}+\beta q^{17}-\beta q^{19}+\cdots\)
8624.2.a.bq	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				4312.2.a.s	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}-q^{9}-q^{11}-2q^{15}+\cdots\)
8624.2.a.br	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				4312.2.a.r	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}-q^{11}-2\beta q^{13}+\cdots\)
8624.2.a.bs	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				1078.2.a.u	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-3\beta q^{5}-q^{9}+q^{11}-6q^{15}+\cdots\)
8624.2.a.bv	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				539.2.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2q^{15}+\cdots\)
8624.2.a.bw	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				1078.2.a.q	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2\beta q^{13}+\cdots\)
8624.2.a.bx	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				2156.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}-\beta q^{5}+5q^{9}+q^{11}+\beta q^{13}+\cdots\)
8624.2.a.bz	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				1078.2.a.v	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+5q^{9}+q^{11}-3\beta q^{13}+2\beta q^{17}+\cdots\)
8624.2.a.cb	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{17}) \)	None	✓				88.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots\)
8624.2.a.cg	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.257.1	None	✓				308.2.i.b	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.ci	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.321.1	None	✓				308.2.i.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.cj	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.1016.1	None	✓				308.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
8624.2.a.cl	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.257.1	None	✓				77.2.e.b	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)
8624.2.a.co	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	\(\Q(\zeta_{18})^+\)	None	✓				77.2.e.a	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8624.2.a.cq	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	\(\Q(\zeta_{14})^+\)	None	✓				616.2.q.c	$1$	$1$	\(0\)	\(5\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-2+\beta _{1}-3\beta _{2})q^{5}+\cdots\)
8624.2.a.cr	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.89289.1	None	✓				616.2.q.d	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.cs	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	\(\Q(\zeta_{24})^+\)	None	✓		✓		2156.2.a.l	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-2\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
8624.2.a.cw	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	\(\Q(\zeta_{24})^+\)	None	✓				4312.2.a.bc	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+3q^{9}-q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
8624.2.a.cx	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.301088.1	None	✓		✓		2156.2.a.m	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(4+\beta _{3})q^{9}-q^{11}+\cdots\)
8624.2.a.da	$8624$	$2$	8624.a	1.a	$1$	$5$	$5$	$68.863$	5.5.352076.1	None	✓		✓		616.2.q.e	$1$	$1$	\(0\)	\(-3\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1}+\beta _{4})q^{5}+\cdots\)
8624.2.a.db	$8624$	$2$	8624.a	1.a	$1$	$5$	$5$	$68.863$	5.5.559701.1	None	✓		✓		616.2.q.f	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)

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