Newform search results

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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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.1.c.a	$900$	$1$	900.c	4.b	$2$	$1$	$1$	$0.449$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$		\(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots\)
900.1.c.b	$900$	$1$	900.c	4.b	$2$	$1$	$1$	$0.449$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots\)
900.1.l.a	$900$	$1$	900.l	5.c	$4$	$4$	$2$	$0.449$	\(\Q(i, \sqrt{6})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{7}-\beta _{3}q^{13}-\beta _{2}q^{19}+q^{31}+\cdots\)
900.1.m.a	$900$	$1$	900.m	60.l	$4$	$4$	$2$	$0.449$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
900.1.t.a	$900$	$1$	900.t	36.f	$6$	$4$	$2$	$0.449$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots\)
900.1.x.a	$900$	$1$	900.x	100.j	$10$	$4$	$1$	$0.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$1$		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
900.1.bb.a	$900$	$1$	900.bb	100.h	$10$	$8$	$2$	$0.449$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots\)
900.1.bd.a	$900$	$1$	900.bd	180.v	$12$	$8$	$2$	$0.449$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
900.1.bh.a	$900$	$1$	900.bh	300.u	$20$	$16$	$2$	$0.449$	\(\Q(\zeta_{40})\)	$D_{20}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+\zeta_{40}^{3}q^{5}+\cdots\)
900.2.a.a	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}+4q^{17}+4q^{23}+6q^{29}+\cdots\)
900.2.a.b	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots\)
900.2.a.c	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-6q^{11}+5q^{13}+6q^{17}+5q^{19}+\cdots\)
900.2.a.d	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-q^{7}-7q^{13}-7q^{19}+11q^{31}-10q^{37}+\cdots\)
900.2.a.e	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-6q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots\)
900.2.a.f	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+q^{7}+7q^{13}-7q^{19}+11q^{31}+10q^{37}+\cdots\)
900.2.a.g	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{7}-2q^{13}+8q^{19}-4q^{31}+10q^{37}+\cdots\)
900.2.a.h	$900$	$2$	900.a	1.a	$1$	$1$	$1$	$7.187$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}-4q^{17}-4q^{23}+6q^{29}+\cdots\)
900.2.d.a	$900$	$2$	900.d	5.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-6q^{11}+5iq^{13}-6iq^{17}+\cdots\)
900.2.d.b	$900$	$2$	900.d	5.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2iq^{7}+iq^{13}-8q^{19}-4q^{31}+\cdots\)
900.2.d.c	$900$	$2$	900.d	5.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-iq^{13}+3iq^{17}+4q^{19}+\cdots\)
900.2.d.d	$900$	$2$	900.d	5.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{7}-7iq^{13}+7q^{19}+11q^{31}+\cdots\)
900.2.e.a	$900$	$2$	900.e	12.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{13}+4q^{16}+\cdots\)
900.2.e.b	$900$	$2$	900.e	12.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-2q^{4}-2\beta q^{8}+4q^{13}+4q^{16}+\cdots\)
900.2.e.c	$900$	$2$	900.e	12.b	$2$	$2$	$2$	$7.187$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-2q^{4}+2\beta q^{8}+6q^{13}+4q^{16}+\cdots\)
900.2.e.d	$900$	$2$	900.e	12.b	$2$	$8$	$8$	$7.187$	8.0.18939904.2	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(1-\beta _{3}-\beta _{4}-\beta _{7})q^{4}+(-2+\cdots)q^{7}+\cdots\)
900.2.e.e	$900$	$2$	900.e	12.b	$2$	$8$	$8$	$7.187$	8.0.64000000.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
900.2.e.f	$900$	$2$	900.e	12.b	$2$	$8$	$8$	$7.187$	8.0.207360000.2	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{5})q^{4}+(\beta _{2}+\beta _{7})q^{7}+\cdots\)
900.2.e.g	$900$	$2$	900.e	12.b	$2$	$8$	$8$	$7.187$	8.0.64000000.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{4}+(-\beta _{4}+\beta _{7})q^{7}+\cdots\)
900.2.h.a	$900$	$2$	900.h	60.h	$2$	$4$	$4$	$7.187$	\(\Q(\zeta_{8})\)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{3}q^{8}+2\zeta_{8}q^{13}+\cdots\)
900.2.h.b	$900$	$2$	900.h	60.h	$2$	$8$	$8$	$7.187$	8.0.18939904.2	$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.c	$900$	$2$	900.h	60.h	$2$	$8$	$8$	$7.187$	8.0.18939904.2	$_{}$	None	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.d	$900$	$2$	900.h	60.h	$2$	$16$	$16$	$7.187$	\(\Q(\zeta_{40})\)	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{40}^{9}q^{2}+\zeta_{40}^{3}q^{4}+(\zeta_{40}^{5}+\zeta_{40}^{10}+\cdots)q^{7}+\cdots\)
900.2.i.a	$900$	$2$	900.i	9.c	$3$	$2$	$1$	$7.187$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
900.2.i.b	$900$	$2$	900.i	9.c	$3$	$2$	$1$	$7.187$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots\)
900.2.i.c	$900$	$2$	900.i	9.c	$3$	$6$	$3$	$7.187$	6.0.954288.1	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\)
900.2.i.d	$900$	$2$	900.i	9.c	$3$	$8$	$4$	$7.187$	8.0.142635249.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{7}+\cdots\)
900.2.i.e	$900$	$2$	900.i	9.c	$3$	$8$	$4$	$7.187$	8.0.142635249.1	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(2\beta _{2}+\beta _{5}-\beta _{6}-\beta _{7})q^{7}+\cdots\)
900.2.i.f	$900$	$2$	900.i	9.c	$3$	$12$	$6$	$7.187$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
900.2.j.a	$900$	$2$	900.j	15.e	$4$	$4$	$2$	$7.187$	\(\Q(\zeta_{8})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
900.2.j.b	$900$	$2$	900.j	15.e	$4$	$8$	$4$	$7.187$	\(\Q(\zeta_{24})\)	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{24}^{3}q^{7}-\zeta_{24}^{5}q^{11}-\zeta_{24}q^{13}+\cdots\)
900.2.k.a	$900$	$2$	900.k	20.e	$4$	$2$	$1$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-5}) \)	None		$4$	$1$	\(-2\)	\(0\)	\(0\)	\(-6\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1+i)q^{2}-2iq^{4}+(-3+3i)q^{7}+\cdots\)
900.2.k.b	$900$	$2$	900.k	20.e	$4$	$2$	$1$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.c	$900$	$2$	900.k	20.e	$4$	$2$	$1$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.d	$900$	$2$	900.k	20.e	$4$	$2$	$1$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots\)
900.2.k.e	$900$	$2$	900.k	20.e	$4$	$2$	$1$	$7.187$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(6\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(1-i)q^{2}-2iq^{4}+(3-3i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
900.2.k.f	$900$	$2$	900.k	20.e	$4$	$8$	$4$	$7.187$	\(\Q(\zeta_{24})\)	$_{}$	None	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
900.2.k.g	$900$	$2$	900.k	20.e	$4$	$8$	$4$	$7.187$	\(\Q(\zeta_{24})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{24}^{4}q^{2}+(-2+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
900.2.k.h	$900$	$2$	900.k	20.e	$4$	$8$	$4$	$7.187$	8.0.157351936.1	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
900.2.k.i	$900$	$2$	900.k	20.e	$4$	$8$	$4$	$7.187$	8.0.3317760000.5	$_{}$	\(\Q(\sqrt{-15}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(\beta _{1}-\beta _{3})q^{8}+\cdots\)
900.2.k.j	$900$	$2$	900.k	20.e	$4$	$8$	$4$	$7.187$	8.0.3317760000.5	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+2\beta _{6}+\cdots)q^{8}+\cdots\)