Newform orbit 220.2.u.a

• Label: 220.2.u.a
• Level: $220$
• Weight: $2$
• Character orbit: 220.u
• Analytic conductor: $1.757$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.75670884447\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(6\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−2.95041	−	0.467300i		0		1.40317	+	1.74101i		0		−0.372695	−	2.35311i		0		5.63340	+	1.83040i		0
13.2		0		−0.834729	−	0.132208i		0		−2.08639	−	0.804354i		0		−0.228981	−	1.44573i		0		−2.17388	−	0.706335i		0
13.3		0		−0.464116	−	0.0735087i		0		−0.794013	+	2.09035i		0		0.413999	+	2.61389i		0		−2.64317	−	0.858818i		0
13.4		0		0.194131	+	0.0307474i		0		1.80035	−	1.32618i		0		−0.509098	−	3.21432i		0		−2.81643	−	0.915113i		0
13.5		0		2.50020	+	0.395993i		0		−0.797801	−	2.08890i		0		0.371734	+	2.34703i		0		3.24104	+	1.05308i		0
13.6		0		2.95172	+	0.467507i		0		0.0236267	+	2.23594i		0		−0.776647	−	4.90356i		0		5.64095	+	1.83285i		0
17.1		0		−2.95041	+	0.467300i		0		1.40317	−	1.74101i		0		−0.372695	+	2.35311i		0		5.63340	−	1.83040i		0
17.2		0		−0.834729	+	0.132208i		0		−2.08639	+	0.804354i		0		−0.228981	+	1.44573i		0		−2.17388	+	0.706335i		0
17.3		0		−0.464116	+	0.0735087i		0		−0.794013	−	2.09035i		0		0.413999	−	2.61389i		0		−2.64317	+	0.858818i		0
17.4		0		0.194131	−	0.0307474i		0		1.80035	+	1.32618i		0		−0.509098	+	3.21432i		0		−2.81643	+	0.915113i		0
17.5		0		2.50020	−	0.395993i		0		−0.797801	+	2.08890i		0		0.371734	−	2.34703i		0		3.24104	−	1.05308i		0
17.6		0		2.95172	−	0.467507i		0		0.0236267	−	2.23594i		0		−0.776647	+	4.90356i		0		5.64095	−	1.83285i		0
57.1		0		−0.467300	+	2.95041i		0		−0.111852	+	2.23327i		0		2.35311	−	0.372695i		0		−5.63340	−	1.83040i		0
57.2		0		−0.132208	+	0.834729i		0		1.21514	−	1.87708i		0		1.44573	−	0.228981i		0		2.17388	+	0.706335i		0
57.3		0		−0.0735087	+	0.464116i		0		1.87104	+	1.22442i		0		−2.61389	+	0.413999i		0		2.64317	+	0.858818i		0
57.4		0		0.0307474	−	0.194131i		0		−2.23602	−	0.0146855i		0		3.21432	−	0.509098i		0		2.81643	+	0.915113i		0
57.5		0		0.395993	−	2.50020i		0		−0.582392	−	2.15889i		0		−2.34703	+	0.371734i		0		−3.24104	−	1.05308i		0
57.6		0		0.467507	−	2.95172i		0		1.29514	+	1.82280i		0		4.90356	−	0.776647i		0		−5.64095	−	1.83285i		0
73.1		0		−2.69137	+	1.37132i		0		−0.0704176	−	2.23496i		0		−0.328865	+	0.645435i		0		3.59960	−	4.95443i		0
73.2		0		−1.23629	+	0.629920i		0		−2.10058	+	0.766533i		0		0.729926	−	1.43256i		0		−0.631750	+	0.869529i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.d	odd	10	1	inner
55.l	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.2.u.a	✓	48
4.b	odd	2	1		880.2.cm.b		48
5.c	odd	4	1	inner	220.2.u.a	✓	48
11.d	odd	10	1	inner	220.2.u.a	✓	48
20.e	even	4	1		880.2.cm.b		48
44.g	even	10	1		880.2.cm.b		48
55.l	even	20	1	inner	220.2.u.a	✓	48
220.w	odd	20	1		880.2.cm.b		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.2.u.a	✓	48	1.a	even	1	1	trivial
220.2.u.a	✓	48	5.c	odd	4	1	inner
220.2.u.a	✓	48	11.d	odd	10	1	inner
220.2.u.a	✓	48	55.l	even	20	1	inner
880.2.cm.b		48	4.b	odd	2	1
880.2.cm.b		48	20.e	even	4	1
880.2.cm.b		48	44.g	even	10	1
880.2.cm.b		48	220.w	odd	20	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(220, [\chi])\).