Newform orbit 255.2.v.a

• Label: 255.2.v.a
• Level: $255$
• Weight: $2$
• Character orbit: 255.v
• Analytic conductor: $2.036$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.03618525154\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 4 q^{3} - 112 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1		−	2.66868i	0.0440451	−	1.73149i	−5.12185			−0.501989	−	2.17899i	−4.62079	−	0.117542i	1.21953	+	2.94420i			8.33122i	−2.99612	−	0.152527i	−5.81503	+	1.33965i
53.2		−	2.58387i	−1.71562	−	0.238013i	−4.67638			−1.29356	+	1.82393i	−0.614995	+	4.43293i	−0.806662	−	1.94745i			6.91540i	2.88670	+	0.816680i	4.71279	+	3.34238i
53.3		−	2.39300i	0.626013	+	1.61496i	−3.72644			−0.890896	+	2.05093i	3.86460	−	1.49805i	1.64966	+	3.98263i			4.13135i	−2.21621	+	2.02198i	4.90786	+	2.13191i
53.4		−	2.24972i	1.73124	+	0.0530263i	−3.06125			−2.19468	−	0.428205i	0.119295	−	3.89481i	−1.07367	−	2.59207i			2.38752i	2.99438	+	0.183603i	−0.963343	+	4.93743i
53.5		−	2.13280i	1.72054	−	0.199374i	−2.54884			2.09025	−	0.794270i	−0.425225	−	3.66957i	0.415126	+	1.00220i			1.17057i	2.92050	−	0.686061i	−1.69402	−	4.45808i
53.6		−	2.06580i	−0.253093	−	1.71346i	−2.26754			1.98657	+	1.02641i	−3.53967	+	0.522841i	−1.22690	−	2.96200i			0.552691i	−2.87189	+	0.867330i	2.12037	−	4.10387i
53.7		−	2.06302i	−1.48115	+	0.897876i	−2.25605			2.23564	+	0.0435725i	1.85234	+	3.05565i	1.34705	+	3.25206i			0.528241i	1.38764	−	2.65979i	0.0898909	−	4.61218i
53.8		−	1.62421i	−1.68259	−	0.410950i	−0.638043			−0.408050	−	2.19852i	−0.667468	+	2.73288i	−0.468443	−	1.13092i		−	2.21210i	2.66224	+	1.38292i	−3.57085	+	0.662757i
53.9		−	1.58848i	−0.568510	+	1.63609i	−0.523272			−2.00518	−	0.989571i	2.59890	+	0.903067i	−0.635580	−	1.53442i		−	2.34575i	−2.35359	−	1.86027i	−1.57191	+	3.18519i
53.10		−	1.32309i	1.13649	−	1.30705i	0.249421			0.0253147	+	2.23592i	−1.72935	−	1.50369i	0.994742	+	2.40152i		−	2.97620i	−0.416773	−	2.97091i	2.95834	−	0.0334937i
53.11		−	1.05079i	0.658378	+	1.60204i	0.895845			1.47528	−	1.68034i	1.68341	−	0.691816i	0.127793	+	0.308520i		−	3.04292i	−2.13308	+	2.10950i	−1.76569	−	1.55020i
53.12		−	0.879564i	1.40081	+	1.01869i	1.22637			0.165442	+	2.22994i	0.896003	−	1.23210i	−1.16872	−	2.82154i		−	2.83780i	0.924540	+	2.85398i	1.96137	−	0.145516i
53.13		−	0.689067i	0.996410	−	1.41675i	1.52519			−1.39707	−	1.74591i	−0.976232	−	0.686593i	0.0928477	+	0.224154i		−	2.42909i	−1.01433	−	2.82332i	−1.20305	+	0.962672i
53.14		−	0.622415i	−1.51280	−	0.843469i	1.61260			1.44235	+	1.70870i	−0.524988	+	0.941589i	0.974787	+	2.35334i		−	2.24854i	1.57712	+	2.55200i	1.06352	−	0.897738i
53.15		−	0.305888i	−1.29107	+	1.15461i	1.90643			−1.85371	+	1.25051i	0.353182	+	0.394924i	0.793243	+	1.91506i		−	1.19493i	0.333748	−	2.98138i	0.382515	+	0.567027i
53.16		−	0.101979i	−0.598391	−	1.62540i	1.98960			−2.03571	+	0.925135i	−0.165756	+	0.0610231i	−1.82059	−	4.39530i		−	0.406854i	−2.28386	+	1.94525i	0.0943440	+	0.207599i
53.17			0.101979i	−1.57246	+	0.726206i	1.98960			2.03571	−	0.925135i	−0.0740575	−	0.160357i	−1.82059	−	4.39530i			0.406854i	1.94525	−	2.28386i	0.0943440	+	0.207599i
53.18			0.305888i	−0.0964945	−	1.72936i	1.90643			1.85371	−	1.25051i	0.528991	−	0.0295165i	0.793243	+	1.91506i			1.19493i	−2.98138	+	0.333748i	0.382515	+	0.567027i
53.19			0.622415i	−1.66613	−	0.473288i	1.61260			−1.44235	−	1.70870i	0.294582	−	1.03703i	0.974787	+	2.35334i			2.24854i	2.55200	+	1.57712i	1.06352	−	0.897738i
53.20			0.689067i	−0.297222	+	1.70636i	1.52519			1.39707	+	1.74591i	−1.17580	−	0.204806i	0.0928477	+	0.224154i			2.42909i	−2.82332	−	1.01433i	−1.20305	+	0.962672i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
85.n	odd	8	1	inner
255.v	even	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	255.2.v.a	✓	128
3.b	odd	2	1	inner	255.2.v.a	✓	128
5.c	odd	4	1		255.2.ba.a	yes	128
15.e	even	4	1		255.2.ba.a	yes	128
17.d	even	8	1		255.2.ba.a	yes	128
51.g	odd	8	1		255.2.ba.a	yes	128
85.n	odd	8	1	inner	255.2.v.a	✓	128
255.v	even	8	1	inner	255.2.v.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
255.2.v.a	✓	128	1.a	even	1	1	trivial
255.2.v.a	✓	128	3.b	odd	2	1	inner
255.2.v.a	✓	128	85.n	odd	8	1	inner
255.2.v.a	✓	128	255.v	even	8	1	inner
255.2.ba.a	yes	128	5.c	odd	4	1
255.2.ba.a	yes	128	15.e	even	4	1
255.2.ba.a	yes	128	17.d	even	8	1
255.2.ba.a	yes	128	51.g	odd	8	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(255, [\chi])\).