Newform orbit 255.2.m.a

• Label: 255.2.m.a
• Level: $255$
• Weight: $2$
• Character orbit: 255.m
• Analytic conductor: $2.036$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.03618525154\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 4 q^{3} - 8 q^{6} - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
137.1	−1.92802	+	1.92802i	0.620496	+	1.61709i		−	5.43454i	−2.09122	−	0.791697i	−4.31412	−	1.92146i	−1.38844	−	1.38844i	6.62187	+	6.62187i	−2.22997	+	2.00680i	5.55834	−	2.50552i
137.2	−1.91907	+	1.91907i	−1.73203	−	0.00903094i		−	5.36567i	0.460548	+	2.18813i	3.34122	−	3.30655i	2.45503	+	2.45503i	6.45896	+	6.45896i	2.99984	+	0.0312837i	−5.08299	−	3.31535i
137.3	−1.64304	+	1.64304i	−1.29999	−	1.14456i		−	3.39914i	−0.666111	−	2.13455i	4.01649	−	0.255387i	−1.51894	−	1.51894i	2.29883	+	2.29883i	0.379971	+	2.97584i	4.60158	+	2.41269i
137.4	−1.62297	+	1.62297i	0.340584	−	1.69824i		−	3.26804i	2.22383	+	0.233627i	2.20342	+	3.30893i	−0.496396	−	0.496396i	2.05798	+	2.05798i	−2.76800	−	1.15678i	−3.98837	+	3.23003i
137.5	−1.56424	+	1.56424i	1.66061	+	0.492318i		−	2.89372i	2.10656	−	0.749937i	−3.36770	+	1.82749i	−0.754731	−	0.754731i	1.39799	+	1.39799i	2.51525	+	1.63510i	−2.12209	+	4.46826i
137.6	−1.41066	+	1.41066i	1.72464	+	0.160092i		−	1.97994i	−0.901847	+	2.04614i	−2.65872	+	2.20704i	1.81779	+	1.81779i	−0.0283011	−	0.0283011i	2.94874	+	0.552201i	−1.61421	−	4.15861i
137.7	−1.36770	+	1.36770i	−0.609960	+	1.62110i		−	1.74121i	0.970496	+	2.01448i	−1.38293	−	3.05142i	−3.11925	−	3.11925i	−0.353944	−	0.353944i	−2.25590	−	1.97761i	−4.08256	−	1.42786i
137.8	−1.30658	+	1.30658i	−1.38638	+	1.03825i		−	1.41430i	0.496081	−	2.18034i	0.454865	−	3.16796i	0.769128	+	0.769128i	−0.765265	−	0.765265i	0.844095	−	2.87880i	2.20062	+	3.49696i
137.9	−0.947040	+	0.947040i	1.40929	−	1.00693i			0.206232i	−2.07417	−	0.835346i	−0.381046	+	2.28825i	−3.23576	−	3.23576i	−2.08939	−	2.08939i	0.972177	−	2.83811i	2.75543	−	1.17322i
137.10	−0.834224	+	0.834224i	0.979166	+	1.42872i			0.608142i	−1.43468	−	1.71514i	−2.00871	−	0.375026i	1.74492	+	1.74492i	−2.17577	−	2.17577i	−1.08247	+	2.79790i	2.62765	+	0.233969i
137.11	−0.794483	+	0.794483i	−1.72047	−	0.199994i			0.737594i	−1.91199	+	1.15944i	1.52577	−	1.20799i	−0.690095	−	0.690095i	−2.17497	−	2.17497i	2.92001	+	0.688164i	0.597888	−	2.44020i
137.12	−0.645382	+	0.645382i	−0.450786	−	1.67236i			1.16696i	0.567951	+	2.16274i	1.37024	+	0.788383i	0.106056	+	0.106056i	−2.04390	−	2.04390i	−2.59358	+	1.50775i	−1.76234	−	1.02925i
137.13	−0.577658	+	0.577658i	0.236036	+	1.71589i			1.33262i	1.64025	+	1.51973i	−1.12755	−	0.854851i	2.55494	+	2.55494i	−1.92512	−	1.92512i	−2.88857	+	0.810025i	−1.82539	+	0.0696208i
137.14	−0.493663	+	0.493663i	1.21296	−	1.23642i			1.51259i	1.10384	−	1.94462i	0.0115804	+	1.20917i	2.08821	+	2.08821i	−1.73404	−	1.73404i	−0.0574579	−	2.99945i	0.415060	+	1.50491i
137.15	−0.173770	+	0.173770i	−1.61487	+	0.626250i			1.93961i	2.20473	−	0.373036i	0.171793	−	0.389440i	0.191216	+	0.191216i	−0.684587	−	0.684587i	2.21562	−	2.02263i	−0.318294	+	0.447939i
137.16	−0.0600202	+	0.0600202i	−1.02979	−	1.39267i			1.99280i	1.21580	−	1.87665i	0.145397	+	0.0217804i	−2.52368	−	2.52368i	−0.239649	−	0.239649i	−0.879072	+	2.86832i	0.0396642	+	0.185610i
137.17	0.0600202	−	0.0600202i	1.39267	+	1.02979i			1.99280i	−1.21580	+	1.87665i	0.145397	−	0.0217804i	−2.52368	−	2.52368i	0.239649	+	0.239649i	0.879072	+	2.86832i	0.0396642	+	0.185610i
137.18	0.173770	−	0.173770i	−0.626250	+	1.61487i			1.93961i	−2.20473	+	0.373036i	0.171793	+	0.389440i	0.191216	+	0.191216i	0.684587	+	0.684587i	−2.21562	−	2.02263i	−0.318294	+	0.447939i
137.19	0.493663	−	0.493663i	1.23642	−	1.21296i			1.51259i	−1.10384	+	1.94462i	0.0115804	−	1.20917i	2.08821	+	2.08821i	1.73404	+	1.73404i	0.0574579	−	2.99945i	0.415060	+	1.50491i
137.20	0.577658	−	0.577658i	−1.71589	−	0.236036i			1.33262i	−1.64025	−	1.51973i	−1.12755	+	0.854851i	2.55494	+	2.55494i	1.92512	+	1.92512i	2.88857	+	0.810025i	−1.82539	+	0.0696208i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	255.2.m.a	✓	64
3.b	odd	2	1	inner	255.2.m.a	✓	64
5.c	odd	4	1	inner	255.2.m.a	✓	64
15.e	even	4	1	inner	255.2.m.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
255.2.m.a	✓	64	1.a	even	1	1	trivial
255.2.m.a	✓	64	3.b	odd	2	1	inner
255.2.m.a	✓	64	5.c	odd	4	1	inner
255.2.m.a	✓	64	15.e	even	4	1	inner

Hecke kernels

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