Newform orbit 255.2.be.a

• Label: 255.2.be.a
• Level: $255$
• Weight: $2$
• Character orbit: 255.be
• Analytic conductor: $2.036$
• Analytic rank: $0$
• Dimension: $32$
• CM discriminant: -15
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.be (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.03618525154\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(4\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−1.97249	+	0.817031i	0.337906	−	1.69877i	1.80895	−	1.80895i	−1.85922	+	1.24229i	0.721432	+	3.62688i		0		−0.456105	+	1.10114i	−2.77164	−	1.14805i	2.65230	−	3.96945i
14.2	−1.16643	+	0.483151i	0.337906	−	1.69877i	−0.287090	+	0.287090i	1.85922	−	1.24229i	0.426618	+	2.14476i		0		1.16246	−	2.80644i	−2.77164	−	1.14805i	−1.56844	+	2.34733i
14.3	1.16643	−	0.483151i	−0.337906	+	1.69877i	−0.287090	+	0.287090i	−1.85922	+	1.24229i	0.426618	+	2.14476i		0		−1.16246	+	2.80644i	−2.77164	−	1.14805i	−1.56844	+	2.34733i
14.4	1.97249	−	0.817031i	−0.337906	+	1.69877i	1.80895	−	1.80895i	1.85922	−	1.24229i	0.721432	+	3.62688i		0		0.456105	−	1.10114i	−2.77164	−	1.14805i	2.65230	−	3.96945i
29.1	−1.07974	−	2.60672i	−1.44015	+	0.962276i	−4.21496	+	4.21496i	−2.19310	−	0.436235i	4.06337	+	2.71506i		0		10.3249	+	4.27669i	1.14805	−	2.77164i	1.23084	+	6.18784i
29.2	−0.343247	−	0.828671i	1.44015	−	0.962276i	0.845337	−	0.845337i	−2.19310	−	0.436235i	−1.29174	−	0.863110i		0		−2.64801	−	1.09684i	1.14805	−	2.77164i	0.391280	+	1.96710i
29.3	0.343247	+	0.828671i	−1.44015	+	0.962276i	0.845337	−	0.845337i	2.19310	+	0.436235i	−1.29174	−	0.863110i		0		2.64801	+	1.09684i	1.14805	−	2.77164i	0.391280	+	1.96710i
29.4	1.07974	+	2.60672i	1.44015	−	0.962276i	−4.21496	+	4.21496i	2.19310	+	0.436235i	4.06337	+	2.71506i		0		−10.3249	−	4.27669i	1.14805	−	2.77164i	1.23084	+	6.18784i
44.1	−1.07974	+	2.60672i	−1.44015	−	0.962276i	−4.21496	−	4.21496i	−2.19310	+	0.436235i	4.06337	−	2.71506i		0		10.3249	−	4.27669i	1.14805	+	2.77164i	1.23084	−	6.18784i
44.2	−0.343247	+	0.828671i	1.44015	+	0.962276i	0.845337	+	0.845337i	−2.19310	+	0.436235i	−1.29174	+	0.863110i		0		−2.64801	+	1.09684i	1.14805	+	2.77164i	0.391280	−	1.96710i
44.3	0.343247	−	0.828671i	−1.44015	−	0.962276i	0.845337	+	0.845337i	2.19310	−	0.436235i	−1.29174	+	0.863110i		0		2.64801	−	1.09684i	1.14805	+	2.77164i	0.391280	−	1.96710i
44.4	1.07974	−	2.60672i	1.44015	+	0.962276i	−4.21496	−	4.21496i	2.19310	−	0.436235i	4.06337	−	2.71506i		0		−10.3249	+	4.27669i	1.14805	+	2.77164i	1.23084	−	6.18784i
74.1	−2.33835	−	0.968575i	1.69877	−	0.337906i	3.11552	+	3.11552i	1.24229	−	1.85922i	−4.29960	−	0.855244i		0		−2.33040	−	5.62608i	2.77164	−	1.14805i	−4.70571	+	3.14425i
74.2	−1.71398	−	0.709953i	−1.69877	+	0.337906i	1.01947	+	1.01947i	1.24229	−	1.85922i	3.15155	+	0.626883i		0		0.396329	+	0.956823i	2.77164	−	1.14805i	−3.44922	+	2.30470i
74.3	1.71398	+	0.709953i	1.69877	−	0.337906i	1.01947	+	1.01947i	−1.24229	+	1.85922i	3.15155	+	0.626883i		0		−0.396329	−	0.956823i	2.77164	−	1.14805i	−3.44922	+	2.30470i
74.4	2.33835	+	0.968575i	−1.69877	+	0.337906i	3.11552	+	3.11552i	−1.24229	+	1.85922i	−4.29960	−	0.855244i		0		2.33040	+	5.62608i	2.77164	−	1.14805i	−4.70571	+	3.14425i
164.1	−1.97249	−	0.817031i	0.337906	+	1.69877i	1.80895	+	1.80895i	−1.85922	−	1.24229i	0.721432	−	3.62688i		0		−0.456105	−	1.10114i	−2.77164	+	1.14805i	2.65230	+	3.96945i
164.2	−1.16643	−	0.483151i	0.337906	+	1.69877i	−0.287090	−	0.287090i	1.85922	+	1.24229i	0.426618	−	2.14476i		0		1.16246	+	2.80644i	−2.77164	+	1.14805i	−1.56844	−	2.34733i
164.3	1.16643	+	0.483151i	−0.337906	−	1.69877i	−0.287090	−	0.287090i	−1.85922	−	1.24229i	0.426618	−	2.14476i		0		−1.16246	−	2.80644i	−2.77164	+	1.14805i	−1.56844	−	2.34733i
164.4	1.97249	+	0.817031i	−0.337906	−	1.69877i	1.80895	+	1.80895i	1.85922	+	1.24229i	0.721432	−	3.62688i		0		0.456105	+	1.10114i	−2.77164	+	1.14805i	2.65230	+	3.96945i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.d	odd	2	1	CM by \(\Q(\sqrt{-15}) \)
3.b	odd	2	1	inner
5.b	even	2	1	inner
17.e	odd	16	1	inner
51.i	even	16	1	inner
85.p	odd	16	1	inner
255.be	even	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	255.2.be.a	✓	32
3.b	odd	2	1	inner	255.2.be.a	✓	32
5.b	even	2	1	inner	255.2.be.a	✓	32
15.d	odd	2	1	CM	255.2.be.a	✓	32
17.e	odd	16	1	inner	255.2.be.a	✓	32
51.i	even	16	1	inner	255.2.be.a	✓	32
85.p	odd	16	1	inner	255.2.be.a	✓	32
255.be	even	16	1	inner	255.2.be.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
255.2.be.a	✓	32	1.a	even	1	1	trivial
255.2.be.a	✓	32	3.b	odd	2	1	inner
255.2.be.a	✓	32	5.b	even	2	1	inner
255.2.be.a	✓	32	15.d	odd	2	1	CM
255.2.be.a	✓	32	17.e	odd	16	1	inner
255.2.be.a	✓	32	51.i	even	16	1	inner
255.2.be.a	✓	32	85.p	odd	16	1	inner
255.2.be.a	✓	32	255.be	even	16	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 224*T2^26 + 4480*T2^24 - 10752*T2^22 + 25088*T2^20 - 491232*T2^18 + 5853762*T2^16 - 24736768*T2^14 + 55444480*T2^12 - 38757600*T2^10 + 269696*T2^8 + 16583168*T2^6 + 55419392*T2^4 + 3042592*T2^2 + 83521