Newform orbit 201.3.b.a

• Label: 201.3.b.a
• Level: $201$
• Weight: $3$
• Character orbit: 201.b
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
133.1		−	3.81177i		−	1.73205i	−10.5296				−	6.86815i	−6.60217					3.56836i			24.8892i	−3.00000			−26.1798
133.2		−	3.60849i			1.73205i	−9.02122					2.97147i	6.25009					2.36023i			18.1190i	−3.00000			10.7225
133.3		−	3.21711i		−	1.73205i	−6.34981					8.83855i	−5.57220					10.0054i			7.55961i	−3.00000			28.4346
133.4		−	3.12361i			1.73205i	−5.75692				−	8.39184i	5.41025					3.67092i			5.48792i	−3.00000			−26.2128
133.5		−	2.88392i			1.73205i	−4.31697					1.18875i	4.99509				−	3.84699i			0.914116i	−3.00000			3.42825
133.6		−	2.74898i		−	1.73205i	−3.55688				−	0.569953i	−4.76137				−	7.88425i		−	1.21813i	−3.00000			−1.56679
133.7		−	1.70381i		−	1.73205i	1.09704					1.67394i	−2.95108					0.231323i		−	8.68437i	−3.00000			2.85207
133.8		−	1.30530i			1.73205i	2.29618					2.19844i	2.26085					9.13473i		−	8.21843i	−3.00000			2.86963
133.9		−	0.952997i			1.73205i	3.09180				−	5.09554i	1.65064				−	5.68326i		−	6.75846i	−3.00000			−4.85603
133.10		−	0.858352i		−	1.73205i	3.26323				−	8.02842i	−1.48671					1.82241i		−	6.23441i	−3.00000			−6.89121
133.11		−	0.465702i			1.73205i	3.78312				−	1.28941i	0.806619				−	11.7488i		−	3.62461i	−3.00000			−0.600481
133.12			0.465702i		−	1.73205i	3.78312					1.28941i	0.806619					11.7488i			3.62461i	−3.00000			−0.600481
133.13			0.858352i			1.73205i	3.26323					8.02842i	−1.48671				−	1.82241i			6.23441i	−3.00000			−6.89121
133.14			0.952997i		−	1.73205i	3.09180					5.09554i	1.65064					5.68326i			6.75846i	−3.00000			−4.85603
133.15			1.30530i		−	1.73205i	2.29618				−	2.19844i	2.26085				−	9.13473i			8.21843i	−3.00000			2.86963
133.16			1.70381i			1.73205i	1.09704				−	1.67394i	−2.95108				−	0.231323i			8.68437i	−3.00000			2.85207
133.17			2.74898i			1.73205i	−3.55688					0.569953i	−4.76137					7.88425i			1.21813i	−3.00000			−1.56679
133.18			2.88392i		−	1.73205i	−4.31697				−	1.18875i	4.99509					3.84699i		−	0.914116i	−3.00000			3.42825
133.19			3.12361i		−	1.73205i	−5.75692					8.39184i	5.41025				−	3.67092i		−	5.48792i	−3.00000			−26.2128
133.20			3.21711i			1.73205i	−6.34981				−	8.83855i	−5.57220				−	10.0054i		−	7.55961i	−3.00000			28.4346

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
67.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	201.3.b.a	✓	22
3.b	odd	2	1		603.3.b.e		22
67.b	odd	2	1	inner	201.3.b.a	✓	22
201.d	even	2	1		603.3.b.e		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
201.3.b.a	✓	22	1.a	even	1	1	trivial
201.3.b.a	✓	22	67.b	odd	2	1	inner
603.3.b.e		22	3.b	odd	2	1
603.3.b.e		22	201.d	even	2	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(201, [\chi])\).