Newform orbit 201.5.b.a

• Label: 201.5.b.a
• Level: $201$
• Weight: $5$
• Character orbit: 201.b
• Analytic conductor: $20.777$
• Analytic rank: $0$
• Dimension: $46$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.7773625799\)
Analytic rank:	\(0\)
Dimension:	\(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \)

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		−	7.92273i			5.19615i	−46.7696				−	21.6231i	41.1677					44.7619i			243.779i	−27.0000			−171.314
133.2		−	7.58193i			5.19615i	−41.4857					47.0403i	39.3969				−	16.7186i			193.231i	−27.0000			356.657
133.3		−	7.56976i		−	5.19615i	−41.3013					14.1982i	−39.3336				−	91.6507i			191.525i	−27.0000			107.477
133.4		−	7.50857i		−	5.19615i	−40.3787					11.1565i	−39.0157					57.6520i			183.049i	−27.0000			83.7695
133.5		−	6.42716i			5.19615i	−25.3083				−	17.3951i	33.3965				−	16.4564i			59.8260i	−27.0000			−111.801
133.6		−	6.38763i		−	5.19615i	−24.8019				−	26.0927i	−33.1911				−	27.5510i			56.2231i	−27.0000			−166.670
133.7		−	5.76041i			5.19615i	−17.1823				−	16.3188i	29.9320					86.3035i			6.81074i	−27.0000			−94.0028
133.8		−	5.58118i			5.19615i	−15.1496					19.0393i	29.0007				−	39.7168i		−	4.74646i	−27.0000			106.262
133.9		−	5.56808i		−	5.19615i	−15.0035				−	37.5105i	−28.9326					91.3831i		−	5.54876i	−27.0000			−208.861
133.10		−	5.06350i		−	5.19615i	−9.63908					45.6253i	−26.3107				−	49.9699i		−	32.2086i	−27.0000			231.024
133.11		−	5.02761i			5.19615i	−9.27688					18.9854i	26.1242					67.2401i		−	33.8013i	−27.0000			95.4513
133.12		−	4.92431i		−	5.19615i	−8.24886					24.9820i	−25.5875					17.9795i		−	38.1691i	−27.0000			123.019
133.13		−	4.05388i		−	5.19615i	−0.433982					2.19375i	−21.0646					19.8533i		−	63.1028i	−27.0000			8.89321
133.14		−	4.01365i			5.19615i	−0.109374				−	45.0940i	20.8555				−	18.6226i		−	63.7794i	−27.0000			−180.991
133.15		−	3.88997i		−	5.19615i	0.868144				−	32.6108i	−20.2129				−	59.7846i		−	65.6166i	−27.0000			−126.855
133.16		−	3.33762i			5.19615i	4.86032					44.8464i	17.3428					17.0019i		−	69.6237i	−27.0000			149.680
133.17		−	2.53609i			5.19615i	9.56827				−	8.16007i	13.1779				−	69.7059i		−	64.8433i	−27.0000			−20.6946
133.18		−	2.40473i		−	5.19615i	10.2173					10.5361i	−12.4953					65.1996i		−	63.0455i	−27.0000			25.3364
133.19		−	2.12514i			5.19615i	11.4838					15.4974i	11.0426				−	14.1489i		−	58.4069i	−27.0000			32.9341
133.20		−	1.39569i		−	5.19615i	14.0521				−	17.8182i	−7.25221				−	70.8079i		−	41.9433i	−27.0000			−24.8687

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	201.5.b.a	✓	46
67.b	odd	2	1	inner	201.5.b.a	✓	46

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
201.5.b.a	✓	46	1.a	even	1	1	trivial
201.5.b.a	✓	46	67.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(201, [\chi])\).