Newform orbit 349.2.b.b

• Label: 349.2.b.b
• Level: $349$
• Weight: $2$
• Character orbit: 349.b
• Analytic conductor: $2.787$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.78677903054\)
Analytic rank:	\(0\)
Dimension:	\(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
348.1		−	2.74676i	−1.22099			−5.54469			1.97385					3.35376i			4.26150i			9.73641i	−1.50918				−	5.42170i
348.2		−	2.61918i	−2.83744			−4.86011			−3.82575					7.43177i		−	2.86678i			7.49115i	5.05107					10.0203i
348.3		−	2.51815i	2.41625			−4.34106			2.06598				−	6.08448i		−	1.34000i			5.89514i	2.83827				−	5.20243i
348.4		−	2.26080i	0.674297			−3.11122			−0.0827003				−	1.52445i		−	1.39223i			2.51226i	−2.54532					0.186969i
348.5		−	2.07129i	−0.0823577			−2.29025			−3.08948					0.170587i			3.12974i			0.601197i	−2.99322					6.39921i
348.6		−	1.88002i	−2.43904			−1.53447			2.91531					4.58543i		−	0.518323i		−	0.875209i	2.94890				−	5.48083i
348.7		−	1.82942i	3.30797			−1.34678			−0.842567				−	6.05168i			2.41293i		−	1.19501i	7.94269					1.54141i
348.8		−	1.36584i	2.13942			0.134484			−3.98594				−	2.92210i		−	4.87861i		−	2.91536i	1.57710					5.44415i
348.9		−	1.25654i	0.849271			0.421101			3.08880				−	1.06714i		−	1.10667i		−	3.04222i	−2.27874				−	3.88121i
348.10		−	1.19339i	−2.66615			0.575830			−1.00436					3.18175i			3.16046i		−	3.07396i	4.10838					1.19859i
348.11		−	0.980996i	−2.39151			1.03765			−1.59459					2.34607i		−	3.49225i		−	2.97992i	2.71933					1.56429i
348.12		−	0.788732i	−0.670838			1.37790			−1.84585					0.529112i		−	0.0300147i		−	2.66426i	−2.54998					1.45588i
348.13		−	0.719982i	1.92112			1.48163			0.227297				−	1.38317i			2.96485i		−	2.50671i	0.690697				−	0.163649i
348.14			0.719982i	1.92112			1.48163			0.227297					1.38317i		−	2.96485i			2.50671i	0.690697					0.163649i
348.15			0.788732i	−0.670838			1.37790			−1.84585				−	0.529112i			0.0300147i			2.66426i	−2.54998				−	1.45588i
348.16			0.980996i	−2.39151			1.03765			−1.59459				−	2.34607i			3.49225i			2.97992i	2.71933				−	1.56429i
348.17			1.19339i	−2.66615			0.575830			−1.00436				−	3.18175i		−	3.16046i			3.07396i	4.10838				−	1.19859i
348.18			1.25654i	0.849271			0.421101			3.08880					1.06714i			1.10667i			3.04222i	−2.27874					3.88121i
348.19			1.36584i	2.13942			0.134484			−3.98594					2.92210i			4.87861i			2.91536i	1.57710				−	5.44415i
348.20			1.82942i	3.30797			−1.34678			−0.842567					6.05168i		−	2.41293i			1.19501i	7.94269				−	1.54141i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	349.2.b.b	✓	26
349.b	even	2	1	inner	349.2.b.b	✓	26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
349.2.b.b	✓	26	1.a	even	1	1	trivial
349.2.b.b	✓	26	349.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^26 + 44*T2^24 + 857*T2^22 + 9752*T2^20 + 72085*T2^18 + 364188*T2^16 + 1288987*T2^14 + 3223971*T2^12 + 5678175*T2^10 + 6932570*T2^8 + 5686545*T2^6 + 2960112*T2^4 + 874838*T2^2 + 110827