Newform orbit 29.12.b.a

• Label: 29.12.b.a
• Level: $29$
• Weight: $12$
• Character orbit: 29.b
• Analytic conductor: $22.282$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.2819522362\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 27660 q^{4} + 3742 q^{5} + 52944 q^{6} - 2108 q^{7} - 1308680 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
28.1		−	84.3319i			8.59331i	−5063.87			3622.47			724.690			78938.8					254334.i	177073.				−	305489.i
28.2		−	82.1690i			761.903i	−4703.74			−12765.3			62604.7			−19001.5					218219.i	−403349.					1.04891e6i
28.3		−	80.4949i		−	377.032i	−4431.44			−2464.48			−30349.1			−54980.1					191854.i	34994.1					198378.i
28.4		−	73.0722i			488.102i	−3291.55			12371.9			35666.7			−70595.9					90868.8i	−61096.4				−	904045.i
28.5		−	60.8271i		−	630.336i	−1651.93			−6941.15			−38341.5			17859.8				−	24091.6i	−220176.					422210.i
28.6		−	60.2977i			243.553i	−1587.82			−2087.21			14685.7			15478.5				−	27748.0i	117829.					125854.i
28.7		−	55.9489i		−	645.371i	−1082.28			11971.0			−36107.8			20163.8				−	54030.8i	−239357.				−	669765.i
28.8		−	38.5584i			672.640i	561.247			4697.27			25935.9			43643.5				−	100608.i	−275297.				−	181119.i
28.9		−	35.1086i		−	154.592i	815.385			5065.37			−5427.51			−43524.6				−	100529.i	153248.				−	177838.i
28.10		−	35.0679i			131.331i	818.240			−10847.8			4605.51			−26774.6				−	100513.i	159899.					380409.i
28.11		−	15.2043i		−	438.789i	1816.83			−7380.21			−6671.48			69524.4				−	58762.1i	−15388.5					112211.i
28.12		−	11.1097i		−	151.390i	1924.57			8388.09			−1681.90			28101.8				−	44134.2i	154228.				−	93189.4i
28.13		−	1.28689i			643.502i	2046.34			−1758.99			828.119			−59887.8				−	5268.99i	−236948.					2263.63i
28.14			1.28689i		−	643.502i	2046.34			−1758.99			828.119			−59887.8					5268.99i	−236948.				−	2263.63i
28.15			11.1097i			151.390i	1924.57			8388.09			−1681.90			28101.8					44134.2i	154228.					93189.4i
28.16			15.2043i			438.789i	1816.83			−7380.21			−6671.48			69524.4					58762.1i	−15388.5				−	112211.i
28.17			35.0679i		−	131.331i	818.240			−10847.8			4605.51			−26774.6					100513.i	159899.				−	380409.i
28.18			35.1086i			154.592i	815.385			5065.37			−5427.51			−43524.6					100529.i	153248.					177838.i
28.19			38.5584i		−	672.640i	561.247			4697.27			25935.9			43643.5					100608.i	−275297.					181119.i
28.20			55.9489i			645.371i	−1082.28			11971.0			−36107.8			20163.8					54030.8i	−239357.					669765.i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	29.12.b.a	✓	26
29.b	even	2	1	inner	29.12.b.a	✓	26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
29.12.b.a	✓	26	1.a	even	1	1	trivial
29.12.b.a	✓	26	29.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(29, [\chi])\).