Newform orbit 229.4.b.a

• Label: 229.4.b.a
• Level: $229$
• Weight: $4$
• Character orbit: 229.b
• Analytic conductor: $13.511$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	229.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.5114373913\)
Analytic rank:	\(0\)
Dimension:	\(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 6 q^{3} - 206 q^{4} + 6 q^{5} + 462 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
228.1		−	5.46388i	−0.767395			−21.8540			9.08219					4.19296i			9.66785i			75.6968i	−26.4111				−	49.6240i
228.2		−	5.17776i	−1.78248			−18.8092			−21.7027					9.22928i		−	17.5058i			55.9675i	−23.8227					112.372i
228.3		−	5.16709i	−9.25041			−18.6988			−4.82603					47.7977i			0.0486628i			55.2818i	58.5701					24.9365i
228.4		−	5.14688i	5.20947			−18.4904			4.78478				−	26.8125i		−	16.0240i			53.9927i	0.138597				−	24.6267i
228.5		−	4.79643i	9.86972			−15.0058			8.19619				−	47.3395i			28.2308i			33.6027i	70.4114				−	39.3125i
228.6		−	4.73268i	5.64513			−14.3982			−13.6820				−	26.7166i			14.8658i			30.2807i	4.86752					64.7527i
228.7		−	4.64893i	−4.95089			−13.6125			20.5643					23.0163i		−	11.7155i			26.0923i	−2.48869				−	95.6018i
228.8		−	4.63097i	−4.43171			−13.4459			−6.29513					20.5231i			29.7869i			25.2199i	−7.35992					29.1526i
228.9		−	3.98943i	−3.89276			−7.91557			−3.32941					15.5299i		−	25.6939i		−	0.336816i	−11.8464					13.2825i
228.10		−	3.77997i	−8.53572			−6.28816			7.69028					32.2648i			4.03200i		−	6.47070i	45.8585				−	29.0690i
228.11		−	3.76451i	4.79341			−6.17150			3.79670				−	18.0448i		−	26.0415i		−	6.88338i	−4.02323				−	14.2927i
228.12		−	3.57109i	−0.590279			−4.75271			7.37429					2.10794i			27.6331i		−	11.5964i	−26.6516				−	26.3343i
228.13		−	3.38044i	2.76698			−3.42738			16.9885				−	9.35360i			19.8245i		−	15.4575i	−19.3438				−	57.4287i
228.14		−	3.35539i	8.67945			−3.25863			18.2820				−	29.1229i		−	17.3772i		−	15.9091i	48.3329				−	61.3433i
228.15		−	3.34142i	4.04082			−3.16510			−10.7024				−	13.5021i			2.38275i		−	16.1554i	−10.6717					35.7613i
228.16		−	2.72781i	−1.51871			0.559045			−3.51675					4.14275i			1.35077i		−	23.3475i	−24.6935					9.59302i
228.17		−	2.68551i	−6.31309			0.788026			−19.7725					16.9539i			10.9949i		−	23.6003i	12.8551					53.0994i
228.18		−	2.63765i	9.14912			1.04282			−12.5471				−	24.1321i		−	11.1082i		−	23.8518i	56.7063					33.0948i
228.19		−	1.77618i	−9.83382			4.84519			−10.1400					17.4666i		−	35.3633i		−	22.8153i	69.7040					18.0105i
228.20		−	1.66353i	−8.39753			5.23268			8.25562					13.9695i			24.2347i		−	22.0129i	43.5185				−	13.7334i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	229.4.b.a	✓	56
229.b	even	2	1	inner	229.4.b.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
229.4.b.a	✓	56	1.a	even	1	1	trivial
229.4.b.a	✓	56	229.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(229, [\chi])\).