Newform orbit 2169.4.a.g

• Label: 2169.4.a.g
• Level: $2169$
• Weight: $4$
• Character orbit: 2169.a
• Self dual: yes
• Analytic conductor: $127.975$
• Analytic rank: $1$
• Dimension: $54$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2169 = 3^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2169.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(127.975142802\)
Analytic rank:	\(1\)
Dimension:	\(54\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 54 q + 178 q^{4} - 136 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−5.41813				0		21.3561			−1.32658				0		−14.2126			−72.3649				0		7.18760
1.2	−4.96015				0		16.6031			3.35893				0		0.793391			−42.6729				0		−16.6608
1.3	−4.95858				0		16.5875			4.17662				0		−23.9163			−42.5816				0		−20.7101
1.4	−4.92018				0		16.2081			16.1480				0		14.7804			−40.3855				0		−79.4511
1.5	−4.80059				0		15.0456			10.8244				0		30.3286			−33.8231				0		−51.9636
1.6	−4.64746				0		13.5988			−2.39979				0		−33.6848			−26.0204				0		11.1529
1.7	−4.61710				0		13.3176			−9.80608				0		−11.0540			−24.5519				0		45.2757
1.8	−4.32652				0		10.7188			−19.7880				0		−10.4546			−11.7628				0		85.6131
1.9	−3.91799				0		7.35067			−4.06386				0		11.7668			2.54407				0		15.9222
1.10	−3.90943				0		7.28361			−6.65495				0		14.3626			2.80066				0		26.0170
1.11	−3.77889				0		6.28000			13.6838				0		9.15553			6.49968				0		−51.7095
1.12	−3.76038				0		6.14043			15.4973				0		−12.8722			6.99267				0		−58.2755
1.13	−3.54158				0		4.54277			−7.67299				0		13.2868			12.2440				0		27.1745
1.14	−3.05067				0		1.30657			−16.5713				0		−32.4650			20.4194				0		50.5535
1.15	−2.85104				0		0.128423			−14.1962				0		−8.24089			22.4422				0		40.4739
1.16	−2.41550				0		−2.16535			4.88645				0		−1.23707			24.5544				0		−11.8032
1.17	−2.10748				0		−3.55852			5.92868				0		−1.92133			24.3594				0		−12.4946
1.18	−1.87593				0		−4.48088			−12.0455				0		−13.2868			23.4133				0		22.5966
1.19	−1.75462				0		−4.92130			−10.7961				0		19.9534			22.6720				0		18.9431
1.20	−1.73135				0		−5.00244			−5.71211				0		19.5729			22.5117				0		9.88963

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(1\)
\(241\)	\(-1\)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2169.4.a.g	✓	54
3.b	odd	2	1	inner	2169.4.a.g	✓	54

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2169.4.a.g	✓	54	1.a	even	1	1	trivial
2169.4.a.g	✓	54	3.b	odd	2	1	inner