Newform orbit 6561.2.a.c

• Label: 6561.2.a.c
• Level: $6561$
• Weight: $2$
• Character orbit: 6561.a
• Self dual: yes
• Analytic conductor: $52.390$
• Analytic rank: $1$
• Dimension: $72$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 6561 = 3^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6561.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(52.3898487662\)
Analytic rank:	\(1\)
Dimension:	\(72\)
Twist minimal:	no (minimal twist has level 81)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 9 q^{2} + 63 q^{4} - 18 q^{5} - 27 q^{8}+O(q^{10}) \)

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	−2.76978				0		5.67166			−1.02650				0		1.57628			−10.1697				0		2.84319
1.2	−2.66973				0		5.12748			−2.53528				0		0.510929			−8.34954				0		6.76852
1.3	−2.66924				0		5.12486			1.81561				0		−2.58238			−8.34102				0		−4.84630
1.4	−2.65582				0		5.05340			−2.84817				0		1.91288			−8.10929				0		7.56425
1.5	−2.63231				0		4.92907			1.23074				0		3.78872			−7.71023				0		−3.23969
1.6	−2.49505				0		4.22529			−1.40756				0		−3.19016			−5.55222				0		3.51194
1.7	−2.45262				0		4.01536			−3.99887				0		−1.31658			−4.94293				0		9.80772
1.8	−2.43593				0		3.93374			2.95122				0		2.28987			−4.71046				0		−7.18896
1.9	−2.38302				0		3.67881			1.07976				0		3.12254			−4.00064				0		−2.57310
1.10	−2.36209				0		3.57945			−2.65977				0		4.59390			−3.73079				0		6.28260
1.11	−2.22247				0		2.93935			−2.94555				0		2.95569			−2.08768				0		6.54639
1.12	−2.11576				0		2.47642			3.89294				0		−3.33519			−1.00799				0		−8.23651
1.13	−2.04685				0		2.18960			0.0207958				0		−1.50444			−0.388080				0		−0.0425659
1.14	−2.01939				0		2.07795			−2.76814				0		−0.611277			−0.157420				0		5.58998
1.15	−1.91259				0		1.65799			2.48473				0		−4.55307			0.654119				0		−4.75227
1.16	−1.73329				0		1.00429			1.91493				0		4.47719			1.72585				0		−3.31913
1.17	−1.73145				0		0.997916			−1.37705				0		3.28825			1.73506				0		2.38429
1.18	−1.71009				0		0.924414			1.37341				0		−0.310223			1.83935				0		−2.34865
1.19	−1.55207				0		0.408920			3.09765				0		1.06604			2.46947				0		−4.80776
1.20	−1.50881				0		0.276511			−2.79694				0		−3.90283			2.60042				0		4.22006

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	6561.2.a.c		72
3.b	odd	2	1		6561.2.a.d		72
81.g	even	27	2		81.2.g.a	✓	144
81.g	even	27	2		729.2.g.c		144
81.g	even	27	2		729.2.g.d		144
81.h	odd	54	2		243.2.g.a		144
81.h	odd	54	2		729.2.g.a		144
81.h	odd	54	2		729.2.g.b		144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
81.2.g.a	✓	144	81.g	even	27	2
243.2.g.a		144	81.h	odd	54	2
729.2.g.a		144	81.h	odd	54	2
729.2.g.b		144	81.h	odd	54	2
729.2.g.c		144	81.g	even	27	2
729.2.g.d		144	81.g	even	27	2
6561.2.a.c		72	1.a	even	1	1	trivial
6561.2.a.d		72	3.b	odd	2	1