Newform orbit 64.22.b.c

• Label: 64.22.b.c
• Level: $64$
• Weight: $22$
• Character orbit: 64.b
• Analytic conductor: $178.866$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(178.865500344\)
Analytic rank:	\(0\)
Dimension:	\(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 77960422492 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
33.1		0			−	195002.i		0			−	2.28326e6i		0		−1.31077e9				0		−2.75656e10				0
33.2		0			−	195002.i		0				2.28326e6i		0		1.31077e9				0		−2.75656e10				0
33.3		0			−	155316.i		0			−	8.02569e6i		0		−7.41453e8				0		−1.36627e10				0
33.4		0			−	155316.i		0				8.02569e6i		0		7.41453e8				0		−1.36627e10				0
33.5		0			−	114658.i		0			−	1.31189e7i		0		8.14201e8				0		−2.68616e9				0
33.6		0			−	114658.i		0				1.31189e7i		0		−8.14201e8				0		−2.68616e9				0
33.7		0			−	113044.i		0			−	2.14177e7i		0		−5.47923e8				0		−2.31853e9				0
33.8		0			−	113044.i		0				2.14177e7i		0		5.47923e8				0		−2.31853e9				0
33.9		0			−	58474.4i		0			−	3.08952e7i		0		2.12266e7				0		7.04110e9				0
33.10		0			−	58474.4i		0				3.08952e7i		0		−2.12266e7				0		7.04110e9				0
33.11		0			−	34688.1i		0			−	3.82313e7i		0		1.41965e9				0		9.25709e9				0
33.12		0			−	34688.1i		0				3.82313e7i		0		−1.41965e9				0		9.25709e9				0
33.13		0			−	3961.43i		0			−	1.30629e7i		0		−3.86143e8				0		1.04447e10				0
33.14		0			−	3961.43i		0				1.30629e7i		0		3.86143e8				0		1.04447e10				0
33.15		0				3961.43i		0			−	1.30629e7i		0		3.86143e8				0		1.04447e10				0
33.16		0				3961.43i		0				1.30629e7i		0		−3.86143e8				0		1.04447e10				0
33.17		0				34688.1i		0			−	3.82313e7i		0		−1.41965e9				0		9.25709e9				0
33.18		0				34688.1i		0				3.82313e7i		0		1.41965e9				0		9.25709e9				0
33.19		0				58474.4i		0			−	3.08952e7i		0		−2.12266e7				0		7.04110e9				0
33.20		0				58474.4i		0				3.08952e7i		0		2.12266e7				0		7.04110e9				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
8.b	even	2	1	inner
8.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.22.b.c	✓	28
4.b	odd	2	1	inner	64.22.b.c	✓	28
8.b	even	2	1	inner	64.22.b.c	✓	28
8.d	odd	2	1	inner	64.22.b.c	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
64.22.b.c	✓	28	1.a	even	1	1	trivial
64.22.b.c	✓	28	4.b	odd	2	1	inner
64.22.b.c	✓	28	8.b	even	2	1	inner
64.22.b.c	✓	28	8.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^14 + 92712578044*T3^12 + 3109229400855451069008*T3^10 + 47098181124777149329095431527104*T3^8 + 324130035862927105782029451191245313606400*T3^6 + 858224396734659178932504734346526305885601373647872*T3^4 + 647413691104965600203764447809282617679881520362786842570752*T3^2 + 9949710829123207440161500418591316525254801116015745519388489302016