Newform orbit 64.20.b.c

• Label: 64.20.b.c
• Level: $64$
• Weight: $20$
• Character orbit: 64.b
• Analytic conductor: $146.443$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(146.442685796\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 13668159064 q^{9}+O(q^{10}) \)

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			−	62198.5i		0			−	6.90970e6i		0		−9.56573e7				0		−2.70640e9				0
33.2		0			−	62198.5i		0				6.90970e6i		0		9.56573e7				0		−2.70640e9				0
33.3		0			−	57731.9i		0			−	1.12559e6i		0		1.42740e8				0		−2.17071e9				0
33.4		0			−	57731.9i		0				1.12559e6i		0		−1.42740e8				0		−2.17071e9				0
33.5		0			−	39259.7i		0			−	4.68412e6i		0		3.30020e7				0		−3.79061e8				0
33.6		0			−	39259.7i		0				4.68412e6i		0		−3.30020e7				0		−3.79061e8				0
33.7		0			−	29668.1i		0			−	8.36506e6i		0		−1.53202e8				0		2.82068e8				0
33.8		0			−	29668.1i		0				8.36506e6i		0		1.53202e8				0		2.82068e8				0
33.9		0			−	23881.9i		0			−	4.57246e6i		0		9.35150e7				0		5.91914e8				0
33.10		0			−	23881.9i		0				4.57246e6i		0		−9.35150e7				0		5.91914e8				0
33.11		0			−	14039.7i		0			−	498596.i		0		1.14336e8				0		9.65148e8				0
33.12		0			−	14039.7i		0				498596.i		0		−1.14336e8				0		9.65148e8				0
33.13		0				14039.7i		0			−	498596.i		0		−1.14336e8				0		9.65148e8				0
33.14		0				14039.7i		0				498596.i		0		1.14336e8				0		9.65148e8				0
33.15		0				23881.9i		0			−	4.57246e6i		0		−9.35150e7				0		5.91914e8				0
33.16		0				23881.9i		0				4.57246e6i		0		9.35150e7				0		5.91914e8				0
33.17		0				29668.1i		0			−	8.36506e6i		0		1.53202e8				0		2.82068e8				0
33.18		0				29668.1i		0				8.36506e6i		0		−1.53202e8				0		2.82068e8				0
33.19		0				39259.7i		0			−	4.68412e6i		0		−3.30020e7				0		−3.79061e8				0
33.20		0				39259.7i		0				4.68412e6i		0		3.30020e7				0		−3.79061e8				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	64.20.b.c	✓	24
4.b	odd	2	1	inner	64.20.b.c	✓	24
8.b	even	2	1	inner	64.20.b.c	✓	24
8.d	odd	2	1	inner	64.20.b.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
64.20.b.c	✓	24	1.a	even	1	1	trivial
64.20.b.c	✓	24	4.b	odd	2	1	inner
64.20.b.c	✓	24	8.b	even	2	1	inner
64.20.b.c	✓	24	8.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^12 + 10390608568*T3^10 + 39187474798595866992*T3^8 + 66395968774816233098318637312*T3^6 + 52516554380310988409666259763568385792*T3^4 + 18033789868076166514302566836722494606075836416*T3^2 + 1966612654666463963960524061421171756609880796471660544