Newform orbit 64.24.b.c

• Label: 64.24.b.c
• Level: $64$
• Weight: $24$
• Character orbit: 64.b
• Analytic conductor: $214.531$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(214.530583901\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 1144353691936 q^{9}+O(q^{10}) \)

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			−	550122.i		0			−	1.00236e8i		0		6.02328e8				0		−2.08491e11				0
33.2		0			−	550122.i		0				1.00236e8i		0		−6.02328e8				0		−2.08491e11				0
33.3		0			−	469167.i		0			−	1.85888e8i		0		3.36313e9				0		−1.25975e11				0
33.4		0			−	469167.i		0				1.85888e8i		0		−3.36313e9				0		−1.25975e11				0
33.5		0			−	400474.i		0			−	1.25309e8i		0		−5.19169e9				0		−6.62363e10				0
33.6		0			−	400474.i		0				1.25309e8i		0		5.19169e9				0		−6.62363e10				0
33.7		0			−	388745.i		0			−	1.69678e8i		0		−7.70460e9				0		−5.69794e10				0
33.8		0			−	388745.i		0				1.69678e8i		0		7.70460e9				0		−5.69794e10				0
33.9		0			−	362079.i		0			−	4.97114e7i		0		7.73685e9				0		−3.69580e10				0
33.10		0			−	362079.i		0				4.97114e7i		0		−7.73685e9				0		−3.69580e10				0
33.11		0			−	240044.i		0			−	1.17086e8i		0		9.52265e9				0		3.65222e10				0
33.12		0			−	240044.i		0				1.17086e8i		0		−9.52265e9				0		3.65222e10				0
33.13		0			−	108714.i		0			−	1.03806e8i		0		−5.33658e8				0		8.23244e10				0
33.14		0			−	108714.i		0				1.03806e8i		0		5.33658e8				0		8.23244e10				0
33.15		0			−	66624.6i		0			−	8.65230e6i		0		3.32693e9				0		8.97043e10				0
33.16		0			−	66624.6i		0				8.65230e6i		0		−3.32693e9				0		8.97043e10				0
33.17		0				66624.6i		0			−	8.65230e6i		0		−3.32693e9				0		8.97043e10				0
33.18		0				66624.6i		0				8.65230e6i		0		3.32693e9				0		8.97043e10				0
33.19		0				108714.i		0			−	1.03806e8i		0		5.33658e8				0		8.23244e10				0
33.20		0				108714.i		0				1.03806e8i		0		−5.33658e8				0		8.23244e10				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	64.24.b.c	✓	32
4.b	odd	2	1	inner	64.24.b.c	✓	32
8.b	even	2	1	inner	64.24.b.c	✓	32
8.d	odd	2	1	inner	64.24.b.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
64.24.b.c	✓	32	1.a	even	1	1	trivial
64.24.b.c	✓	32	4.b	odd	2	1	inner
64.24.b.c	✓	32	8.b	even	2	1	inner
64.24.b.c	✓	32	8.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^16 + 1039233853600*T3^14 + 435370496651085702670272*T3^12 + 94460321040967217744454216270509568*T3^10 + 11284325659321365251912676745228950291388245504*T3^8 + 721708374624256379840316014236033790937311199363019726848*T3^6 + 21770934423165115384132640956135061962525331860218333092225492434944*T3^4 + 227517531085371400339655885692894349473419107765731022881578480302040796495872*T3^2 + 639853565015953921272403509453868293801980570204062351132961137783204679005764300374016