Newform orbit 64.8.e.a

• Label: 64.8.e.a
• Level: $64$
• Weight: $8$
• Character orbit: 64.e
• Analytic conductor: $19.993$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.9926416310\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Relative dimension:	\(13\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−61.7547	−	61.7547i		0		160.824	−	160.824i		0				1202.46i		0				5440.30i		0
17.2		0		−50.5872	−	50.5872i		0		−364.370	+	364.370i		0			−	182.346i		0				2931.14i		0
17.3		0		−42.2145	−	42.2145i		0		46.9348	−	46.9348i		0			−	1384.27i		0				1377.13i		0
17.4		0		−26.1364	−	26.1364i		0		−31.6175	+	31.6175i		0			−	444.381i		0			−	820.775i		0
17.5		0		−20.1662	−	20.1662i		0		269.345	−	269.345i		0				147.771i		0			−	1373.65i		0
17.6		0		−8.25573	−	8.25573i		0		63.0500	−	63.0500i		0				847.676i		0			−	2050.69i		0
17.7		0		−2.27414	−	2.27414i		0		−242.456	+	242.456i		0				1642.72i		0			−	2176.66i		0
17.8		0		12.2643	+	12.2643i		0		−210.432	+	210.432i		0			−	920.183i		0			−	1886.17i		0
17.9		0		21.1050	+	21.1050i		0		328.807	−	328.807i		0			−	874.718i		0			−	1296.15i		0
17.10		0		35.6625	+	35.6625i		0		50.2015	−	50.2015i		0			−	699.226i		0				356.628i		0
17.11		0		37.3394	+	37.3394i		0		−233.214	+	233.214i		0				241.506i		0				601.466i		0
17.12		0		49.4488	+	49.4488i		0		252.094	−	252.094i		0				1482.88i		0				2703.37i		0
17.13		0		56.5688	+	56.5688i		0		−90.1684	+	90.1684i		0			−	373.897i		0				4213.06i		0
49.1		0		−61.7547	+	61.7547i		0		160.824	+	160.824i		0			−	1202.46i		0			−	5440.30i		0
49.2		0		−50.5872	+	50.5872i		0		−364.370	−	364.370i		0				182.346i		0			−	2931.14i		0
49.3		0		−42.2145	+	42.2145i		0		46.9348	+	46.9348i		0				1384.27i		0			−	1377.13i		0
49.4		0		−26.1364	+	26.1364i		0		−31.6175	−	31.6175i		0				444.381i		0				820.775i		0
49.5		0		−20.1662	+	20.1662i		0		269.345	+	269.345i		0			−	147.771i		0				1373.65i		0
49.6		0		−8.25573	+	8.25573i		0		63.0500	+	63.0500i		0			−	847.676i		0				2050.69i		0
49.7		0		−2.27414	+	2.27414i		0		−242.456	−	242.456i		0			−	1642.72i		0				2176.66i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.8.e.a		26
4.b	odd	2	1		16.8.e.a	✓	26
8.b	even	2	1		128.8.e.a		26
8.d	odd	2	1		128.8.e.b		26
16.e	even	4	1	inner	64.8.e.a		26
16.e	even	4	1		128.8.e.a		26
16.f	odd	4	1		16.8.e.a	✓	26
16.f	odd	4	1		128.8.e.b		26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.8.e.a	✓	26	4.b	odd	2	1
16.8.e.a	✓	26	16.f	odd	4	1
64.8.e.a		26	1.a	even	1	1	trivial
64.8.e.a		26	16.e	even	4	1	inner
128.8.e.a		26	8.b	even	2	1
128.8.e.a		26	16.e	even	4	1
128.8.e.b		26	8.d	odd	2	1
128.8.e.b		26	16.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(64, [\chi])\).