Newform orbit 64.20.e.a

• Label: 64.20.e.a
• Level: $64$
• Weight: $20$
• Character orbit: 64.e
• Analytic conductor: $146.443$
• Analytic rank: $0$
• Dimension: $74$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(146.442685796\)
Analytic rank:	\(0\)
Dimension:	\(74\)
Relative dimension:	\(37\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 74 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \)

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		−44301.5	−	44301.5i		0		2.75310e6	−	2.75310e6i		0			−	9.02228e7i		0				2.76298e9i		0
17.2		0		−42135.4	−	42135.4i		0		−3.60880e6	+	3.60880e6i		0				1.90652e8i		0				2.38852e9i		0
17.3		0		−41276.6	−	41276.6i		0		1.93285e6	−	1.93285e6i		0			−	5.84483e7i		0				2.24525e9i		0
17.4		0		−37550.7	−	37550.7i		0		−871067.	+	871067.i		0			−	6.95820e7i		0				1.65785e9i		0
17.5		0		−37232.5	−	37232.5i		0		−1.68693e6	+	1.68693e6i		0				8.40002e7i		0				1.61026e9i		0
17.6		0		−36217.6	−	36217.6i		0		−5.07791e6	+	5.07791e6i		0			−	6.82116e7i		0				1.46117e9i		0
17.7		0		−31083.9	−	31083.9i		0		4.67376e6	−	4.67376e6i		0				5.10598e7i		0				7.70159e8i		0
17.8		0		−29061.4	−	29061.4i		0		3.69217e6	−	3.69217e6i		0				1.48589e8i		0				5.26864e8i		0
17.9		0		−26937.6	−	26937.6i		0		−5.75592e6	+	5.75592e6i		0			−	8.04648e7i		0				2.89010e8i		0
17.10		0		−23817.0	−	23817.0i		0		1.71535e6	−	1.71535e6i		0				1.57761e8i		0			−	2.77646e7i		0
17.11		0		−20499.7	−	20499.7i		0		5.50901e6	−	5.50901e6i		0			−	1.06467e8i		0			−	3.21788e8i		0
17.12		0		−20001.7	−	20001.7i		0		−160282.	+	160282.i		0			−	1.77970e8i		0			−	3.62125e8i		0
17.13		0		−15255.1	−	15255.1i		0		−1.98094e6	+	1.98094e6i		0				3.83254e7i		0			−	6.96828e8i		0
17.14		0		−14906.4	−	14906.4i		0		−497430.	+	497430.i		0			−	1.32373e8i		0			−	7.17857e8i		0
17.15		0		−10219.4	−	10219.4i		0		−874334.	+	874334.i		0				1.31849e7i		0			−	9.53391e8i		0
17.16		0		−8027.04	−	8027.04i		0		−3.58124e6	+	3.58124e6i		0				2.91204e7i		0			−	1.03339e9i		0
17.17		0		−6657.76	−	6657.76i		0		−1.03514e6	+	1.03514e6i		0				1.15949e8i		0			−	1.07361e9i		0
17.18		0		−2944.14	−	2944.14i		0		3.79583e6	−	3.79583e6i		0				6.01043e7i		0			−	1.14493e9i		0
17.19		0		3594.61	+	3594.61i		0		5.33235e6	−	5.33235e6i		0			−	1.18416e8i		0			−	1.13642e9i		0
17.20		0		4275.26	+	4275.26i		0		1.79117e6	−	1.79117e6i		0			−	1.14366e8i		0			−	1.12571e9i		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	64.20.e.a		74
4.b	odd	2	1		16.20.e.a	✓	74
16.e	even	4	1	inner	64.20.e.a		74
16.f	odd	4	1		16.20.e.a	✓	74

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.20.e.a	✓	74	4.b	odd	2	1
16.20.e.a	✓	74	16.f	odd	4	1
64.20.e.a		74	1.a	even	1	1	trivial
64.20.e.a		74	16.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{20}^{\mathrm{new}}(64, [\chi])\).