Newform orbit 64.24.e.a

• Label: 64.24.e.a
• Level: $64$
• Weight: $24$
• Character orbit: 64.e
• Analytic conductor: $214.531$
• Analytic rank: $0$
• Dimension: $90$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(214.530583901\)
Analytic rank:	\(0\)
Dimension:	\(90\)
Relative dimension:	\(45\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 90 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \)

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		−417071.	−	417071.i		0		−1.17592e8	+	1.17592e8i		0				1.67834e9i		0				2.53754e11i		0
17.2		0		−391132.	−	391132.i		0		8.92131e7	−	8.92131e7i		0				2.94140e9i		0				2.11825e11i		0
17.3		0		−387560.	−	387560.i		0		1.05971e8	−	1.05971e8i		0			−	7.59178e9i		0				2.06262e11i		0
17.4		0		−367312.	−	367312.i		0		3.42346e7	−	3.42346e7i		0				1.00506e10i		0				1.75693e11i		0
17.5		0		−358807.	−	358807.i		0		−1.40867e7	+	1.40867e7i		0			−	6.29989e9i		0				1.63341e11i		0
17.6		0		−332866.	−	332866.i		0		−6.54212e7	+	6.54212e7i		0				3.71667e9i		0				1.27456e11i		0
17.7		0		−303564.	−	303564.i		0		−5.98803e7	+	5.98803e7i		0			−	4.78358e9i		0				9.01589e10i		0
17.8		0		−286130.	−	286130.i		0		−1.30247e8	+	1.30247e8i		0			−	1.92081e9i		0				6.95980e10i		0
17.9		0		−277696.	−	277696.i		0		4.72704e7	−	4.72704e7i		0			−	2.08272e9i		0				6.00869e10i		0
17.10		0		−267941.	−	267941.i		0		6.26290e7	−	6.26290e7i		0				1.19784e9i		0				4.94417e10i		0
17.11		0		−220155.	−	220155.i		0		1.17841e7	−	1.17841e7i		0				6.12920e9i		0				2.79345e9i		0
17.12		0		−198285.	−	198285.i		0		−1.18292e8	+	1.18292e8i		0				6.05722e9i		0			−	1.55096e10i		0
17.13		0		−186750.	−	186750.i		0		−4.02332e7	+	4.02332e7i		0			−	5.66827e9i		0			−	2.43918e10i		0
17.14		0		−177640.	−	177640.i		0		1.42580e8	−	1.42580e8i		0				6.56907e8i		0			−	3.10312e10i		0
17.15		0		−158154.	−	158154.i		0		−2.60550e7	+	2.60550e7i		0				6.36490e9i		0			−	4.41178e10i		0
17.16		0		−120876.	−	120876.i		0		−7.90014e6	+	7.90014e6i		0			−	8.37748e9i		0			−	6.49214e10i		0
17.17		0		−107278.	−	107278.i		0		1.32256e8	−	1.32256e8i		0				2.70816e9i		0			−	7.11262e10i		0
17.18		0		−94609.7	−	94609.7i		0		9.23513e7	−	9.23513e7i		0			−	5.80111e9i		0			−	7.62412e10i		0
17.19		0		−85271.2	−	85271.2i		0		−7.95847e7	+	7.95847e7i		0			−	8.89876e9i		0			−	7.96008e10i		0
17.20		0		−68436.9	−	68436.9i		0		−2.70386e6	+	2.70386e6i		0				2.28175e9i		0			−	8.47760e10i		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	64.24.e.a		90
4.b	odd	2	1		16.24.e.a	✓	90
16.e	even	4	1	inner	64.24.e.a		90
16.f	odd	4	1		16.24.e.a	✓	90

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.24.e.a	✓	90	4.b	odd	2	1
16.24.e.a	✓	90	16.f	odd	4	1
64.24.e.a		90	1.a	even	1	1	trivial
64.24.e.a		90	16.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{24}^{\mathrm{new}}(64, [\chi])\).