Newform orbit 1020.3.c.a

• Label: 1020.3.c.a
• Level: $1020$
• Weight: $3$
• Character orbit: 1020.c
• Analytic conductor: $27.793$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.7929869648\)
Analytic rank:	\(0\)
Dimension:	\(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
749.1		0		−2.99338	−	0.199162i		0		−1.43815	−	4.78871i		0				7.67912i		0		8.92067	+	1.19233i		0
749.2		0		−2.99338	+	0.199162i		0		−1.43815	+	4.78871i		0			−	7.67912i		0		8.92067	−	1.19233i		0
749.3		0		−2.93021	−	0.643305i		0		−4.94654	+	0.729173i		0				7.75132i		0		8.17232	+	3.77004i		0
749.4		0		−2.93021	+	0.643305i		0		−4.94654	−	0.729173i		0			−	7.75132i		0		8.17232	−	3.77004i		0
749.5		0		−2.92163	−	0.681215i		0		4.84156	+	1.24873i		0				7.77331i		0		8.07189	+	3.98052i		0
749.6		0		−2.92163	+	0.681215i		0		4.84156	−	1.24873i		0			−	7.77331i		0		8.07189	−	3.98052i		0
749.7		0		−2.85374	−	0.925284i		0		0.0596211	−	4.99964i		0				1.40244i		0		7.28770	+	5.28104i		0
749.8		0		−2.85374	+	0.925284i		0		0.0596211	+	4.99964i		0			−	1.40244i		0		7.28770	−	5.28104i		0
749.9		0		−2.75746	−	1.18170i		0		4.98117	+	0.433573i		0			−	13.3287i		0		6.20715	+	6.51700i		0
749.10		0		−2.75746	+	1.18170i		0		4.98117	−	0.433573i		0				13.3287i		0		6.20715	−	6.51700i		0
749.11		0		−2.64199	−	1.42123i		0		0.374787	+	4.98593i		0				7.36271i		0		4.96020	+	7.50975i		0
749.12		0		−2.64199	+	1.42123i		0		0.374787	−	4.98593i		0			−	7.36271i		0		4.96020	−	7.50975i		0
749.13		0		−2.51407	−	1.63690i		0		3.67787	+	3.38722i		0			−	1.43482i		0		3.64110	+	8.23058i		0
749.14		0		−2.51407	+	1.63690i		0		3.67787	−	3.38722i		0				1.43482i		0		3.64110	−	8.23058i		0
749.15		0		−2.38351	−	1.82178i		0		−4.02880	+	2.96122i		0			−	6.33355i		0		2.36220	+	8.68447i		0
749.16		0		−2.38351	+	1.82178i		0		−4.02880	−	2.96122i		0				6.33355i		0		2.36220	−	8.68447i		0
749.17		0		−2.10707	−	2.13547i		0		3.36937	−	3.69423i		0				1.66609i		0		−0.120501	+	8.99919i		0
749.18		0		−2.10707	+	2.13547i		0		3.36937	+	3.69423i		0			−	1.66609i		0		−0.120501	−	8.99919i		0
749.19		0		−1.37670	−	2.66546i		0		−4.94379	−	0.747601i		0			−	0.358072i		0		−5.20939	+	7.33909i		0
749.20		0		−1.37670	+	2.66546i		0		−4.94379	+	0.747601i		0				0.358072i		0		−5.20939	−	7.33909i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1020.3.c.a	✓	64
3.b	odd	2	1	inner	1020.3.c.a	✓	64
5.b	even	2	1	inner	1020.3.c.a	✓	64
15.d	odd	2	1	inner	1020.3.c.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1020.3.c.a	✓	64	1.a	even	1	1	trivial
1020.3.c.a	✓	64	3.b	odd	2	1	inner
1020.3.c.a	✓	64	5.b	even	2	1	inner
1020.3.c.a	✓	64	15.d	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1020, [\chi])\).