Newform orbit 1020.3.u.a

• Label: 1020.3.u.a
• Level: $1020$
• Weight: $3$
• Character orbit: 1020.u
• Analytic conductor: $27.793$
• Analytic rank: $0$
• Dimension: $72$
• 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.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.7929869648\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(i)\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
373.1		0		−1.22474	+	1.22474i		0		0.788354	−	4.93746i		0		9.22187	+	9.22187i		0			−	3.00000i		0
373.2		0		−1.22474	+	1.22474i		0		−1.50197	+	4.76908i		0		8.47662	+	8.47662i		0			−	3.00000i		0
373.3		0		−1.22474	+	1.22474i		0		4.57473	+	2.01788i		0		7.13297	+	7.13297i		0			−	3.00000i		0
373.4		0		−1.22474	+	1.22474i		0		2.35229	+	4.41211i		0		−4.58023	−	4.58023i		0			−	3.00000i		0
373.5		0		−1.22474	+	1.22474i		0		1.87783	−	4.63398i		0		2.82991	+	2.82991i		0			−	3.00000i		0
373.6		0		−1.22474	+	1.22474i		0		−4.92510	−	0.862214i		0		2.11345	+	2.11345i		0			−	3.00000i		0
373.7		0		−1.22474	+	1.22474i		0		−2.30949	−	4.43466i		0		1.79186	+	1.79186i		0			−	3.00000i		0
373.8		0		−1.22474	+	1.22474i		0		3.97448	+	3.03373i		0		−0.414350	−	0.414350i		0			−	3.00000i		0
373.9		0		−1.22474	+	1.22474i		0		3.58788	−	3.48240i		0		−1.35608	−	1.35608i		0			−	3.00000i		0
373.10		0		−1.22474	+	1.22474i		0		0.589800	+	4.96509i		0		−3.10876	−	3.10876i		0			−	3.00000i		0
373.11		0		−1.22474	+	1.22474i		0		4.98934	+	0.326262i		0		3.34665	+	3.34665i		0			−	3.00000i		0
373.12		0		−1.22474	+	1.22474i		0		−4.94458	+	0.742378i		0		3.61401	+	3.61401i		0			−	3.00000i		0
373.13		0		−1.22474	+	1.22474i		0		−3.63576	+	3.43239i		0		3.95113	+	3.95113i		0			−	3.00000i		0
373.14		0		−1.22474	+	1.22474i		0		−0.518294	+	4.97306i		0		−4.15720	−	4.15720i		0			−	3.00000i		0
373.15		0		−1.22474	+	1.22474i		0		−2.16435	−	4.50728i		0		−6.10228	−	6.10228i		0			−	3.00000i		0
373.16		0		−1.22474	+	1.22474i		0		−3.37020	−	3.69347i		0		−7.07714	−	7.07714i		0			−	3.00000i		0
373.17		0		−1.22474	+	1.22474i		0		3.85731	−	3.18137i		0		−7.37362	−	7.37362i		0			−	3.00000i		0
373.18		0		−1.22474	+	1.22474i		0		−4.44702	+	2.28561i		0		−8.30882	−	8.30882i		0			−	3.00000i		0
373.19		0		1.22474	−	1.22474i		0		4.44702	−	2.28561i		0		8.30882	+	8.30882i		0			−	3.00000i		0
373.20		0		1.22474	−	1.22474i		0		−3.85731	+	3.18137i		0		7.37362	+	7.37362i		0			−	3.00000i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
17.b	even	2	1	inner
85.g	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1020.3.u.a	✓	72
5.c	odd	4	1	inner	1020.3.u.a	✓	72
17.b	even	2	1	inner	1020.3.u.a	✓	72
85.g	odd	4	1	inner	1020.3.u.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1020.3.u.a	✓	72	1.a	even	1	1	trivial
1020.3.u.a	✓	72	5.c	odd	4	1	inner
1020.3.u.a	✓	72	17.b	even	2	1	inner
1020.3.u.a	✓	72	85.g	odd	4	1	inner

Hecke kernels

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