Newform orbit 2052.3.s.a

• Label: 2052.3.s.a
• Level: $2052$
• Weight: $3$
• Character orbit: 2052.s
• Analytic conductor: $55.913$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2052.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(55.9129502467\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(40\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 684)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
829.1		0			0			0		−4.66990	+	8.08850i		0		0.278827	−	0.482942i		0			0			0
829.2		0			0			0		−4.35575	+	7.54438i		0		5.71458	−	9.89794i		0			0			0
829.3		0			0			0		−4.34684	+	7.52895i		0		0.405593	−	0.702508i		0			0			0
829.4		0			0			0		−3.94439	+	6.83189i		0		6.38121	−	11.0526i		0			0			0
829.5		0			0			0		−3.64833	+	6.31909i		0		−4.80976	+	8.33075i		0			0			0
829.6		0			0			0		−3.56049	+	6.16694i		0		−5.30926	+	9.19591i		0			0			0
829.7		0			0			0		−3.46044	+	5.99365i		0		−3.78976	+	6.56406i		0			0			0
829.8		0			0			0		−2.84714	+	4.93140i		0		0.968090	−	1.67678i		0			0			0
829.9		0			0			0		−2.77840	+	4.81232i		0		0.506731	−	0.877684i		0			0			0
829.10		0			0			0		−2.16848	+	3.75592i		0		−1.29489	+	2.24282i		0			0			0
829.11		0			0			0		−1.96284	+	3.39973i		0		2.56510	−	4.44288i		0			0			0
829.12		0			0			0		−1.91242	+	3.31241i		0		−3.97487	+	6.88467i		0			0			0
829.13		0			0			0		−1.65331	+	2.86362i		0		0.469266	−	0.812792i		0			0			0
829.14		0			0			0		−1.51878	+	2.63060i		0		−4.58926	+	7.94883i		0			0			0
829.15		0			0			0		−1.49069	+	2.58196i		0		4.88733	−	8.46511i		0			0			0
829.16		0			0			0		−1.33945	+	2.31999i		0		3.94899	−	6.83985i		0			0			0
829.17		0			0			0		−1.21776	+	2.10923i		0		−1.46858	+	2.54365i		0			0			0
829.18		0			0			0		−0.340706	+	0.590120i		0		−2.79581	+	4.84248i		0			0			0
829.19		0			0			0		−0.267948	+	0.464100i		0		4.62209	−	8.00569i		0			0			0
829.20		0			0			0		−0.236809	+	0.410166i		0		−1.14656	+	1.98590i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
171.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2052.3.s.a		80
3.b	odd	2	1		684.3.s.a	✓	80
9.c	even	3	1		2052.3.bl.a		80
9.d	odd	6	1		684.3.bl.a	yes	80
19.d	odd	6	1		2052.3.bl.a		80
57.f	even	6	1		684.3.bl.a	yes	80
171.i	odd	6	1	inner	2052.3.s.a		80
171.t	even	6	1		684.3.s.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
684.3.s.a	✓	80	3.b	odd	2	1
684.3.s.a	✓	80	171.t	even	6	1
684.3.bl.a	yes	80	9.d	odd	6	1
684.3.bl.a	yes	80	57.f	even	6	1
2052.3.s.a		80	1.a	even	1	1	trivial
2052.3.s.a		80	171.i	odd	6	1	inner
2052.3.bl.a		80	9.c	even	3	1
2052.3.bl.a		80	19.d	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(2052, [\chi])\).