Newform orbit 1064.2.bs.a

• Label: 1064.2.bs.a
• Level: $1064$
• Weight: $2$
• Character orbit: 1064.bs
• Analytic conductor: $8.496$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.49608277506\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(40\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
601.1		0		−1.68576	−	2.91983i		0		−0.829659	+	0.479004i		0		−2.64093	+	0.159638i		0		−4.18360	+	7.24621i		0
601.2		0		−1.57827	−	2.73364i		0		−2.51304	+	1.45091i		0		2.47721	−	0.929198i		0		−3.48187	+	6.03078i		0
601.3		0		−1.55354	−	2.69080i		0		3.26135	−	1.88294i		0		1.25248	−	2.33052i		0		−3.32695	+	5.76244i		0
601.4		0		−1.28746	−	2.22994i		0		1.31851	−	0.761241i		0		2.22242	+	1.43557i		0		−1.81508	+	3.14382i		0
601.5		0		−1.27739	−	2.21251i		0		0.677095	−	0.390921i		0		−2.39637	+	1.12134i		0		−1.76347	+	3.05443i		0
601.6		0		−1.16077	−	2.01051i		0		1.24042	−	0.716157i		0		0.575455	+	2.58241i		0		−1.19476	+	2.06938i		0
601.7		0		−1.10995	−	1.92250i		0		−0.170002	+	0.0981506i		0		−1.32115	−	2.29228i		0		−0.963992	+	1.66968i		0
601.8		0		−1.09267	−	1.89255i		0		−0.700602	+	0.404493i		0		1.21517	+	2.35019i		0		−0.887842	+	1.53779i		0
601.9		0		−1.03615	−	1.79466i		0		−3.26418	+	1.88457i		0		2.57547	+	0.605759i		0		−0.647215	+	1.12101i		0
601.10		0		−1.00573	−	1.74198i		0		−2.37786	+	1.37286i		0		−0.203547	−	2.63791i		0		−0.523001	+	0.905865i		0
601.11		0		−0.962281	−	1.66672i		0		3.30011	−	1.90532i		0		−0.745323	−	2.53860i		0		−0.351971	+	0.609631i		0
601.12		0		−0.785124	−	1.35987i		0		3.13872	−	1.81214i		0		−1.86219	+	1.87943i		0		0.267162	−	0.462738i		0
601.13		0		−0.672849	−	1.16541i		0		−2.98844	+	1.72538i		0		−0.914860	+	2.48255i		0		0.594548	−	1.02979i		0
601.14		0		−0.671070	−	1.16233i		0		−1.45152	+	0.838037i		0		−2.52760	+	0.781818i		0		0.599331	−	1.03807i		0
601.15		0		−0.533201	−	0.923532i		0		1.33570	−	0.771164i		0		2.29948	−	1.30859i		0		0.931393	−	1.61322i		0
601.16		0		−0.512261	−	0.887262i		0		0.585048	−	0.337777i		0		−2.48500	−	0.908181i		0		0.975178	−	1.68906i		0
601.17		0		−0.253825	−	0.439637i		0		−0.00696226	+	0.00401966i		0		−0.734059	−	2.54188i		0		1.37115	−	2.37489i		0
601.18		0		−0.170770	−	0.295782i		0		2.29788	−	1.32668i		0		2.14854	+	1.54395i		0		1.44168	−	2.49706i		0
601.19		0		−0.104895	−	0.181683i		0		1.15207	−	0.665146i		0		1.97428	−	1.76131i		0		1.47799	−	2.55996i		0
601.20		0		−0.0966133	−	0.167339i		0		3.57515	−	2.06411i		0		−1.90947	+	1.83137i		0		1.48133	−	2.56574i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
19.d	odd	6	1	inner
133.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1064.2.bs.a	✓	80
7.b	odd	2	1	inner	1064.2.bs.a	✓	80
19.d	odd	6	1	inner	1064.2.bs.a	✓	80
133.p	even	6	1	inner	1064.2.bs.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1064.2.bs.a	✓	80	1.a	even	1	1	trivial
1064.2.bs.a	✓	80	7.b	odd	2	1	inner
1064.2.bs.a	✓	80	19.d	odd	6	1	inner
1064.2.bs.a	✓	80	133.p	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1064, [\chi])\).