Newform orbit 276.3.n.a

• Label: 276.3.n.a
• Level: $276$
• Weight: $3$
• Character orbit: 276.n
• Analytic conductor: $7.520$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.n (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.52045529634\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(16\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q + 2 q^{3} - 26 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1		0		−2.99271	+	0.209008i		0		−0.115554	−	0.179806i		0		−0.580701	+	4.03887i		0		8.91263	−	1.25100i		0
29.2		0		−2.81081	+	1.04851i		0		3.74188	+	5.82248i		0		1.60805	−	11.1843i		0		6.80126	−	5.89430i		0
29.3		0		−2.40463	−	1.79381i		0		0.115554	+	0.179806i		0		−0.580701	+	4.03887i		0		2.56449	+	8.62690i		0
29.4		0		−1.79773	−	2.40170i		0		−3.74188	−	5.82248i		0		1.60805	−	11.1843i		0		−2.53630	+	8.63523i		0
29.5		0		−1.79406	+	2.40444i		0		−4.16386	−	6.47910i		0		−0.669624	+	4.65734i		0		−2.56271	−	8.62743i		0
29.6		0		−1.30132	+	2.70307i		0		−0.453644	−	0.705884i		0		0.206617	−	1.43705i		0		−5.61313	−	7.03511i		0
29.7		0		−0.838150	+	2.88054i		0		4.84577	+	7.54017i		0		−1.87166	+	13.0177i		0		−7.59501	−	4.82865i		0
29.8		0		−0.209317	−	2.99269i		0		4.16386	+	6.47910i		0		−0.669624	+	4.65734i		0		−8.91237	+	1.25284i		0
29.9		0		0.366646	−	2.97751i		0		0.453644	+	0.705884i		0		0.206617	−	1.43705i		0		−8.73114	−	2.18339i		0
29.10		0		0.428526	+	2.96924i		0		−1.34647	−	2.09514i		0		1.51241	−	10.5190i		0		−8.63273	+	2.54479i		0
29.11		0		0.852240	−	2.87640i		0		−4.84577	−	7.54017i		0		−1.87166	+	13.0177i		0		−7.54737	−	4.90277i		0
29.12		0		1.83446	+	2.37376i		0		−1.00772	−	1.56805i		0		−0.801773	+	5.57645i		0		−2.26949	+	8.70916i		0
29.13		0		1.96579	−	2.26620i		0		1.34647	+	2.09514i		0		1.51241	−	10.5190i		0		−1.27134	−	8.90975i		0
29.14		0		2.60551	+	1.48705i		0		4.08545	+	6.35708i		0		0.596685	−	4.15004i		0		4.57734	+	7.74906i		0
29.15		0		2.82660	−	1.00515i		0		1.00772	+	1.56805i		0		−0.801773	+	5.57645i		0		6.97935	−	5.68232i		0
29.16		0		2.99585	+	0.157654i		0		−4.08545	−	6.35708i		0		0.596685	−	4.15004i		0		8.95029	+	0.944619i		0
41.1		0		−2.99167	−	0.223384i		0		0.927446	+	0.133347i		0		−0.147770	−	0.323572i		0		8.90020	+	1.33658i		0
41.2		0		−2.76980	+	1.15248i		0		0.813236	+	0.116926i		0		−2.44206	−	5.34737i		0		6.34356	−	6.38429i		0
41.3		0		−2.20929	−	2.02955i		0		−6.70100	−	0.963458i		0		0.618048	+	1.35334i		0		0.761887	+	8.96769i		0
41.4		0		−2.11541	+	2.12721i		0		8.41743	+	1.21024i		0		4.60033	+	10.0733i		0		−0.0500522	−	8.99986i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
23.c	even	11	1	inner
69.h	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	276.3.n.a	✓	160
3.b	odd	2	1	inner	276.3.n.a	✓	160
23.c	even	11	1	inner	276.3.n.a	✓	160
69.h	odd	22	1	inner	276.3.n.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.3.n.a	✓	160	1.a	even	1	1	trivial
276.3.n.a	✓	160	3.b	odd	2	1	inner
276.3.n.a	✓	160	23.c	even	11	1	inner
276.3.n.a	✓	160	69.h	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(276, [\chi])\).