Newform orbit 1340.2.j.a

• Label: 1340.2.j.a
• Level: $1340$
• Weight: $2$
• Character orbit: 1340.j
• Analytic conductor: $10.700$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1340.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.6999538709\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(34\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
133.1		0		−2.37556	+	2.37556i		0		−1.11373	−	1.93897i		0		−2.52323	−	2.52323i		0			−	8.28653i		0
133.2		0		−2.25371	+	2.25371i		0		2.22096	+	0.259492i		0		−0.740770	−	0.740770i		0			−	7.15842i		0
133.3		0		−2.07282	+	2.07282i		0		0.454545	+	2.18938i		0		1.98451	+	1.98451i		0			−	5.59316i		0
133.4		0		−1.98398	+	1.98398i		0		−1.89639	−	1.18479i		0		1.30022	+	1.30022i		0			−	4.87234i		0
133.5		0		−1.88688	+	1.88688i		0		−0.683365	+	2.12909i		0		−3.39697	−	3.39697i		0			−	4.12063i		0
133.6		0		−1.76050	+	1.76050i		0		−1.99394	+	1.01203i		0		1.79004	+	1.79004i		0			−	3.19874i		0
133.7		0		−1.63577	+	1.63577i		0		1.84705	−	1.26032i		0		0.504292	+	0.504292i		0			−	2.35150i		0
133.8		0		−1.15379	+	1.15379i		0		2.15062	+	0.612240i		0		−2.03760	−	2.03760i		0				0.337553i		0
133.9		0		−1.13952	+	1.13952i		0		−2.12496	+	0.696099i		0		−2.05547	−	2.05547i		0				0.403000i		0
133.10		0		−1.11748	+	1.11748i		0		0.0508793	−	2.23549i		0		−0.815905	−	0.815905i		0				0.502470i		0
133.11		0		−1.02854	+	1.02854i		0		−2.06512	−	0.857483i		0		0.567959	+	0.567959i		0				0.884210i		0
133.12		0		−0.823495	+	0.823495i		0		2.22529	−	0.219246i		0		2.82849	+	2.82849i		0				1.64371i		0
133.13		0		−0.698627	+	0.698627i		0		−0.164280	−	2.23003i		0		2.49150	+	2.49150i		0				2.02384i		0
133.14		0		−0.476086	+	0.476086i		0		−1.92004	+	1.14605i		0		−0.457271	−	0.457271i		0				2.54668i		0
133.15		0		−0.461766	+	0.461766i		0		1.48773	+	1.66933i		0		2.23548	+	2.23548i		0				2.57354i		0
133.16		0		−0.408190	+	0.408190i		0		0.669563	+	2.13347i		0		−1.24198	−	1.24198i		0				2.66676i		0
133.17		0		−0.0147967	+	0.0147967i		0		−1.19776	+	1.88822i		0		3.18368	+	3.18368i		0				2.99956i		0
133.18		0		0.0147967	−	0.0147967i		0		1.19776	−	1.88822i		0		−3.18368	−	3.18368i		0				2.99956i		0
133.19		0		0.408190	−	0.408190i		0		−0.669563	−	2.13347i		0		1.24198	+	1.24198i		0				2.66676i		0
133.20		0		0.461766	−	0.461766i		0		−1.48773	−	1.66933i		0		−2.23548	−	2.23548i		0				2.57354i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
67.b	odd	2	1	inner
335.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1340.2.j.a	✓	68
5.c	odd	4	1	inner	1340.2.j.a	✓	68
67.b	odd	2	1	inner	1340.2.j.a	✓	68
335.f	even	4	1	inner	1340.2.j.a	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1340.2.j.a	✓	68	1.a	even	1	1	trivial
1340.2.j.a	✓	68	5.c	odd	4	1	inner
1340.2.j.a	✓	68	67.b	odd	2	1	inner
1340.2.j.a	✓	68	335.f	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1340, [\chi])\).