Newform orbit 1148.2.r.a

• Label: 1148.2.r.a
• Level: $1148$
• Weight: $2$
• Character orbit: 1148.r
• Analytic conductor: $9.167$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.16682615204\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
81.1		0		−2.89464	−	1.67122i		0		1.42784	+	2.47308i		0		−1.36322	+	2.26752i		0		4.08596	+	7.07710i		0
81.2		0		−2.68013	−	1.54737i		0		0.0658562	+	0.114066i		0		−0.113033	−	2.64334i		0		3.28873	+	5.69624i		0
81.3		0		−2.67190	−	1.54262i		0		−1.10096	−	1.90691i		0		2.60761	+	0.447649i		0		3.25937	+	5.64540i		0
81.4		0		−1.90271	−	1.09853i		0		−1.32827	−	2.30063i		0		−2.55338	−	0.693005i		0		0.913540	+	1.58230i		0
81.5		0		−1.85927	−	1.07345i		0		−0.972000	−	1.68355i		0		−1.16501	+	2.37545i		0		0.804601	+	1.39361i		0
81.6		0		−1.79608	−	1.03697i		0		−0.904853	−	1.56725i		0		2.10654	−	1.60077i		0		0.650613	+	1.12689i		0
81.7		0		−1.64009	−	0.946908i		0		1.83233	+	3.17368i		0		0.288265	−	2.63000i		0		0.293269	+	0.507958i		0
81.8		0		−1.59496	−	0.920850i		0		1.70544	+	2.95391i		0		2.57642	−	0.601730i		0		0.195929	+	0.339358i		0
81.9		0		−1.48683	−	0.858424i		0		1.14679	+	1.98629i		0		−2.58388	+	0.568830i		0		−0.0262152	−	0.0454060i		0
81.10		0		−1.32068	−	0.762496i		0		0.729632	+	1.26376i		0		0.676296	+	2.55786i		0		−0.337200	−	0.584047i		0
81.11		0		−0.900937	−	0.520156i		0		−0.292521	−	0.506661i		0		−2.31637	−	1.27845i		0		−0.958875	−	1.66082i		0
81.12		0		−0.507835	−	0.293199i		0		1.03735	+	1.79674i		0		1.44101	+	2.21889i		0		−1.32807	−	2.30028i		0
81.13		0		−0.388672	−	0.224400i		0		−0.254464	−	0.440744i		0		2.49203	−	0.888703i		0		−1.39929	−	2.42364i		0
81.14		0		−0.294024	−	0.169755i		0		−2.09216	−	3.62373i		0		0.0873039	−	2.64431i		0		−1.44237	−	2.49825i		0
81.15		0		0.294024	+	0.169755i		0		−2.09216	−	3.62373i		0		−0.0873039	+	2.64431i		0		−1.44237	−	2.49825i		0
81.16		0		0.388672	+	0.224400i		0		−0.254464	−	0.440744i		0		−2.49203	+	0.888703i		0		−1.39929	−	2.42364i		0
81.17		0		0.507835	+	0.293199i		0		1.03735	+	1.79674i		0		−1.44101	−	2.21889i		0		−1.32807	−	2.30028i		0
81.18		0		0.900937	+	0.520156i		0		−0.292521	−	0.506661i		0		2.31637	+	1.27845i		0		−0.958875	−	1.66082i		0
81.19		0		1.32068	+	0.762496i		0		0.729632	+	1.26376i		0		−0.676296	−	2.55786i		0		−0.337200	−	0.584047i		0
81.20		0		1.48683	+	0.858424i		0		1.14679	+	1.98629i		0		2.58388	−	0.568830i		0		−0.0262152	−	0.0454060i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
41.b	even	2	1	inner
287.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1148.2.r.a	✓	56
7.c	even	3	1	inner	1148.2.r.a	✓	56
41.b	even	2	1	inner	1148.2.r.a	✓	56
287.j	even	6	1	inner	1148.2.r.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1148.2.r.a	✓	56	1.a	even	1	1	trivial
1148.2.r.a	✓	56	7.c	even	3	1	inner
1148.2.r.a	✓	56	41.b	even	2	1	inner
1148.2.r.a	✓	56	287.j	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1148, [\chi])\).