Newform orbit 268.2.i.a

• Label: 268.2.i.a
• Level: $268$
• Weight: $2$
• Character orbit: 268.i
• Analytic conductor: $2.140$
• Analytic rank: $0$
• Dimension: $50$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 268 = 2^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	268.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.13999077417\)
Analytic rank:	\(0\)
Dimension:	\(50\)
Relative dimension:	\(5\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 50 q + 2 q^{7} - 7 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−1.63923	−	0.481321i		0		−0.594412	+	0.685987i		0		−0.150761	−	0.0968884i		0		−0.0683567	−	0.0439302i		0
9.2		0		−0.461370	−	0.135470i		0		−0.892315	+	1.02979i		0		−4.13116	−	2.65494i		0		−2.32925	−	1.49692i		0
9.3		0		−0.0516548	−	0.0151672i		0		1.75015	−	2.01978i		0		1.94065	+	1.24718i		0		−2.52132	−	1.62036i		0
9.4		0		1.48789	+	0.436884i		0		−2.76995	+	3.19669i		0		2.18881	+	1.40666i		0		−0.500812	−	0.321852i		0
9.5		0		2.55182	+	0.749281i		0		1.01041	−	1.16608i		0		−0.546471	−	0.351195i		0		3.42659	+	2.20214i		0
25.1		0		−1.91984	+	2.21561i		0		−2.76750	+	1.77857i		0		−0.0983445	−	0.684001i		0		−0.796210	−	5.53776i		0
25.2		0		−1.29216	+	1.49123i		0		2.77916	−	1.78606i		0		−0.580189	−	4.03531i		0		−0.127150	−	0.884347i		0
25.3		0		−0.210145	+	0.242521i		0		−0.821895	+	0.528200i		0		0.293030	+	2.03807i		0		0.412289	+	2.86754i		0
25.4		0		0.897867	−	1.03619i		0		2.66185	−	1.71067i		0		0.281717	+	1.95938i		0		0.159412	+	1.10874i		0
25.5		0		1.79380	−	2.07016i		0		−0.868046	+	0.557859i		0		−0.169313	−	1.17760i		0		−0.640885	−	4.45745i		0
81.1		0		−2.77506	−	1.78342i		0		−0.107008	−	0.744259i		0		−1.12992	−	2.47417i		0		3.27411	+	7.16931i		0
81.2		0		−1.32149	−	0.849270i		0		0.198398	+	1.37989i		0		1.02122	+	2.23616i		0		−0.221169	−	0.484293i		0
81.3		0		−0.942113	−	0.605459i		0		−0.451946	−	3.14336i		0		1.77196	+	3.88006i		0		−0.725249	−	1.58807i		0
81.4		0		0.912795	+	0.586618i		0		−0.417105	−	2.90103i		0		−1.43055	−	3.13247i		0		−0.757171	−	1.65797i		0
81.5		0		1.81257	+	1.16487i		0		0.219931	+	1.52966i		0		0.311360	+	0.681784i		0		0.682258	+	1.49394i		0
89.1		0		−0.377832	−	2.62788i		0		1.27473	−	2.79126i		0		1.95766	−	0.574821i		0		−3.88450	+	1.14059i		0
89.2		0		−0.194994	−	1.35621i		0		0.469617	−	1.02832i		0		−2.32548	+	0.682821i		0		1.07718	−	0.316289i		0
89.3		0		−0.0943563	−	0.656262i		0		−0.835152	+	1.82873i		0		2.11914	−	0.622236i		0		2.45670	−	0.721353i		0
89.4		0		0.279796	+	1.94602i		0		1.07014	−	2.34327i		0		3.01331	−	0.884788i		0		−0.830237	+	0.243780i		0
89.5		0		0.300679	+	2.09127i		0		−0.604422	+	1.32350i		0		−3.15028	+	0.925007i		0		−1.40452	+	0.412404i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
67.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	268.2.i.a	✓	50
67.e	even	11	1	inner	268.2.i.a	✓	50

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
268.2.i.a	✓	50	1.a	even	1	1	trivial
268.2.i.a	✓	50	67.e	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(268, [\chi])\).