Newform orbit 867.2.i.j

• Label: 867.2.i.j
• Level: $867$
• Weight: $2$
• Character orbit: 867.i
• Analytic conductor: $6.923$
• Analytic rank: $0$
• Dimension: $48$
• CM discriminant: -3
• Inner twists: $32$

Newspace parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.92302985525\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(6\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
65.1		0		−0.337906	+	1.69877i	1.41421	−	1.41421i		0			0		−2.77519	−	1.85432i		0		−2.77164	−	1.14805i		0
65.2		0		−0.337906	+	1.69877i	1.41421	−	1.41421i		0			0		−1.56907	−	1.04842i		0		−2.77164	−	1.14805i		0
65.3		0		−0.337906	+	1.69877i	1.41421	−	1.41421i		0			0		4.34427	+	2.90275i		0		−2.77164	−	1.14805i		0
65.4		0		0.337906	−	1.69877i	1.41421	−	1.41421i		0			0		−4.34427	−	2.90275i		0		−2.77164	−	1.14805i		0
65.5		0		0.337906	−	1.69877i	1.41421	−	1.41421i		0			0		1.56907	+	1.04842i		0		−2.77164	−	1.14805i		0
65.6		0		0.337906	−	1.69877i	1.41421	−	1.41421i		0			0		2.77519	+	1.85432i		0		−2.77164	−	1.14805i		0
131.1		0		−1.44015	+	0.962276i	−1.41421	+	1.41421i		0			0		−5.12441	+	1.01931i		0		1.14805	−	2.77164i		0
131.2		0		−1.44015	+	0.962276i	−1.41421	+	1.41421i		0			0		1.85085	−	0.368157i		0		1.14805	−	2.77164i		0
131.3		0		−1.44015	+	0.962276i	−1.41421	+	1.41421i		0			0		3.27356	−	0.651152i		0		1.14805	−	2.77164i		0
131.4		0		1.44015	−	0.962276i	−1.41421	+	1.41421i		0			0		−3.27356	+	0.651152i		0		1.14805	−	2.77164i		0
131.5		0		1.44015	−	0.962276i	−1.41421	+	1.41421i		0			0		−1.85085	+	0.368157i		0		1.14805	−	2.77164i		0
131.6		0		1.44015	−	0.962276i	−1.41421	+	1.41421i		0			0		5.12441	−	1.01931i		0		1.14805	−	2.77164i		0
158.1		0		−0.962276	−	1.44015i	−1.41421	+	1.41421i		0			0		−0.651152	−	3.27356i		0		−1.14805	+	2.77164i		0
158.2		0		−0.962276	−	1.44015i	−1.41421	+	1.41421i		0			0		−0.368157	−	1.85085i		0		−1.14805	+	2.77164i		0
158.3		0		−0.962276	−	1.44015i	−1.41421	+	1.41421i		0			0		1.01931	+	5.12441i		0		−1.14805	+	2.77164i		0
158.4		0		0.962276	+	1.44015i	−1.41421	+	1.41421i		0			0		−1.01931	−	5.12441i		0		−1.14805	+	2.77164i		0
158.5		0		0.962276	+	1.44015i	−1.41421	+	1.41421i		0			0		0.368157	+	1.85085i		0		−1.14805	+	2.77164i		0
158.6		0		0.962276	+	1.44015i	−1.41421	+	1.41421i		0			0		0.651152	+	3.27356i		0		−1.14805	+	2.77164i		0
224.1		0		−1.69877	−	0.337906i	1.41421	−	1.41421i		0			0		−1.85432	+	2.77519i		0		2.77164	+	1.14805i		0
224.2		0		−1.69877	−	0.337906i	1.41421	−	1.41421i		0			0		−1.04842	+	1.56907i		0		2.77164	+	1.14805i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by \(\Q(\sqrt{-3}) \)
17.b	even	2	1	inner
17.c	even	4	2	inner
17.d	even	8	4	inner
17.e	odd	16	8	inner
51.c	odd	2	1	inner
51.f	odd	4	2	inner
51.g	odd	8	4	inner
51.i	even	16	8	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	867.2.i.j	✓	48
3.b	odd	2	1	CM	867.2.i.j	✓	48
17.b	even	2	1	inner	867.2.i.j	✓	48
17.c	even	4	2	inner	867.2.i.j	✓	48
17.d	even	8	4	inner	867.2.i.j	✓	48
17.e	odd	16	8	inner	867.2.i.j	✓	48
51.c	odd	2	1	inner	867.2.i.j	✓	48
51.f	odd	4	2	inner	867.2.i.j	✓	48
51.g	odd	8	4	inner	867.2.i.j	✓	48
51.i	even	16	8	inner	867.2.i.j	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
867.2.i.j	✓	48	1.a	even	1	1	trivial
867.2.i.j	✓	48	3.b	odd	2	1	CM
867.2.i.j	✓	48	17.b	even	2	1	inner
867.2.i.j	✓	48	17.c	even	4	2	inner
867.2.i.j	✓	48	17.d	even	8	4	inner
867.2.i.j	✓	48	17.e	odd	16	8	inner
867.2.i.j	✓	48	51.c	odd	2	1	inner
867.2.i.j	✓	48	51.f	odd	4	2	inner
867.2.i.j	✓	48	51.g	odd	8	4	inner
867.2.i.j	✓	48	51.i	even	16	8	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(867, [\chi])\):

\( T_{2} \)

\( T_{5} \)

\( T_{7}^{48} + 308643387066T_{7}^{32} + 73167636837666909573T_{7}^{16} + 1892464114417162481155041 \)