Newform orbit 891.2.d.c

• Label: 891.2.d.c
• Level: $891$
• Weight: $2$
• Character orbit: 891.d
• Analytic conductor: $7.115$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.11467082010\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
890.1	−2.72623				0		5.43234				−	3.56048i		0			−	1.74007i	−9.35736				0				9.70671i
890.2	−2.72623				0		5.43234					3.56048i		0				1.74007i	−9.35736				0			−	9.70671i
890.3	−2.29736				0		3.27787				−	1.02695i		0				2.98168i	−2.93572				0				2.35926i
890.4	−2.29736				0		3.27787					1.02695i		0			−	2.98168i	−2.93572				0			−	2.35926i
890.5	−1.78114				0		1.17248				−	2.30190i		0				1.42536i	1.47394				0				4.10001i
890.6	−1.78114				0		1.17248					2.30190i		0			−	1.42536i	1.47394				0			−	4.10001i
890.7	−1.28235				0		−0.355579				−	2.71071i		0				0.132015i	3.02068				0				3.47607i
890.8	−1.28235				0		−0.355579					2.71071i		0			−	0.132015i	3.02068				0			−	3.47607i
890.9	−0.587929				0		−1.65434				−	3.09798i		0			−	4.55548i	2.14849				0				1.82139i
890.10	−0.587929				0		−1.65434					3.09798i		0				4.55548i	2.14849				0			−	1.82139i
890.11	−0.356696				0		−1.87277				−	0.155629i		0			−	2.69819i	1.38140				0				0.0555122i
890.12	−0.356696				0		−1.87277					0.155629i		0				2.69819i	1.38140				0			−	0.0555122i
890.13	0.356696				0		−1.87277				−	0.155629i		0				2.69819i	−1.38140				0			−	0.0555122i
890.14	0.356696				0		−1.87277					0.155629i		0			−	2.69819i	−1.38140				0				0.0555122i
890.15	0.587929				0		−1.65434				−	3.09798i		0				4.55548i	−2.14849				0			−	1.82139i
890.16	0.587929				0		−1.65434					3.09798i		0			−	4.55548i	−2.14849				0				1.82139i
890.17	1.28235				0		−0.355579				−	2.71071i		0			−	0.132015i	−3.02068				0			−	3.47607i
890.18	1.28235				0		−0.355579					2.71071i		0				0.132015i	−3.02068				0				3.47607i
890.19	1.78114				0		1.17248				−	2.30190i		0			−	1.42536i	−1.47394				0			−	4.10001i
890.20	1.78114				0		1.17248					2.30190i		0				1.42536i	−1.47394				0				4.10001i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.b	odd	2	1	inner
33.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	891.2.d.c	✓	24
3.b	odd	2	1	inner	891.2.d.c	✓	24
9.c	even	3	2		891.2.g.f		48
9.d	odd	6	2		891.2.g.f		48
11.b	odd	2	1	inner	891.2.d.c	✓	24
33.d	even	2	1	inner	891.2.d.c	✓	24
99.g	even	6	2		891.2.g.f		48
99.h	odd	6	2		891.2.g.f		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
891.2.d.c	✓	24	1.a	even	1	1	trivial
891.2.d.c	✓	24	3.b	odd	2	1	inner
891.2.d.c	✓	24	11.b	odd	2	1	inner
891.2.d.c	✓	24	33.d	even	2	1	inner
891.2.g.f		48	9.c	even	3	2
891.2.g.f		48	9.d	odd	6	2
891.2.g.f		48	99.g	even	6	2
891.2.g.f		48	99.h	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} - 18T_{2}^{10} + 114T_{2}^{8} - 306T_{2}^{6} + 330T_{2}^{4} - 108T_{2}^{2} + 9 \) acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\).