Newform orbit 1232.2.j.b

• Label: 1232.2.j.b
• Level: $1232$
• Weight: $2$
• Character orbit: 1232.j
• Analytic conductor: $9.838$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.83756952902\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{9} + 20 q^{21} - 56 q^{29} + 40 q^{37} - 8 q^{49} + 16 q^{53} + 8 q^{57} - 96 q^{65} - 4 q^{77} + 40 q^{81} - 32 q^{85} + 8 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
111.1		0		−3.13533				0				0.346215i		0		0.914125	−	2.48282i		0		6.83028				0
111.2		0		−3.13533				0			−	0.346215i		0		0.914125	+	2.48282i		0		6.83028				0
111.3		0		−2.46270				0			−	0.426276i		0		−2.25474	−	1.38425i		0		3.06490				0
111.4		0		−2.46270				0				0.426276i		0		−2.25474	+	1.38425i		0		3.06490				0
111.5		0		−2.09096				0				4.10846i		0		−1.54971	+	2.14439i		0		1.37213				0
111.6		0		−2.09096				0			−	4.10846i		0		−1.54971	−	2.14439i		0		1.37213				0
111.7		0		−1.03324				0				2.56834i		0		−0.330305	−	2.62505i		0		−1.93241				0
111.8		0		−1.03324				0			−	2.56834i		0		−0.330305	+	2.62505i		0		−1.93241				0
111.9		0		−0.750319				0				2.20615i		0		2.61623	−	0.394113i		0		−2.43702				0
111.10		0		−0.750319				0			−	2.20615i		0		2.61623	+	0.394113i		0		−2.43702				0
111.11		0		−0.319573				0			−	1.16428i		0		−2.17374	+	1.50826i		0		−2.89787				0
111.12		0		−0.319573				0				1.16428i		0		−2.17374	−	1.50826i		0		−2.89787				0
111.13		0		0.319573				0			−	1.16428i		0		2.17374	−	1.50826i		0		−2.89787				0
111.14		0		0.319573				0				1.16428i		0		2.17374	+	1.50826i		0		−2.89787				0
111.15		0		0.750319				0				2.20615i		0		−2.61623	+	0.394113i		0		−2.43702				0
111.16		0		0.750319				0			−	2.20615i		0		−2.61623	−	0.394113i		0		−2.43702				0
111.17		0		1.03324				0				2.56834i		0		0.330305	+	2.62505i		0		−1.93241				0
111.18		0		1.03324				0			−	2.56834i		0		0.330305	−	2.62505i		0		−1.93241				0
111.19		0		2.09096				0				4.10846i		0		1.54971	−	2.14439i		0		1.37213				0
111.20		0		2.09096				0			−	4.10846i		0		1.54971	+	2.14439i		0		1.37213				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.b	odd	2	1	inner
28.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1232.2.j.b	✓	24
4.b	odd	2	1	inner	1232.2.j.b	✓	24
7.b	odd	2	1	inner	1232.2.j.b	✓	24
28.d	even	2	1	inner	1232.2.j.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1232.2.j.b	✓	24	1.a	even	1	1	trivial
1232.2.j.b	✓	24	4.b	odd	2	1	inner
1232.2.j.b	✓	24	7.b	odd	2	1	inner
1232.2.j.b	✓	24	28.d	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 22T_{3}^{10} + 165T_{3}^{8} - 500T_{3}^{6} + 552T_{3}^{4} - 208T_{3}^{2} + 16 \) acting on \(S_{2}^{\mathrm{new}}(1232, [\chi])\).