Newform orbit 1044.2.z.c

• Label: 1044.2.z.c
• Level: $1044$
• Weight: $2$
• Character orbit: 1044.z
• Analytic conductor: $8.336$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1044.z (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.33638197102\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(4\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
109.1		0			0			0		−0.700940	−	3.07102i		0		2.15220	+	1.03645i		0			0			0
109.2		0			0			0		−0.0963412	−	0.422098i		0		−1.75124	−	0.843350i		0			0			0
109.3		0			0			0		0.0963412	+	0.422098i		0		−1.75124	−	0.843350i		0			0			0
109.4		0			0			0		0.700940	+	3.07102i		0		2.15220	+	1.03645i		0			0			0
325.1		0			0			0		−1.81616	+	2.27739i		0		−0.620985	+	2.72071i		0			0			0
325.2		0			0			0		−1.39542	+	1.74981i		0		0.343506	−	1.50500i		0			0			0
325.3		0			0			0		1.39542	−	1.74981i		0		0.343506	−	1.50500i		0			0			0
325.4		0			0			0		1.81616	−	2.27739i		0		−0.620985	+	2.72071i		0			0			0
361.1		0			0			0		−2.10154	−	1.01205i		0		−2.51961	+	3.15949i		0			0			0
361.2		0			0			0		−1.25988	−	0.606724i		0		1.39612	−	1.75068i		0			0			0
361.3		0			0			0		1.25988	+	0.606724i		0		1.39612	−	1.75068i		0			0			0
361.4		0			0			0		2.10154	+	1.01205i		0		−2.51961	+	3.15949i		0			0			0
469.1		0			0			0		−1.81616	−	2.27739i		0		−0.620985	−	2.72071i		0			0			0
469.2		0			0			0		−1.39542	−	1.74981i		0		0.343506	+	1.50500i		0			0			0
469.3		0			0			0		1.39542	+	1.74981i		0		0.343506	+	1.50500i		0			0			0
469.4		0			0			0		1.81616	+	2.27739i		0		−0.620985	−	2.72071i		0			0			0
613.1		0			0			0		−0.700940	+	3.07102i		0		2.15220	−	1.03645i		0			0			0
613.2		0			0			0		−0.0963412	+	0.422098i		0		−1.75124	+	0.843350i		0			0			0
613.3		0			0			0		0.0963412	−	0.422098i		0		−1.75124	+	0.843350i		0			0			0
613.4		0			0			0		0.700940	−	3.07102i		0		2.15220	−	1.03645i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
29.e	even	14	1	inner
87.h	odd	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1044.2.z.c	✓	24
3.b	odd	2	1	inner	1044.2.z.c	✓	24
29.e	even	14	1	inner	1044.2.z.c	✓	24
87.h	odd	14	1	inner	1044.2.z.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1044.2.z.c	✓	24	1.a	even	1	1	trivial
1044.2.z.c	✓	24	3.b	odd	2	1	inner
1044.2.z.c	✓	24	29.e	even	14	1	inner
1044.2.z.c	✓	24	87.h	odd	14	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 15*T5^22 + 146*T5^20 + 1005*T5^18 + 5207*T5^16 + 13270*T5^14 + 256711*T5^12 - 19912*T5^10 + 5121749*T5^8 - 9215069*T5^6 + 16611432*T5^4 + 6414307*T5^2 + 707281