Newform orbit 1472.2.h.c

• Label: 1472.2.h.c
• Level: $1472$
• Weight: $2$
• Character orbit: 1472.h
• Analytic conductor: $11.754$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.7539791775\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 40 q^{9} + 32 q^{25} + 8 q^{41} + 48 q^{49} - 104 q^{73} + 112 q^{81}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
735.1		0		−3.22426				0		−3.21270				0		−2.55933				0		7.39585				0
735.2		0		−3.22426				0		3.21270				0		2.55933				0		7.39585				0
735.3		0		−3.22426				0		3.21270				0		2.55933				0		7.39585				0
735.4		0		−3.22426				0		−3.21270				0		−2.55933				0		7.39585				0
735.5		0		−2.11141				0		−2.66434				0		1.46622				0		1.45804				0
735.6		0		−2.11141				0		2.66434				0		−1.46622				0		1.45804				0
735.7		0		−2.11141				0		2.66434				0		−1.46622				0		1.45804				0
735.8		0		−2.11141				0		−2.66434				0		1.46622				0		1.45804				0
735.9		0		−1.29814				0		−0.128981				0		1.95094				0		−1.31484				0
735.10		0		−1.29814				0		0.128981				0		−1.95094				0		−1.31484				0
735.11		0		−1.29814				0		0.128981				0		−1.95094				0		−1.31484				0
735.12		0		−1.29814				0		−0.128981				0		1.95094				0		−1.31484				0
735.13		0		−0.678936				0		2.56187				0		4.63615				0		−2.53905				0
735.14		0		−0.678936				0		−2.56187				0		−4.63615				0		−2.53905				0
735.15		0		−0.678936				0		−2.56187				0		−4.63615				0		−2.53905				0
735.16		0		−0.678936				0		2.56187				0		4.63615				0		−2.53905				0
735.17		0		0.678936				0		2.56187				0		−4.63615				0		−2.53905				0
735.18		0		0.678936				0		−2.56187				0		4.63615				0		−2.53905				0
735.19		0		0.678936				0		−2.56187				0		4.63615				0		−2.53905				0
735.20		0		0.678936				0		2.56187				0		−4.63615				0		−2.53905				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
8.b	even	2	1	inner
8.d	odd	2	1	inner
23.b	odd	2	1	inner
92.b	even	2	1	inner
184.e	odd	2	1	inner
184.h	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1472.2.h.c	✓	32
4.b	odd	2	1	inner	1472.2.h.c	✓	32
8.b	even	2	1	inner	1472.2.h.c	✓	32
8.d	odd	2	1	inner	1472.2.h.c	✓	32
23.b	odd	2	1	inner	1472.2.h.c	✓	32
92.b	even	2	1	inner	1472.2.h.c	✓	32
184.e	odd	2	1	inner	1472.2.h.c	✓	32
184.h	even	2	1	inner	1472.2.h.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1472.2.h.c	✓	32	1.a	even	1	1	trivial
1472.2.h.c	✓	32	4.b	odd	2	1	inner
1472.2.h.c	✓	32	8.b	even	2	1	inner
1472.2.h.c	✓	32	8.d	odd	2	1	inner
1472.2.h.c	✓	32	23.b	odd	2	1	inner
1472.2.h.c	✓	32	92.b	even	2	1	inner
1472.2.h.c	✓	32	184.e	odd	2	1	inner
1472.2.h.c	✓	32	184.h	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{8} - 17T_{3}^{6} + 79T_{3}^{4} - 111T_{3}^{2} + 36 \) acting on \(S_{2}^{\mathrm{new}}(1472, [\chi])\).