Newform orbit 4140.2.f.d

• Label: 4140.2.f.d
• Level: $4140$
• Weight: $2$
• Character orbit: 4140.f
• Analytic conductor: $33.058$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4140.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(33.0580664368\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{19} - 8 q^{25} - 12 q^{31} - 28 q^{49} - 16 q^{55} - 16 q^{61} + 8 q^{79} + 12 q^{85} - 16 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
829.1		0			0			0		−2.23083	−	0.152950i		0			−	4.09652i		0			0			0
829.2		0			0			0		−2.23083	+	0.152950i		0				4.09652i		0			0			0
829.3		0			0			0		−2.09906	−	0.770673i		0			−	2.34084i		0			0			0
829.4		0			0			0		−2.09906	+	0.770673i		0				2.34084i		0			0			0
829.5		0			0			0		−1.79970	−	1.32706i		0				0.476731i		0			0			0
829.6		0			0			0		−1.79970	+	1.32706i		0			−	0.476731i		0			0			0
829.7		0			0			0		−1.06710	−	1.96502i		0				3.96013i		0			0			0
829.8		0			0			0		−1.06710	+	1.96502i		0			−	3.96013i		0			0			0
829.9		0			0			0		−0.405664	−	2.19896i		0			−	3.23277i		0			0			0
829.10		0			0			0		−0.405664	+	2.19896i		0				3.23277i		0			0			0
829.11		0			0			0		−0.274117	−	2.21920i		0			−	0.615120i		0			0			0
829.12		0			0			0		−0.274117	+	2.21920i		0				0.615120i		0			0			0
829.13		0			0			0		0.274117	−	2.21920i		0				0.615120i		0			0			0
829.14		0			0			0		0.274117	+	2.21920i		0			−	0.615120i		0			0			0
829.15		0			0			0		0.405664	−	2.19896i		0				3.23277i		0			0			0
829.16		0			0			0		0.405664	+	2.19896i		0			−	3.23277i		0			0			0
829.17		0			0			0		1.06710	−	1.96502i		0			−	3.96013i		0			0			0
829.18		0			0			0		1.06710	+	1.96502i		0				3.96013i		0			0			0
829.19		0			0			0		1.79970	−	1.32706i		0			−	0.476731i		0			0			0
829.20		0			0			0		1.79970	+	1.32706i		0				0.476731i		0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4140.2.f.d	✓	24
3.b	odd	2	1	inner	4140.2.f.d	✓	24
5.b	even	2	1	inner	4140.2.f.d	✓	24
15.d	odd	2	1	inner	4140.2.f.d	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4140.2.f.d	✓	24	1.a	even	1	1	trivial
4140.2.f.d	✓	24	3.b	odd	2	1	inner
4140.2.f.d	✓	24	5.b	even	2	1	inner
4140.2.f.d	✓	24	15.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{12} + 49T_{7}^{10} + 867T_{7}^{8} + 6563T_{7}^{6} + 18808T_{7}^{4} + 9648T_{7}^{2} + 1296 \) acting on \(S_{2}^{\mathrm{new}}(4140, [\chi])\).