Newform orbit 140.3.v.a

• Label: 140.3.v.a
• Level: $140$
• Weight: $3$
• Character orbit: 140.v
• Analytic conductor: $3.815$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.81472370104\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 2 q^{5} + 14 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1		0		−4.50237	−	1.20641i		0		−4.21691	−	2.68657i		0		6.42104	+	2.78752i		0		11.0217	+	6.36340i		0
37.2		0		−3.88617	−	1.04130i		0		2.15135	+	4.51350i		0		4.09938	−	5.67407i		0		6.22381	+	3.59332i		0
37.3		0		−2.98414	−	0.799597i		0		3.75317	−	3.30359i		0		−5.40088	+	4.45315i		0		0.471494	+	0.272217i		0
37.4		0		−0.317678	−	0.0851214i		0		0.508888	+	4.97404i		0		−3.93451	+	5.78962i		0		−7.70056	−	4.44592i		0
37.5		0		0.162004	+	0.0434089i		0		−4.71847	−	1.65409i		0		−3.83953	−	5.85303i		0		−7.76987	−	4.48594i		0
37.6		0		2.08109	+	0.557625i		0		2.10855	−	4.53365i		0		6.36074	+	2.92249i		0		−3.77426	−	2.17907i		0
37.7		0		3.77365	+	1.01115i		0		4.62825	+	1.89192i		0		−0.148507	−	6.99842i		0		5.42377	+	3.13141i		0
37.8		0		5.67362	+	1.52024i		0		−4.71482	+	1.66448i		0		−0.923768	+	6.93878i		0		22.0847	+	12.7506i		0
53.1		0		−4.50237	+	1.20641i		0		−4.21691	+	2.68657i		0		6.42104	−	2.78752i		0		11.0217	−	6.36340i		0
53.2		0		−3.88617	+	1.04130i		0		2.15135	−	4.51350i		0		4.09938	+	5.67407i		0		6.22381	−	3.59332i		0
53.3		0		−2.98414	+	0.799597i		0		3.75317	+	3.30359i		0		−5.40088	−	4.45315i		0		0.471494	−	0.272217i		0
53.4		0		−0.317678	+	0.0851214i		0		0.508888	−	4.97404i		0		−3.93451	−	5.78962i		0		−7.70056	+	4.44592i		0
53.5		0		0.162004	−	0.0434089i		0		−4.71847	+	1.65409i		0		−3.83953	+	5.85303i		0		−7.76987	+	4.48594i		0
53.6		0		2.08109	−	0.557625i		0		2.10855	+	4.53365i		0		6.36074	−	2.92249i		0		−3.77426	+	2.17907i		0
53.7		0		3.77365	−	1.01115i		0		4.62825	−	1.89192i		0		−0.148507	+	6.99842i		0		5.42377	−	3.13141i		0
53.8		0		5.67362	−	1.52024i		0		−4.71482	−	1.66448i		0		−0.923768	−	6.93878i		0		22.0847	−	12.7506i		0
93.1		0		−1.52024	+	5.67362i		0		0.915925	+	4.91539i		0		6.93878	+	0.923768i		0		−22.0847	−	12.7506i		0
93.2		0		−1.01115	+	3.77365i		0		−3.95257	−	3.06222i		0		−6.99842	+	0.148507i		0		−5.42377	−	3.13141i		0
93.3		0		−0.557625	+	2.08109i		0		2.87198	−	4.09288i		0		2.92249	−	6.36074i		0		3.77426	+	2.17907i		0
93.4		0		−0.0434089	+	0.162004i		0		3.79172	+	3.25927i		0		−5.85303	+	3.83953i		0		7.76987	+	4.48594i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.c	even	3	1	inner
35.l	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	140.3.v.a	✓	32
5.b	even	2	1		700.3.bd.b		32
5.c	odd	4	1	inner	140.3.v.a	✓	32
5.c	odd	4	1		700.3.bd.b		32
7.c	even	3	1	inner	140.3.v.a	✓	32
7.c	even	3	1		980.3.l.f		16
7.d	odd	6	1		980.3.l.e		16
35.j	even	6	1		700.3.bd.b		32
35.k	even	12	1		980.3.l.e		16
35.l	odd	12	1	inner	140.3.v.a	✓	32
35.l	odd	12	1		700.3.bd.b		32
35.l	odd	12	1		980.3.l.f		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.3.v.a	✓	32	1.a	even	1	1	trivial
140.3.v.a	✓	32	5.c	odd	4	1	inner
140.3.v.a	✓	32	7.c	even	3	1	inner
140.3.v.a	✓	32	35.l	odd	12	1	inner
700.3.bd.b		32	5.b	even	2	1
700.3.bd.b		32	5.c	odd	4	1
700.3.bd.b		32	35.j	even	6	1
700.3.bd.b		32	35.l	odd	12	1
980.3.l.e		16	7.d	odd	6	1
980.3.l.e		16	35.k	even	12	1
980.3.l.f		16	7.c	even	3	1
980.3.l.f		16	35.l	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(140, [\chi])\).