Newform orbit 1440.3.p.a

• Label: 1440.3.p.a
• Level: $1440$
• Weight: $3$
• Character orbit: 1440.p
• Self dual: yes
• Analytic conductor: $39.237$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -40
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1440.p (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(39.2371580679\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

q - 5 * q^5 - 6 * q^7 - 18 * q^11 - 6 * q^13 + 2 * q^19 - 26 * q^23 + 25 * q^25 + 30 * q^35 - 54 * q^37 + 78 * q^41 + 86 * q^47 - 13 * q^49 - 74 * q^53 + 90 * q^55 + 78 * q^59 + 30 * q^65 + 108 * q^77 - 18 * q^89 + 36 * q^91 - 10 * q^95

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\)	\(577\)	\(641\)	\(901\)	\(991\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

559.1

0

0

0

0

−5.00000

0

−6.00000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by \(\Q(\sqrt{-10}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1440.3.p.a		1
3.b	odd	2	1		160.3.e.b		1
4.b	odd	2	1		360.3.p.b		1
5.b	even	2	1		1440.3.p.b		1
8.b	even	2	1		360.3.p.a		1
8.d	odd	2	1		1440.3.p.b		1
12.b	even	2	1		40.3.e.a	✓	1
15.d	odd	2	1		160.3.e.a		1
15.e	even	4	2		800.3.g.c		2
20.d	odd	2	1		360.3.p.a		1
24.f	even	2	1		160.3.e.a		1
24.h	odd	2	1		40.3.e.b	yes	1
40.e	odd	2	1	CM	1440.3.p.a		1
40.f	even	2	1		360.3.p.b		1
48.i	odd	4	2		1280.3.h.c		2
48.k	even	4	2		1280.3.h.b		2
60.h	even	2	1		40.3.e.b	yes	1
60.l	odd	4	2		200.3.g.c		2
120.i	odd	2	1		40.3.e.a	✓	1
120.m	even	2	1		160.3.e.b		1
120.q	odd	4	2		800.3.g.c		2
120.w	even	4	2		200.3.g.c		2
240.t	even	4	2		1280.3.h.c		2
240.bm	odd	4	2		1280.3.h.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
40.3.e.a	✓	1	12.b	even	2	1
40.3.e.a	✓	1	120.i	odd	2	1
40.3.e.b	yes	1	24.h	odd	2	1
40.3.e.b	yes	1	60.h	even	2	1
160.3.e.a		1	15.d	odd	2	1
160.3.e.a		1	24.f	even	2	1
160.3.e.b		1	3.b	odd	2	1
160.3.e.b		1	120.m	even	2	1
200.3.g.c		2	60.l	odd	4	2
200.3.g.c		2	120.w	even	4	2
360.3.p.a		1	8.b	even	2	1
360.3.p.a		1	20.d	odd	2	1
360.3.p.b		1	4.b	odd	2	1
360.3.p.b		1	40.f	even	2	1
800.3.g.c		2	15.e	even	4	2
800.3.g.c		2	120.q	odd	4	2
1280.3.h.b		2	48.k	even	4	2
1280.3.h.b		2	240.bm	odd	4	2
1280.3.h.c		2	48.i	odd	4	2
1280.3.h.c		2	240.t	even	4	2
1440.3.p.a		1	1.a	even	1	1	trivial
1440.3.p.a		1	40.e	odd	2	1	CM
1440.3.p.b		1	5.b	even	2	1
1440.3.p.b		1	8.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1440, [\chi])\):

\( T_{7} + 6 \)

\( T_{23} + 26 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T + 5 \)
$7$	\( T + 6 \)
$11$	\( T + 18 \)