Newform orbit 1440.3.p.i

• Label: 1440.3.p.i
• Level: $1440$
• Weight: $3$
• Character orbit: 1440.p
• Analytic conductor: $39.237$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

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:	no
Analytic conductor:	\(39.2371580679\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 120)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 32 q^{19} - 24 q^{25} + 96 q^{35} + 80 q^{41} + 168 q^{49} + 128 q^{59} - 16 q^{65} + 400 q^{89} - 384 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
559.1		0			0			0		−4.79248	−	1.42554i		0		−5.41487				0			0			0
559.2		0			0			0		−4.79248	+	1.42554i		0		−5.41487				0			0			0
559.3		0			0			0		−4.40648	−	2.36283i		0		−6.07322				0			0			0
559.4		0			0			0		−4.40648	+	2.36283i		0		−6.07322				0			0			0
559.5		0			0			0		−4.00162	−	2.99784i		0		0.116466				0			0			0
559.6		0			0			0		−4.00162	+	2.99784i		0		0.116466				0			0			0
559.7		0			0			0		−3.24023	−	3.80801i		0		13.5060				0			0			0
559.8		0			0			0		−3.24023	+	3.80801i		0		13.5060				0			0			0
559.9		0			0			0		−1.72202	−	4.69411i		0		−9.26960				0			0			0
559.10		0			0			0		−1.72202	+	4.69411i		0		−9.26960				0			0			0
559.11		0			0			0		−0.371139	−	4.98621i		0		1.20123				0			0			0
559.12		0			0			0		−0.371139	+	4.98621i		0		1.20123				0			0			0
559.13		0			0			0		0.371139	−	4.98621i		0		−1.20123				0			0			0
559.14		0			0			0		0.371139	+	4.98621i		0		−1.20123				0			0			0
559.15		0			0			0		1.72202	−	4.69411i		0		9.26960				0			0			0
559.16		0			0			0		1.72202	+	4.69411i		0		9.26960				0			0			0
559.17		0			0			0		3.24023	−	3.80801i		0		−13.5060				0			0			0
559.18		0			0			0		3.24023	+	3.80801i		0		−13.5060				0			0			0
559.19		0			0			0		4.00162	−	2.99784i		0		−0.116466				0			0			0
559.20		0			0			0		4.00162	+	2.99784i		0		−0.116466				0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.d	odd	2	1	inner
40.e	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1440.3.p.i		24
3.b	odd	2	1		480.3.p.a		24
4.b	odd	2	1		360.3.p.i		24
5.b	even	2	1	inner	1440.3.p.i		24
8.b	even	2	1		360.3.p.i		24
8.d	odd	2	1	inner	1440.3.p.i		24
12.b	even	2	1		120.3.p.a	✓	24
15.d	odd	2	1		480.3.p.a		24
15.e	even	4	2		2400.3.g.e		24
20.d	odd	2	1		360.3.p.i		24
24.f	even	2	1		480.3.p.a		24
24.h	odd	2	1		120.3.p.a	✓	24
40.e	odd	2	1	inner	1440.3.p.i		24
40.f	even	2	1		360.3.p.i		24
60.h	even	2	1		120.3.p.a	✓	24
60.l	odd	4	2		600.3.g.e		24
120.i	odd	2	1		120.3.p.a	✓	24
120.m	even	2	1		480.3.p.a		24
120.q	odd	4	2		2400.3.g.e		24
120.w	even	4	2		600.3.g.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.3.p.a	✓	24	12.b	even	2	1
120.3.p.a	✓	24	24.h	odd	2	1
120.3.p.a	✓	24	60.h	even	2	1
120.3.p.a	✓	24	120.i	odd	2	1
360.3.p.i		24	4.b	odd	2	1
360.3.p.i		24	8.b	even	2	1
360.3.p.i		24	20.d	odd	2	1
360.3.p.i		24	40.f	even	2	1
480.3.p.a		24	3.b	odd	2	1
480.3.p.a		24	15.d	odd	2	1
480.3.p.a		24	24.f	even	2	1
480.3.p.a		24	120.m	even	2	1
600.3.g.e		24	60.l	odd	4	2
600.3.g.e		24	120.w	even	4	2
1440.3.p.i		24	1.a	even	1	1	trivial
1440.3.p.i		24	5.b	even	2	1	inner
1440.3.p.i		24	8.d	odd	2	1	inner
1440.3.p.i		24	40.e	odd	2	1	inner
2400.3.g.e		24	15.e	even	4	2
2400.3.g.e		24	120.q	odd	4	2

Hecke kernels

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

\( T_{7}^{12} - 336T_{7}^{10} + 35008T_{7}^{8} - 1378176T_{7}^{6} + 18885632T_{7}^{4} - 24715264T_{7}^{2} + 331776 \)

T23^12 - 4360*T23^10 + 7043344*T23^8 - 5492439040*T23^6 + 2171871887360*T23^4 - 399197538877440*T23^2 + 23613096954167296