Newform orbit 1540.3.f.a

• Label: 1540.3.f.a
• Level: $1540$
• Weight: $3$
• Character orbit: 1540.f
• Analytic conductor: $41.962$
• Analytic rank: $0$
• Dimension: $72$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1540 = 2^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1540.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(41.9619607115\)
Analytic rank:	\(0\)
Dimension:	\(72\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 6 q^{5} - 232 q^{9} + 6 q^{11} + 26 q^{15} + 18 q^{25} + 92 q^{31} - 264 q^{45} + 504 q^{49} + 58 q^{55} - 228 q^{59} + 308 q^{69} - 396 q^{71} + 94 q^{75} + 608 q^{81} + 116 q^{89} - 84 q^{91} + 864 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1429.1		0			−	4.93754i		0		−2.01498	−	4.57601i		0		2.64575				0		−15.3793				0
1429.2		0				4.93754i		0		−2.01498	+	4.57601i		0		2.64575				0		−15.3793				0
1429.3		0			−	1.16268i		0		−0.499384	+	4.97500i		0		−2.64575				0		7.64817				0
1429.4		0				1.16268i		0		−0.499384	−	4.97500i		0		−2.64575				0		7.64817				0
1429.5		0			−	0.620613i		0		4.13274	−	2.81433i		0		2.64575				0		8.61484				0
1429.6		0				0.620613i		0		4.13274	+	2.81433i		0		2.64575				0		8.61484				0
1429.7		0			−	2.25266i		0		4.67965	+	1.76094i		0		2.64575				0		3.92554				0
1429.8		0				2.25266i		0		4.67965	−	1.76094i		0		2.64575				0		3.92554				0
1429.9		0			−	3.72296i		0		−3.95351	−	3.06101i		0		−2.64575				0		−4.86047				0
1429.10		0				3.72296i		0		−3.95351	+	3.06101i		0		−2.64575				0		−4.86047				0
1429.11		0			−	4.68761i		0		2.45713	−	4.35460i		0		−2.64575				0		−12.9737				0
1429.12		0				4.68761i		0		2.45713	+	4.35460i		0		−2.64575				0		−12.9737				0
1429.13		0			−	4.12266i		0		4.95701	+	0.654263i		0		2.64575				0		−7.99634				0
1429.14		0				4.12266i		0		4.95701	−	0.654263i		0		2.64575				0		−7.99634				0
1429.15		0			−	5.13443i		0		1.03590	+	4.89151i		0		2.64575				0		−17.3624				0
1429.16		0				5.13443i		0		1.03590	−	4.89151i		0		2.64575				0		−17.3624				0
1429.17		0			−	4.00453i		0		2.27812	+	4.45086i		0		2.64575				0		−7.03629				0
1429.18		0				4.00453i		0		2.27812	−	4.45086i		0		2.64575				0		−7.03629				0
1429.19		0			−	5.01331i		0		−4.04975	+	2.93249i		0		−2.64575				0		−16.1333				0
1429.20		0				5.01331i		0		−4.04975	−	2.93249i		0		−2.64575				0		−16.1333				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1540.3.f.a	✓	72
5.b	even	2	1	inner	1540.3.f.a	✓	72
11.b	odd	2	1	inner	1540.3.f.a	✓	72
55.d	odd	2	1	inner	1540.3.f.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1540.3.f.a	✓	72	1.a	even	1	1	trivial
1540.3.f.a	✓	72	5.b	even	2	1	inner
1540.3.f.a	✓	72	11.b	odd	2	1	inner
1540.3.f.a	✓	72	55.d	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1540, [\chi])\).