Newform orbit 1860.3.e.a

• Label: 1860.3.e.a
• Level: $1860$
• Weight: $3$
• Character orbit: 1860.e
• Analytic conductor: $50.681$
• Analytic rank: $0$
• Dimension: $64$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1860.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(50.6813291710\)
Analytic rank:	\(0\)
Dimension:	\(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 192 q^{9} - 8 q^{19} - 16 q^{25} + 48 q^{31} + 36 q^{35} - 24 q^{39} - 64 q^{41} - 384 q^{49} - 408 q^{59} + 584 q^{71} + 576 q^{81} - 68 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1549.1		0		−1.73205				0		−4.72048	−	1.64836i		0			−	11.3695i		0		3.00000				0
1549.2		0		−1.73205				0		−4.72048	+	1.64836i		0				11.3695i		0		3.00000				0
1549.3		0		−1.73205				0		−4.70035	−	1.70490i		0				7.69740i		0		3.00000				0
1549.4		0		−1.73205				0		−4.70035	+	1.70490i		0			−	7.69740i		0		3.00000				0
1549.5		0		−1.73205				0		−4.41328	−	2.35009i		0				6.38134i		0		3.00000				0
1549.6		0		−1.73205				0		−4.41328	+	2.35009i		0			−	6.38134i		0		3.00000				0
1549.7		0		−1.73205				0		−4.40643	−	2.36291i		0			−	0.138944i		0		3.00000				0
1549.8		0		−1.73205				0		−4.40643	+	2.36291i		0				0.138944i		0		3.00000				0
1549.9		0		−1.73205				0		−3.53306	−	3.53801i		0				1.83950i		0		3.00000				0
1549.10		0		−1.73205				0		−3.53306	+	3.53801i		0			−	1.83950i		0		3.00000				0
1549.11		0		−1.73205				0		−2.07885	−	4.54735i		0			−	6.86029i		0		3.00000				0
1549.12		0		−1.73205				0		−2.07885	+	4.54735i		0				6.86029i		0		3.00000				0
1549.13		0		−1.73205				0		−1.49788	−	4.77036i		0			−	7.41663i		0		3.00000				0
1549.14		0		−1.73205				0		−1.49788	+	4.77036i		0				7.41663i		0		3.00000				0
1549.15		0		−1.73205				0		−0.0667084	−	4.99955i		0				12.5178i		0		3.00000				0
1549.16		0		−1.73205				0		−0.0667084	+	4.99955i		0			−	12.5178i		0		3.00000				0
1549.17		0		−1.73205				0		1.11186	−	4.87481i		0				3.53605i		0		3.00000				0
1549.18		0		−1.73205				0		1.11186	+	4.87481i		0			−	3.53605i		0		3.00000				0
1549.19		0		−1.73205				0		1.83089	−	4.65272i		0			−	1.95219i		0		3.00000				0
1549.20		0		−1.73205				0		1.83089	+	4.65272i		0				1.95219i		0		3.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
31.b	odd	2	1	inner
155.c	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1860.3.e.a	✓	64
5.b	even	2	1	inner	1860.3.e.a	✓	64
31.b	odd	2	1	inner	1860.3.e.a	✓	64
155.c	odd	2	1	inner	1860.3.e.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1860.3.e.a	✓	64	1.a	even	1	1	trivial
1860.3.e.a	✓	64	5.b	even	2	1	inner
1860.3.e.a	✓	64	31.b	odd	2	1	inner
1860.3.e.a	✓	64	155.c	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1860, [\chi])\).