Newform orbit 1380.3.v.a

• Label: 1380.3.v.a
• Level: $1380$
• Weight: $3$
• Character orbit: 1380.v
• Analytic conductor: $37.602$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1380.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(37.6022764817\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(44\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 16 q^{5} - 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
277.1		0		−1.22474	+	1.22474i		0		−3.40158	+	3.66459i		0		9.42912	+	9.42912i		0			−	3.00000i		0
277.2		0		−1.22474	+	1.22474i		0		−4.63542	+	1.87428i		0		−9.22892	−	9.22892i		0			−	3.00000i		0
277.3		0		−1.22474	+	1.22474i		0		−0.526722	−	4.97218i		0		7.67284	+	7.67284i		0			−	3.00000i		0
277.4		0		−1.22474	+	1.22474i		0		−2.04681	−	4.56186i		0		−7.12564	−	7.12564i		0			−	3.00000i		0
277.5		0		−1.22474	+	1.22474i		0		1.57872	+	4.74422i		0		−6.58095	−	6.58095i		0			−	3.00000i		0
277.6		0		−1.22474	+	1.22474i		0		4.99409	−	0.242975i		0		−6.51621	−	6.51621i		0			−	3.00000i		0
277.7		0		−1.22474	+	1.22474i		0		−4.59646	+	1.96789i		0		−6.41029	−	6.41029i		0			−	3.00000i		0
277.8		0		−1.22474	+	1.22474i		0		1.55102	−	4.75335i		0		−6.05286	−	6.05286i		0			−	3.00000i		0
277.9		0		−1.22474	+	1.22474i		0		0.781620	−	4.93853i		0		−4.68723	−	4.68723i		0			−	3.00000i		0
277.10		0		−1.22474	+	1.22474i		0		−2.12370	+	4.52657i		0		−4.15416	−	4.15416i		0			−	3.00000i		0
277.11		0		−1.22474	+	1.22474i		0		4.91724	+	0.905963i		0		−4.05991	−	4.05991i		0			−	3.00000i		0
277.12		0		−1.22474	+	1.22474i		0		−4.49037	+	2.19921i		0		4.20797	+	4.20797i		0			−	3.00000i		0
277.13		0		−1.22474	+	1.22474i		0		−4.62388	−	1.90255i		0		3.50113	+	3.50113i		0			−	3.00000i		0
277.14		0		−1.22474	+	1.22474i		0		−4.99639	+	0.189894i		0		3.06562	+	3.06562i		0			−	3.00000i		0
277.15		0		−1.22474	+	1.22474i		0		3.12244	+	3.90517i		0		2.65258	+	2.65258i		0			−	3.00000i		0
277.16		0		−1.22474	+	1.22474i		0		−4.25453	−	2.62659i		0		−0.977118	−	0.977118i		0			−	3.00000i		0
277.17		0		−1.22474	+	1.22474i		0		4.24991	−	2.63405i		0		0.194916	+	0.194916i		0			−	3.00000i		0
277.18		0		−1.22474	+	1.22474i		0		−3.18978	−	3.85036i		0		0.566585	+	0.566585i		0			−	3.00000i		0
277.19		0		−1.22474	+	1.22474i		0		0.286603	+	4.99178i		0		−0.552836	−	0.552836i		0			−	3.00000i		0
277.20		0		−1.22474	+	1.22474i		0		1.99233	+	4.58592i		0		4.73218	+	4.73218i		0			−	3.00000i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1380.3.v.a	✓	88
5.c	odd	4	1	inner	1380.3.v.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1380.3.v.a	✓	88	1.a	even	1	1	trivial
1380.3.v.a	✓	88	5.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1380, [\chi])\).