Newform orbit 4028.2.c.a

• Label: 4028.2.c.a
• Level: $4028$
• Weight: $2$
• Character orbit: 4028.c
• Analytic conductor: $32.164$
• Analytic rank: $0$
• Dimension: $82$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4028.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(32.1637419342\)
Analytic rank:	\(0\)
Dimension:	\(82\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 82 q - 8 q^{7} - 82 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3497.1		0			−	3.43171i		0				2.90667i		0		−0.616337				0		−8.77663				0
3497.2		0			−	3.32000i		0			−	0.481923i		0		4.89204				0		−8.02243				0
3497.3		0			−	3.26219i		0				2.63587i		0		−3.36239				0		−7.64188				0
3497.4		0			−	3.23093i		0			−	3.15613i		0		−4.75851				0		−7.43889				0
3497.5		0			−	3.07917i		0				0.328536i		0		−0.0673750				0		−6.48127				0
3497.6		0			−	3.02294i		0			−	2.23488i		0		1.30562				0		−6.13814				0
3497.7		0			−	2.92218i		0				2.97792i		0		2.58698				0		−5.53915				0
3497.8		0			−	2.85178i		0			−	0.944719i		0		0.420631				0		−5.13267				0
3497.9		0			−	2.65407i		0			−	1.30709i		0		−2.08185				0		−4.04406				0
3497.10		0			−	2.57074i		0				2.44297i		0		3.60312				0		−3.60868				0
3497.11		0			−	2.47054i		0				0.894697i		0		−2.25054				0		−3.10359				0
3497.12		0			−	2.46723i		0			−	4.35102i		0		1.12403				0		−3.08725				0
3497.13		0			−	2.38052i		0				1.77530i		0		−1.28291				0		−2.66687				0
3497.14		0			−	2.33396i		0			−	3.41794i		0		2.47388				0		−2.44737				0
3497.15		0			−	2.31112i		0				0.310021i		0		2.57819				0		−2.34128				0
3497.16		0			−	2.26231i		0			−	0.110491i		0		−4.79793				0		−2.11803				0
3497.17		0			−	2.19213i		0				3.88947i		0		−3.90251				0		−1.80545				0
3497.18		0			−	2.07591i		0			−	1.80942i		0		1.11331				0		−1.30941				0
3497.19		0			−	2.06657i		0				3.50814i		0		2.22099				0		−1.27069				0
3497.20		0			−	1.77695i		0			−	3.36332i		0		−1.55852				0		−0.157556				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
53.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4028.2.c.a	✓	82
53.b	even	2	1	inner	4028.2.c.a	✓	82

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4028.2.c.a	✓	82	1.a	even	1	1	trivial
4028.2.c.a	✓	82	53.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(4028, [\chi])\).