Newform orbit 1620.3.l.e

• Label: 1620.3.l.e
• Level: $1620$
• Weight: $3$
• Character orbit: 1620.l
• Analytic conductor: $44.142$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(44.1418028264\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
973.1		0			0			0		−4.46472	−	2.25083i		0		−7.12164	+	7.12164i		0			0			0
973.2		0			0			0		−4.17193	+	2.75591i		0		7.80125	−	7.80125i		0			0			0
973.3		0			0			0		−4.14721	+	2.79296i		0		0.325388	−	0.325388i		0			0			0
973.4		0			0			0		−3.20358	−	3.83889i		0		0.271286	−	0.271286i		0			0			0
973.5		0			0			0		−1.49326	−	4.77181i		0		3.29784	−	3.29784i		0			0			0
973.6		0			0			0		−0.684981	+	4.95286i		0		−7.57413	+	7.57413i		0			0			0
973.7		0			0			0		0.684981	−	4.95286i		0		−7.57413	+	7.57413i		0			0			0
973.8		0			0			0		1.49326	+	4.77181i		0		3.29784	−	3.29784i		0			0			0
973.9		0			0			0		3.20358	+	3.83889i		0		0.271286	−	0.271286i		0			0			0
973.10		0			0			0		4.14721	−	2.79296i		0		0.325388	−	0.325388i		0			0			0
973.11		0			0			0		4.17193	−	2.75591i		0		7.80125	−	7.80125i		0			0			0
973.12		0			0			0		4.46472	+	2.25083i		0		−7.12164	+	7.12164i		0			0			0
1297.1		0			0			0		−4.46472	+	2.25083i		0		−7.12164	−	7.12164i		0			0			0
1297.2		0			0			0		−4.17193	−	2.75591i		0		7.80125	+	7.80125i		0			0			0
1297.3		0			0			0		−4.14721	−	2.79296i		0		0.325388	+	0.325388i		0			0			0
1297.4		0			0			0		−3.20358	+	3.83889i		0		0.271286	+	0.271286i		0			0			0
1297.5		0			0			0		−1.49326	+	4.77181i		0		3.29784	+	3.29784i		0			0			0
1297.6		0			0			0		−0.684981	−	4.95286i		0		−7.57413	−	7.57413i		0			0			0
1297.7		0			0			0		0.684981	+	4.95286i		0		−7.57413	−	7.57413i		0			0			0
1297.8		0			0			0		1.49326	−	4.77181i		0		3.29784	+	3.29784i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
15.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1620.3.l.e	✓	24
3.b	odd	2	1	inner	1620.3.l.e	✓	24
5.c	odd	4	1	inner	1620.3.l.e	✓	24
15.e	even	4	1	inner	1620.3.l.e	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1620.3.l.e	✓	24	1.a	even	1	1	trivial
1620.3.l.e	✓	24	3.b	odd	2	1	inner
1620.3.l.e	✓	24	5.c	odd	4	1	inner
1620.3.l.e	✓	24	15.e	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1620, [\chi])\):

T7^12 + 6*T7^11 + 18*T7^10 - 344*T7^9 + 17145*T7^8 + 87114*T7^7 + 273242*T7^6 - 5289996*T7^5 + 36913464*T7^4 - 40337080*T7^3 + 22984200*T7^2 - 6644400*T7 + 960400

T11^12 - 942*T11^10 + 260949*T11^8 - 18633368*T11^6 + 482612916*T11^4 - 4632468000*T11^2 + 9880360000