Newform orbit 1728.4.c.l

• Label: 1728.4.c.l
• Level: $1728$
• Weight: $4$
• Character orbit: 1728.c
• Analytic conductor: $101.955$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1728.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(101.955300490\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 864)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 72 q^{13} - 264 q^{25} - 24 q^{37} + 456 q^{61} + 2184 q^{73} - 3072 q^{85} - 3672 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1727.1		0			0			0			−	20.1103i		0			−	5.50399i		0			0			0
1727.2		0			0			0			−	20.1103i		0				5.50399i		0			0			0
1727.3		0			0			0			−	12.8736i		0			−	18.8903i		0			0			0
1727.4		0			0			0			−	12.8736i		0				18.8903i		0			0			0
1727.5		0			0			0			−	12.0582i		0			−	1.19407i		0			0			0
1727.6		0			0			0			−	12.0582i		0				1.19407i		0			0			0
1727.7		0			0			0			−	8.05443i		0			−	20.0504i		0			0			0
1727.8		0			0			0			−	8.05443i		0				20.0504i		0			0			0
1727.9		0			0			0			−	5.36372i		0			−	29.2067i		0			0			0
1727.10		0			0			0			−	5.36372i		0				29.2067i		0			0			0
1727.11		0			0			0			−	2.60859i		0			−	20.3565i		0			0			0
1727.12		0			0			0			−	2.60859i		0				20.3565i		0			0			0
1727.13		0			0			0				2.60859i		0			−	20.3565i		0			0			0
1727.14		0			0			0				2.60859i		0				20.3565i		0			0			0
1727.15		0			0			0				5.36372i		0			−	29.2067i		0			0			0
1727.16		0			0			0				5.36372i		0				29.2067i		0			0			0
1727.17		0			0			0				8.05443i		0			−	20.0504i		0			0			0
1727.18		0			0			0				8.05443i		0				20.0504i		0			0			0
1727.19		0			0			0				12.0582i		0			−	1.19407i		0			0			0
1727.20		0			0			0				12.0582i		0				1.19407i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1728.4.c.l		24
3.b	odd	2	1	inner	1728.4.c.l		24
4.b	odd	2	1	inner	1728.4.c.l		24
8.b	even	2	1		864.4.c.a	✓	24
8.d	odd	2	1		864.4.c.a	✓	24
12.b	even	2	1	inner	1728.4.c.l		24
24.f	even	2	1		864.4.c.a	✓	24
24.h	odd	2	1		864.4.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
864.4.c.a	✓	24	8.b	even	2	1
864.4.c.a	✓	24	8.d	odd	2	1
864.4.c.a	✓	24	24.f	even	2	1
864.4.c.a	✓	24	24.h	odd	2	1
1728.4.c.l		24	1.a	even	1	1	trivial
1728.4.c.l		24	3.b	odd	2	1	inner
1728.4.c.l		24	4.b	odd	2	1	inner
1728.4.c.l		24	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(1728, [\chi])\):

\( T_{5}^{12} + 816T_{5}^{10} + 224304T_{5}^{8} + 26609152T_{5}^{6} + 1363342080T_{5}^{4} + 26302623744T_{5}^{2} + 123768868864 \)

T7^12 + 2058*T7^10 + 1523055*T7^8 + 496425932*T7^6 + 65049243279*T7^4 + 1627953299850*T7^2 + 2190349680289

T11^12 - 8496*T11^10 + 22954032*T11^8 - 25669993984*T11^6 + 11675439330048*T11^4 - 1658844751343616*T11^2 + 25483335779160064