Newform orbit 4140.3.d.c

• Label: 4140.3.d.c
• Level: $4140$
• Weight: $3$
• Character orbit: 4140.d
• Analytic conductor: $112.807$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	4140.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(112.806829445\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 1380)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2161.1		0			0			0			−	2.23607i		0			−	11.7218i		0			0			0
2161.2		0			0			0			−	2.23607i		0			−	10.9556i		0			0			0
2161.3		0			0			0			−	2.23607i		0			−	10.0406i		0			0			0
2161.4		0			0			0			−	2.23607i		0			−	4.23458i		0			0			0
2161.5		0			0			0			−	2.23607i		0			−	3.01539i		0			0			0
2161.6		0			0			0			−	2.23607i		0			−	2.98794i		0			0			0
2161.7		0			0			0			−	2.23607i		0			−	2.71701i		0			0			0
2161.8		0			0			0			−	2.23607i		0			−	1.24316i		0			0			0
2161.9		0			0			0			−	2.23607i		0				0.509961i		0			0			0
2161.10		0			0			0			−	2.23607i		0				2.07606i		0			0			0
2161.11		0			0			0			−	2.23607i		0				4.95389i		0			0			0
2161.12		0			0			0			−	2.23607i		0				8.75590i		0			0			0
2161.13		0			0			0			−	2.23607i		0				9.24833i		0			0			0
2161.14		0			0			0			−	2.23607i		0				11.3307i		0			0			0
2161.15		0			0			0			−	2.23607i		0				11.5587i		0			0			0
2161.16		0			0			0			−	2.23607i		0				11.8989i		0			0			0
2161.17		0			0			0				2.23607i		0			−	11.8989i		0			0			0
2161.18		0			0			0				2.23607i		0			−	11.5587i		0			0			0
2161.19		0			0			0				2.23607i		0			−	11.3307i		0			0			0
2161.20		0			0			0				2.23607i		0			−	9.24833i		0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4140.3.d.c		32
3.b	odd	2	1		1380.3.d.a	✓	32
23.b	odd	2	1	inner	4140.3.d.c		32
69.c	even	2	1		1380.3.d.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1380.3.d.a	✓	32	3.b	odd	2	1
1380.3.d.a	✓	32	69.c	even	2	1
4140.3.d.c		32	1.a	even	1	1	trivial
4140.3.d.c		32	23.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^32 + 998*T7^30 + 441911*T7^28 + 114285060*T7^26 + 19123041207*T7^24 + 2167506294182*T7^22 + 169468469656969*T7^20 + 9148609299263408*T7^18 + 337296882595376408*T7^16 + 8342589709149555936*T7^14 + 135820228576108313232*T7^12 + 1424840298882821309952*T7^10 + 9338538397675839015936*T7^8 + 36165033901355670241280*T7^6 + 74169893386904850333696*T7^4 + 63507320713643340857344*T7^2 + 12094542306440711766016