Newform orbit 1368.3.bv.d

• Label: 1368.3.bv.d
• Level: $1368$
• Weight: $3$
• Character orbit: 1368.bv
• Analytic conductor: $37.275$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1368.bv (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(37.2753001645\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
145.1		0			0			0		−4.54571	−	7.87340i		0		7.94434				0			0			0
145.2		0			0			0		−3.97287	−	6.88121i		0		−5.83385				0			0			0
145.3		0			0			0		−3.54017	−	6.13176i		0		−4.56107				0			0			0
145.4		0			0			0		−2.82237	−	4.88849i		0		−9.31227				0			0			0
145.5		0			0			0		−2.40892	−	4.17237i		0		5.58667				0			0			0
145.6		0			0			0		−2.14462	−	3.71458i		0		−1.65941				0			0			0
145.7		0			0			0		−2.07988	−	3.60245i		0		7.74230				0			0			0
145.8		0			0			0		−1.74091	−	3.01535i		0		9.70331				0			0			0
145.9		0			0			0		−1.10587	−	1.91542i		0		−9.34465				0			0			0
145.10		0			0			0		−1.03557	−	1.79365i		0		3.73463				0			0			0
145.11		0			0			0		1.03557	+	1.79365i		0		3.73463				0			0			0
145.12		0			0			0		1.10587	+	1.91542i		0		−9.34465				0			0			0
145.13		0			0			0		1.74091	+	3.01535i		0		9.70331				0			0			0
145.14		0			0			0		2.07988	+	3.60245i		0		7.74230				0			0			0
145.15		0			0			0		2.14462	+	3.71458i		0		−1.65941				0			0			0
145.16		0			0			0		2.40892	+	4.17237i		0		5.58667				0			0			0
145.17		0			0			0		2.82237	+	4.88849i		0		−9.31227				0			0			0
145.18		0			0			0		3.54017	+	6.13176i		0		−4.56107				0			0			0
145.19		0			0			0		3.97287	+	6.88121i		0		−5.83385				0			0			0
145.20		0			0			0		4.54571	+	7.87340i		0		7.94434				0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
19.d	odd	6	1	inner
57.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1368.3.bv.d	✓	40
3.b	odd	2	1	inner	1368.3.bv.d	✓	40
19.d	odd	6	1	inner	1368.3.bv.d	✓	40
57.f	even	6	1	inner	1368.3.bv.d	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1368.3.bv.d	✓	40	1.a	even	1	1	trivial
1368.3.bv.d	✓	40	3.b	odd	2	1	inner
1368.3.bv.d	✓	40	19.d	odd	6	1	inner
1368.3.bv.d	✓	40	57.f	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^40 + 308*T5^38 + 55288*T5^36 + 6622304*T5^34 + 590610700*T5^32 + 40446545536*T5^30 + 2198054476768*T5^28 + 95835775223552*T5^26 + 3400571338998608*T5^24 + 98571542971075968*T5^22 + 2348028102362903424*T5^20 + 45864871591779977216*T5^18 + 734033475785161774848*T5^16 + 9530145518799980826624*T5^14 + 99529182612145468594176*T5^12 + 817553425287976338513920*T5^10 + 5195270502729648049623040*T5^8 + 24388526253112493154959360*T5^6 + 83738423749701399680385024*T5^4 + 185237184389547108153163776*T5^2 + 245499507162126852152098816