Newform orbit 1320.2.z.c

• Label: 1320.2.z.c
• Level: $1320$
• Weight: $2$
• Character orbit: 1320.z
• Analytic conductor: $10.540$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.z (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.5402530668\)
Analytic rank:	\(0\)
Dimension:	\(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 40 q^{3} - 4 q^{4} + 40 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
571.1	−1.39442	−	0.235803i	−1.00000			1.88879	+	0.657615i		−	1.00000i	1.39442	+	0.235803i	3.89918			−2.47870	−	1.36237i	1.00000			−0.235803	+	1.39442i
571.2	−1.39442	+	0.235803i	−1.00000			1.88879	−	0.657615i			1.00000i	1.39442	−	0.235803i	3.89918			−2.47870	+	1.36237i	1.00000			−0.235803	−	1.39442i
571.3	−1.38654	−	0.278425i	−1.00000			1.84496	+	0.772093i		−	1.00000i	1.38654	+	0.278425i	−5.22492			−2.34313	−	1.58422i	1.00000			−0.278425	+	1.38654i
571.4	−1.38654	+	0.278425i	−1.00000			1.84496	−	0.772093i			1.00000i	1.38654	−	0.278425i	−5.22492			−2.34313	+	1.58422i	1.00000			−0.278425	−	1.38654i
571.5	−1.31229	−	0.527154i	−1.00000			1.44422	+	1.38356i			1.00000i	1.31229	+	0.527154i	−0.872914			−1.16589	−	2.57696i	1.00000			0.527154	−	1.31229i
571.6	−1.31229	+	0.527154i	−1.00000			1.44422	−	1.38356i		−	1.00000i	1.31229	−	0.527154i	−0.872914			−1.16589	+	2.57696i	1.00000			0.527154	+	1.31229i
571.7	−1.27011	−	0.621946i	−1.00000			1.22637	+	1.57988i			1.00000i	1.27011	+	0.621946i	0.446826			−0.575024	−	2.76936i	1.00000			0.621946	−	1.27011i
571.8	−1.27011	+	0.621946i	−1.00000			1.22637	−	1.57988i		−	1.00000i	1.27011	−	0.621946i	0.446826			−0.575024	+	2.76936i	1.00000			0.621946	+	1.27011i
571.9	−0.900130	−	1.09076i	−1.00000			−0.379532	+	1.96366i			1.00000i	0.900130	+	1.09076i	−1.41975			2.48352	−	1.35357i	1.00000			1.09076	−	0.900130i
571.10	−0.900130	+	1.09076i	−1.00000			−0.379532	−	1.96366i		−	1.00000i	0.900130	−	1.09076i	−1.41975			2.48352	+	1.35357i	1.00000			1.09076	+	0.900130i
571.11	−0.841503	−	1.13661i	−1.00000			−0.583746	+	1.91291i		−	1.00000i	0.841503	+	1.13661i	−4.18431			2.66545	−	0.946233i	1.00000			−1.13661	+	0.841503i
571.12	−0.841503	+	1.13661i	−1.00000			−0.583746	−	1.91291i			1.00000i	0.841503	−	1.13661i	−4.18431			2.66545	+	0.946233i	1.00000			−1.13661	−	0.841503i
571.13	−0.703151	−	1.22702i	−1.00000			−1.01116	+	1.72556i			1.00000i	0.703151	+	1.22702i	2.91379			2.82829	+	0.0273833i	1.00000			1.22702	−	0.703151i
571.14	−0.703151	+	1.22702i	−1.00000			−1.01116	−	1.72556i		−	1.00000i	0.703151	−	1.22702i	2.91379			2.82829	−	0.0273833i	1.00000			1.22702	+	0.703151i
571.15	−0.475657	−	1.33182i	−1.00000			−1.54750	+	1.26698i		−	1.00000i	0.475657	+	1.33182i	−2.80730			2.42347	+	1.45835i	1.00000			−1.33182	+	0.475657i
571.16	−0.475657	+	1.33182i	−1.00000			−1.54750	−	1.26698i			1.00000i	0.475657	−	1.33182i	−2.80730			2.42347	−	1.45835i	1.00000			−1.33182	−	0.475657i
571.17	−0.189044	−	1.40152i	−1.00000			−1.92853	+	0.529897i			1.00000i	0.189044	+	1.40152i	−2.93445			1.10724	+	2.60270i	1.00000			1.40152	−	0.189044i
571.18	−0.189044	+	1.40152i	−1.00000			−1.92853	−	0.529897i		−	1.00000i	0.189044	−	1.40152i	−2.93445			1.10724	−	2.60270i	1.00000			1.40152	+	0.189044i
571.19	−0.151862	−	1.40604i	−1.00000			−1.95388	+	0.427048i			1.00000i	0.151862	+	1.40604i	0.169445			0.897166	+	2.68237i	1.00000			1.40604	−	0.151862i
571.20	−0.151862	+	1.40604i	−1.00000			−1.95388	−	0.427048i		−	1.00000i	0.151862	−	1.40604i	0.169445			0.897166	−	2.68237i	1.00000			1.40604	+	0.151862i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
11.b	odd	2	1	inner
88.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1320.2.z.c	✓	40
4.b	odd	2	1		5280.2.z.c		40
8.b	even	2	1		5280.2.z.c		40
8.d	odd	2	1	inner	1320.2.z.c	✓	40
11.b	odd	2	1	inner	1320.2.z.c	✓	40
44.c	even	2	1		5280.2.z.c		40
88.b	odd	2	1		5280.2.z.c		40
88.g	even	2	1	inner	1320.2.z.c	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1320.2.z.c	✓	40	1.a	even	1	1	trivial
1320.2.z.c	✓	40	8.d	odd	2	1	inner
1320.2.z.c	✓	40	11.b	odd	2	1	inner
1320.2.z.c	✓	40	88.g	even	2	1	inner
5280.2.z.c		40	4.b	odd	2	1
5280.2.z.c		40	8.b	even	2	1
5280.2.z.c		40	44.c	even	2	1
5280.2.z.c		40	88.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^20 - 88*T7^18 + 3124*T7^16 - 58080*T7^14 + 611504*T7^12 - 3660928*T7^10 + 11748608*T7^8 - 17494784*T7^6 + 9913600*T7^4 - 1554432*T7^2 + 36864