Newform orbit 3900.2.bm.c

• Label: 3900.2.bm.c
• Level: $3900$
• Weight: $2$
• Character orbit: 3900.bm
• Analytic conductor: $31.142$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bm (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(31.1416567883\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2257.1		0		−0.707107	+	0.707107i		0			0			0		4.64330				0			−	1.00000i		0
2257.2		0		−0.707107	+	0.707107i		0			0			0		−3.54113				0			−	1.00000i		0
2257.3		0		−0.707107	+	0.707107i		0			0			0		3.56068				0			−	1.00000i		0
2257.4		0		−0.707107	+	0.707107i		0			0			0		−3.42424				0			−	1.00000i		0
2257.5		0		−0.707107	+	0.707107i		0			0			0		0.0776760				0			−	1.00000i		0
2257.6		0		−0.707107	+	0.707107i		0			0			0		−0.203531				0			−	1.00000i		0
2257.7		0		−0.707107	+	0.707107i		0			0			0		1.09376				0			−	1.00000i		0
2257.8		0		−0.707107	+	0.707107i		0			0			0		−1.70861				0			−	1.00000i		0
2257.9		0		−0.707107	+	0.707107i		0			0			0		−2.08284				0			−	1.00000i		0
2257.10		0		−0.707107	+	0.707107i		0			0			0		2.99915				0			−	1.00000i		0
2257.11		0		0.707107	−	0.707107i		0			0			0		−2.99915				0			−	1.00000i		0
2257.12		0		0.707107	−	0.707107i		0			0			0		2.08284				0			−	1.00000i		0
2257.13		0		0.707107	−	0.707107i		0			0			0		1.70861				0			−	1.00000i		0
2257.14		0		0.707107	−	0.707107i		0			0			0		−1.09376				0			−	1.00000i		0
2257.15		0		0.707107	−	0.707107i		0			0			0		0.203531				0			−	1.00000i		0
2257.16		0		0.707107	−	0.707107i		0			0			0		−0.0776760				0			−	1.00000i		0
2257.17		0		0.707107	−	0.707107i		0			0			0		3.42424				0			−	1.00000i		0
2257.18		0		0.707107	−	0.707107i		0			0			0		−3.56068				0			−	1.00000i		0
2257.19		0		0.707107	−	0.707107i		0			0			0		3.54113				0			−	1.00000i		0
2257.20		0		0.707107	−	0.707107i		0			0			0		−4.64330				0			−	1.00000i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
65.f	even	4	1	inner
65.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3900.2.bm.c	yes	40
5.b	even	2	1	inner	3900.2.bm.c	yes	40
5.c	odd	4	2		3900.2.r.c	✓	40
13.d	odd	4	1		3900.2.r.c	✓	40
65.f	even	4	1	inner	3900.2.bm.c	yes	40
65.g	odd	4	1		3900.2.r.c	✓	40
65.k	even	4	1	inner	3900.2.bm.c	yes	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3900.2.r.c	✓	40	5.c	odd	4	2
3900.2.r.c	✓	40	13.d	odd	4	1
3900.2.r.c	✓	40	65.g	odd	4	1
3900.2.bm.c	yes	40	1.a	even	1	1	trivial
3900.2.bm.c	yes	40	5.b	even	2	1	inner
3900.2.bm.c	yes	40	65.f	even	4	1	inner
3900.2.bm.c	yes	40	65.k	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^20 - 76*T7^18 + 2373*T7^16 - 39516*T7^14 + 379746*T7^12 - 2122652*T7^10 + 6601702*T7^8 - 10225364*T7^6 + 5949569*T7^4 - 262424*T7^2 + 1369