Newform orbit 980.2.m.b

• Label: 980.2.m.b
• Level: $980$
• Weight: $2$
• Character orbit: 980.m
• Analytic conductor: $7.825$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82533939809\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{11} - 48 q^{23} + 32 q^{25} - 32 q^{37} + 16 q^{43} + 48 q^{51} - 24 q^{53} + 64 q^{65} - 32 q^{67} + 8 q^{81} - 64 q^{85} - 96 q^{93} + 64 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
97.1		0		−2.10245	−	2.10245i		0		1.53410	+	1.62682i		0			0			0				5.84062i		0
97.2		0		−1.62809	−	1.62809i		0		1.99300	+	1.01388i		0			0			0				2.30136i		0
97.3		0		−1.42564	−	1.42564i		0		−2.11555	+	0.724199i		0			0			0				1.06489i		0
97.4		0		−0.650442	−	0.650442i		0		2.05263	−	0.886973i		0			0			0			−	2.15385i		0
97.5		0		−0.562914	−	0.562914i		0		−1.87811	−	1.21356i		0			0			0			−	2.36626i		0
97.6		0		−0.395749	−	0.395749i		0		0.677040	−	2.13111i		0			0			0			−	2.68677i		0
97.7		0		0.395749	+	0.395749i		0		−0.677040	+	2.13111i		0			0			0			−	2.68677i		0
97.8		0		0.562914	+	0.562914i		0		1.87811	+	1.21356i		0			0			0			−	2.36626i		0
97.9		0		0.650442	+	0.650442i		0		−2.05263	+	0.886973i		0			0			0			−	2.15385i		0
97.10		0		1.42564	+	1.42564i		0		2.11555	−	0.724199i		0			0			0				1.06489i		0
97.11		0		1.62809	+	1.62809i		0		−1.99300	−	1.01388i		0			0			0				2.30136i		0
97.12		0		2.10245	+	2.10245i		0		−1.53410	−	1.62682i		0			0			0				5.84062i		0
293.1		0		−2.10245	+	2.10245i		0		1.53410	−	1.62682i		0			0			0			−	5.84062i		0
293.2		0		−1.62809	+	1.62809i		0		1.99300	−	1.01388i		0			0			0			−	2.30136i		0
293.3		0		−1.42564	+	1.42564i		0		−2.11555	−	0.724199i		0			0			0			−	1.06489i		0
293.4		0		−0.650442	+	0.650442i		0		2.05263	+	0.886973i		0			0			0				2.15385i		0
293.5		0		−0.562914	+	0.562914i		0		−1.87811	+	1.21356i		0			0			0				2.36626i		0
293.6		0		−0.395749	+	0.395749i		0		0.677040	+	2.13111i		0			0			0				2.68677i		0
293.7		0		0.395749	−	0.395749i		0		−0.677040	−	2.13111i		0			0			0				2.68677i		0
293.8		0		0.562914	−	0.562914i		0		1.87811	−	1.21356i		0			0			0				2.36626i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.b	odd	2	1	inner
35.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	980.2.m.b	✓	24
5.c	odd	4	1	inner	980.2.m.b	✓	24
7.b	odd	2	1	inner	980.2.m.b	✓	24
7.c	even	3	2		980.2.v.c		48
7.d	odd	6	2		980.2.v.c		48
35.f	even	4	1	inner	980.2.m.b	✓	24
35.k	even	12	2		980.2.v.c		48
35.l	odd	12	2		980.2.v.c		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
980.2.m.b	✓	24	1.a	even	1	1	trivial
980.2.m.b	✓	24	5.c	odd	4	1	inner
980.2.m.b	✓	24	7.b	odd	2	1	inner
980.2.m.b	✓	24	35.f	even	4	1	inner
980.2.v.c		48	7.c	even	3	2
980.2.v.c		48	7.d	odd	6	2
980.2.v.c		48	35.k	even	12	2
980.2.v.c		48	35.l	odd	12	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 124T_{3}^{20} + 4102T_{3}^{16} + 41148T_{3}^{12} + 45697T_{3}^{8} + 14528T_{3}^{4} + 1024 \) acting on \(S_{2}^{\mathrm{new}}(980, [\chi])\).