Newform orbit 1980.2.br.a

• Label: 1980.2.br.a
• Level: $1980$
• Weight: $2$
• Character orbit: 1980.br
• Analytic conductor: $15.810$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1980.br (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.8103796002\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(24\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
629.1		0			0			0		−2.23026	+	0.161029i		0		−2.69953	−	1.96132i		0			0			0
629.2		0			0			0		−2.20413	−	0.376602i		0		−2.50986	−	1.82352i		0			0			0
629.3		0			0			0		−2.13873	−	0.652560i		0		2.42034	+	1.75848i		0			0			0
629.4		0			0			0		−2.06363	−	0.861053i		0		−2.02295	−	1.46976i		0			0			0
629.5		0			0			0		−1.89897	+	1.18064i		0		2.69953	+	1.96132i		0			0			0
629.6		0			0			0		−1.56181	+	1.60023i		0		2.50986	+	1.82352i		0			0			0
629.7		0			0			0		−1.37155	−	1.76603i		0		2.61066	+	1.89676i		0			0			0
629.8		0			0			0		−1.34670	+	1.78505i		0		−2.42034	−	1.75848i		0			0			0
629.9		0			0			0		−1.16340	+	1.90958i		0		2.02295	+	1.46976i		0			0			0
629.10		0			0			0		−0.911891	−	2.04168i		0		0.504595	+	0.366610i		0			0			0
629.11		0			0			0		−0.462334	−	2.18775i		0		−0.504595	−	0.366610i		0			0			0
629.12		0			0			0		−0.0715579	+	2.23492i		0		−2.61066	−	1.89676i		0			0			0
629.13		0			0			0		0.0715579	−	2.23492i		0		−2.61066	−	1.89676i		0			0			0
629.14		0			0			0		0.462334	+	2.18775i		0		−0.504595	−	0.366610i		0			0			0
629.15		0			0			0		0.911891	+	2.04168i		0		0.504595	+	0.366610i		0			0			0
629.16		0			0			0		1.16340	−	1.90958i		0		2.02295	+	1.46976i		0			0			0
629.17		0			0			0		1.34670	−	1.78505i		0		−2.42034	−	1.75848i		0			0			0
629.18		0			0			0		1.37155	+	1.76603i		0		2.61066	+	1.89676i		0			0			0
629.19		0			0			0		1.56181	−	1.60023i		0		2.50986	+	1.82352i		0			0			0
629.20		0			0			0		1.89897	−	1.18064i		0		2.69953	+	1.96132i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
11.d	odd	10	1	inner
15.d	odd	2	1	inner
33.f	even	10	1	inner
55.h	odd	10	1	inner
165.r	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1980.2.br.a	✓	96
3.b	odd	2	1	inner	1980.2.br.a	✓	96
5.b	even	2	1	inner	1980.2.br.a	✓	96
11.d	odd	10	1	inner	1980.2.br.a	✓	96
15.d	odd	2	1	inner	1980.2.br.a	✓	96
33.f	even	10	1	inner	1980.2.br.a	✓	96
55.h	odd	10	1	inner	1980.2.br.a	✓	96
165.r	even	10	1	inner	1980.2.br.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1980.2.br.a	✓	96	1.a	even	1	1	trivial
1980.2.br.a	✓	96	3.b	odd	2	1	inner
1980.2.br.a	✓	96	5.b	even	2	1	inner
1980.2.br.a	✓	96	11.d	odd	10	1	inner
1980.2.br.a	✓	96	15.d	odd	2	1	inner
1980.2.br.a	✓	96	33.f	even	10	1	inner
1980.2.br.a	✓	96	55.h	odd	10	1	inner
1980.2.br.a	✓	96	165.r	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1980, [\chi])\).