Newform orbit 2070.3.b.a

• Label: 2070.3.b.a
• Level: $2070$
• Weight: $3$
• Character orbit: 2070.b
• Analytic conductor: $56.403$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2070.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(56.4034147226\)
Analytic rank:	\(0\)
Dimension:	\(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 176 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1979.1	−1.41421				0		2.00000			−4.96053	−	0.627034i		0				3.53315i	−2.82843				0		7.01524	+	0.886760i
1979.2	−1.41421				0		2.00000			−4.96053	+	0.627034i		0			−	3.53315i	−2.82843				0		7.01524	−	0.886760i
1979.3	−1.41421				0		2.00000			−4.93341	−	0.813292i		0				9.64163i	−2.82843				0		6.97690	+	1.15017i
1979.4	−1.41421				0		2.00000			−4.93341	+	0.813292i		0			−	9.64163i	−2.82843				0		6.97690	−	1.15017i
1979.5	−1.41421				0		2.00000			−4.92404	−	0.868256i		0			−	6.42375i	−2.82843				0		6.96364	+	1.22790i
1979.6	−1.41421				0		2.00000			−4.92404	+	0.868256i		0				6.42375i	−2.82843				0		6.96364	−	1.22790i
1979.7	−1.41421				0		2.00000			−3.64768	−	3.41971i		0				6.32766i	−2.82843				0		5.15860	+	4.83620i
1979.8	−1.41421				0		2.00000			−3.64768	+	3.41971i		0			−	6.32766i	−2.82843				0		5.15860	−	4.83620i
1979.9	−1.41421				0		2.00000			−3.27849	−	3.77512i		0			−	9.66442i	−2.82843				0		4.63649	+	5.33882i
1979.10	−1.41421				0		2.00000			−3.27849	+	3.77512i		0				9.66442i	−2.82843				0		4.63649	−	5.33882i
1979.11	−1.41421				0		2.00000			−3.17549	−	3.86216i		0			−	11.7407i	−2.82843				0		4.49082	+	5.46191i
1979.12	−1.41421				0		2.00000			−3.17549	+	3.86216i		0				11.7407i	−2.82843				0		4.49082	−	5.46191i
1979.13	−1.41421				0		2.00000			−1.94774	−	4.60503i		0				3.15648i	−2.82843				0		2.75452	+	6.51250i
1979.14	−1.41421				0		2.00000			−1.94774	+	4.60503i		0			−	3.15648i	−2.82843				0		2.75452	−	6.51250i
1979.15	−1.41421				0		2.00000			−1.64710	−	4.72092i		0				4.64897i	−2.82843				0		2.32936	+	6.67638i
1979.16	−1.41421				0		2.00000			−1.64710	+	4.72092i		0			−	4.64897i	−2.82843				0		2.32936	−	6.67638i
1979.17	−1.41421				0		2.00000			−1.10475	−	4.87643i		0				0.421478i	−2.82843				0		1.56235	+	6.89631i
1979.18	−1.41421				0		2.00000			−1.10475	+	4.87643i		0			−	0.421478i	−2.82843				0		1.56235	−	6.89631i
1979.19	−1.41421				0		2.00000			−0.938812	−	4.91107i		0				11.6897i	−2.82843				0		1.32768	+	6.94531i
1979.20	−1.41421				0		2.00000			−0.938812	+	4.91107i		0			−	11.6897i	−2.82843				0		1.32768	−	6.94531i

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
15.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2070.3.b.a	✓	88
3.b	odd	2	1	inner	2070.3.b.a	✓	88
5.b	even	2	1	inner	2070.3.b.a	✓	88
15.d	odd	2	1	inner	2070.3.b.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2070.3.b.a	✓	88	1.a	even	1	1	trivial
2070.3.b.a	✓	88	3.b	odd	2	1	inner
2070.3.b.a	✓	88	5.b	even	2	1	inner
2070.3.b.a	✓	88	15.d	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(2070, [\chi])\).