Newform orbit 2070.3.c.b

• Label: 2070.3.c.b
• Level: $2070$
• Weight: $3$
• Character orbit: 2070.c
• Analytic conductor: $56.403$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(56.4034147226\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 690)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 64 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
91.1	−1.41421				0		2.00000				−	2.23607i		0			−	11.4203i	−2.82843				0				3.16228i
91.2	−1.41421				0		2.00000				−	2.23607i		0			−	3.95881i	−2.82843				0				3.16228i
91.3	−1.41421				0		2.00000				−	2.23607i		0			−	3.80775i	−2.82843				0				3.16228i
91.4	−1.41421				0		2.00000				−	2.23607i		0			−	1.37049i	−2.82843				0				3.16228i
91.5	−1.41421				0		2.00000				−	2.23607i		0				6.64524i	−2.82843				0				3.16228i
91.6	−1.41421				0		2.00000				−	2.23607i		0				7.54509i	−2.82843				0				3.16228i
91.7	−1.41421				0		2.00000				−	2.23607i		0				7.96402i	−2.82843				0				3.16228i
91.8	−1.41421				0		2.00000				−	2.23607i		0				11.8194i	−2.82843				0				3.16228i
91.9	−1.41421				0		2.00000					2.23607i		0			−	11.8194i	−2.82843				0			−	3.16228i
91.10	−1.41421				0		2.00000					2.23607i		0			−	7.96402i	−2.82843				0			−	3.16228i
91.11	−1.41421				0		2.00000					2.23607i		0			−	7.54509i	−2.82843				0			−	3.16228i
91.12	−1.41421				0		2.00000					2.23607i		0			−	6.64524i	−2.82843				0			−	3.16228i
91.13	−1.41421				0		2.00000					2.23607i		0				1.37049i	−2.82843				0			−	3.16228i
91.14	−1.41421				0		2.00000					2.23607i		0				3.80775i	−2.82843				0			−	3.16228i
91.15	−1.41421				0		2.00000					2.23607i		0				3.95881i	−2.82843				0			−	3.16228i
91.16	−1.41421				0		2.00000					2.23607i		0				11.4203i	−2.82843				0			−	3.16228i
91.17	1.41421				0		2.00000				−	2.23607i		0			−	12.3097i	2.82843				0			−	3.16228i
91.18	1.41421				0		2.00000				−	2.23607i		0			−	5.52876i	2.82843				0			−	3.16228i
91.19	1.41421				0		2.00000				−	2.23607i		0			−	1.52229i	2.82843				0			−	3.16228i
91.20	1.41421				0		2.00000				−	2.23607i		0				0.411309i	2.82843				0			−	3.16228i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	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.c.b		32
3.b	odd	2	1		690.3.c.a	✓	32
23.b	odd	2	1	inner	2070.3.c.b		32
69.c	even	2	1		690.3.c.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
690.3.c.a	✓	32	3.b	odd	2	1
690.3.c.a	✓	32	69.c	even	2	1
2070.3.c.b		32	1.a	even	1	1	trivial
2070.3.c.b		32	23.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^32 + 956*T7^30 + 404546*T7^28 + 100070460*T7^26 + 16105686735*T7^24 + 1777239005864*T7^22 + 138101029163644*T7^20 + 7641873673604696*T7^18 + 301034080570037423*T7^16 + 8351755281099154860*T7^14 + 159640181933592944898*T7^12 + 2027498661252019008108*T7^10 + 16145034383308106074977*T7^8 + 73128112930174585469936*T7^6 + 159024519166851411837024*T7^4 + 135832254657198030181120*T7^2 + 18769275101392048128256