Newform orbit 810.3.j.g

• Label: 810.3.j.g
• Level: $810$
• Weight: $3$
• Character orbit: 810.j
• Analytic conductor: $22.071$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.0709014132\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
269.1	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	4.43710	+	2.30480i		0		6.62225	+	3.82336i	2.82843				0		−5.96030	+	3.80458i
269.2	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	2.51279	+	4.32272i		0		5.12645	+	2.95976i	2.82843				0		−7.07104	+	0.0209028i
269.3	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	−1.24727	−	4.84193i		0		0.315907	+	0.182389i	2.82843				0		6.81209	+	1.89618i
269.4	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	−4.52502	+	2.12701i		0		−1.70200	−	0.982651i	2.82843				0		0.594626	−	7.04602i
269.5	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	3.23698	−	3.81077i		0		−8.15650	−	4.70916i	2.82843				0		2.37833	+	6.65909i
269.6	−0.707107	+	1.22474i		0		−1.00000	−	1.73205i	−4.41458	+	2.34766i		0		−8.20611	−	4.73780i	2.82843				0		0.246293	−	7.06678i
269.7	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	−4.43710	−	2.30480i		0		6.62225	+	3.82336i	−2.82843				0		−5.96030	+	3.80458i
269.8	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	4.52502	−	2.12701i		0		−1.70200	−	0.982651i	−2.82843				0		0.594626	−	7.04602i
269.9	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	−2.51279	−	4.32272i		0		5.12645	+	2.95976i	−2.82843				0		−7.07104	+	0.0209028i
269.10	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	−3.23698	+	3.81077i		0		−8.15650	−	4.70916i	−2.82843				0		2.37833	+	6.65909i
269.11	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	1.24727	+	4.84193i		0		0.315907	+	0.182389i	−2.82843				0		6.81209	+	1.89618i
269.12	0.707107	−	1.22474i		0		−1.00000	−	1.73205i	4.41458	−	2.34766i		0		−8.20611	−	4.73780i	−2.82843				0		0.246293	−	7.06678i
539.1	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	4.43710	−	2.30480i		0		6.62225	−	3.82336i	2.82843				0		−5.96030	−	3.80458i
539.2	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	2.51279	−	4.32272i		0		5.12645	−	2.95976i	2.82843				0		−7.07104	−	0.0209028i
539.3	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	−1.24727	+	4.84193i		0		0.315907	−	0.182389i	2.82843				0		6.81209	−	1.89618i
539.4	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	−4.52502	−	2.12701i		0		−1.70200	+	0.982651i	2.82843				0		0.594626	+	7.04602i
539.5	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	3.23698	+	3.81077i		0		−8.15650	+	4.70916i	2.82843				0		2.37833	−	6.65909i
539.6	−0.707107	−	1.22474i		0		−1.00000	+	1.73205i	−4.41458	−	2.34766i		0		−8.20611	+	4.73780i	2.82843				0		0.246293	+	7.06678i
539.7	0.707107	+	1.22474i		0		−1.00000	+	1.73205i	−4.43710	+	2.30480i		0		6.62225	−	3.82336i	−2.82843				0		−5.96030	−	3.80458i
539.8	0.707107	+	1.22474i		0		−1.00000	+	1.73205i	−2.51279	+	4.32272i		0		5.12645	−	2.95976i	−2.82843				0		−7.07104	−	0.0209028i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
45.h	odd	6	1	inner
45.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	810.3.j.g		24
3.b	odd	2	1	inner	810.3.j.g		24
5.b	even	2	1		810.3.j.h		24
9.c	even	3	1		810.3.b.c	✓	24
9.c	even	3	1		810.3.j.h		24
9.d	odd	6	1		810.3.b.c	✓	24
9.d	odd	6	1		810.3.j.h		24
15.d	odd	2	1		810.3.j.h		24
45.h	odd	6	1		810.3.b.c	✓	24
45.h	odd	6	1	inner	810.3.j.g		24
45.j	even	6	1		810.3.b.c	✓	24
45.j	even	6	1	inner	810.3.j.g		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
810.3.b.c	✓	24	9.c	even	3	1
810.3.b.c	✓	24	9.d	odd	6	1
810.3.b.c	✓	24	45.h	odd	6	1
810.3.b.c	✓	24	45.j	even	6	1
810.3.j.g		24	1.a	even	1	1	trivial
810.3.j.g		24	3.b	odd	2	1	inner
810.3.j.g		24	45.h	odd	6	1	inner
810.3.j.g		24	45.j	even	6	1	inner
810.3.j.h		24	5.b	even	2	1
810.3.j.h		24	9.c	even	3	1
810.3.j.h		24	9.d	odd	6	1
810.3.j.h		24	15.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(810, [\chi])\):

T7^12 + 12*T7^11 - 66*T7^10 - 1368*T7^9 + 5598*T7^8 + 97800*T7^7 - 139180*T7^6 - 3380928*T7^5 + 8604420*T7^4 + 41415120*T7^3 + 34859232*T7^2 - 33709440*T7 + 8386816

T17^12 - 1464*T17^10 + 793137*T17^8 - 199784716*T17^6 + 23433607236*T17^4 - 1040615269800*T17^2 + 1460109722500