Newform orbit 1008.2.cj.e

• Label: 1008.2.cj.e
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.cj
• Analytic conductor: $8.049$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.04892052375\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
527.1		0		−1.67965	−	0.422826i		0		−1.72654	+	0.996819i		0		1.05011	+	2.42843i		0		2.64244	+	1.42040i		0
527.2		0		−1.65364	+	0.515254i		0		1.18190	−	0.682369i		0		−2.63670	+	0.218628i		0		2.46903	−	1.70409i		0
527.3		0		−1.56011	−	0.752368i		0		1.17582	−	0.678857i		0		1.81673	−	1.92340i		0		1.86789	+	2.34755i		0
527.4		0		−1.21604	+	1.23339i		0		−2.67963	+	1.54708i		0		1.60577	−	2.10274i		0		−0.0425024	−	2.99970i		0
527.5		0		−1.16022	−	1.28603i		0		−3.01183	+	1.73888i		0		−2.38887	−	1.13724i		0		−0.307759	+	2.98417i		0
527.6		0		−0.689798	+	1.58877i		0		3.31879	−	1.91610i		0		2.63984	−	0.176805i		0		−2.04836	−	2.19186i		0
527.7		0		−0.443769	−	1.67424i		0		1.72437	−	0.995563i		0		0.267794	−	2.63216i		0		−2.60614	+	1.48595i		0
527.8		0		−0.112712	−	1.72838i		0		0.0171311	−	0.00989066i		0		1.25256	+	2.33047i		0		−2.97459	+	0.389620i		0
527.9		0		0.112712	+	1.72838i		0		0.0171311	−	0.00989066i		0		−1.25256	−	2.33047i		0		−2.97459	+	0.389620i		0
527.10		0		0.443769	+	1.67424i		0		1.72437	−	0.995563i		0		−0.267794	+	2.63216i		0		−2.60614	+	1.48595i		0
527.11		0		0.689798	−	1.58877i		0		3.31879	−	1.91610i		0		−2.63984	+	0.176805i		0		−2.04836	−	2.19186i		0
527.12		0		1.16022	+	1.28603i		0		−3.01183	+	1.73888i		0		2.38887	+	1.13724i		0		−0.307759	+	2.98417i		0
527.13		0		1.21604	−	1.23339i		0		−2.67963	+	1.54708i		0		−1.60577	+	2.10274i		0		−0.0425024	−	2.99970i		0
527.14		0		1.56011	+	0.752368i		0		1.17582	−	0.678857i		0		−1.81673	+	1.92340i		0		1.86789	+	2.34755i		0
527.15		0		1.65364	−	0.515254i		0		1.18190	−	0.682369i		0		2.63670	−	0.218628i		0		2.46903	−	1.70409i		0
527.16		0		1.67965	+	0.422826i		0		−1.72654	+	0.996819i		0		−1.05011	−	2.42843i		0		2.64244	+	1.42040i		0
767.1		0		−1.67965	+	0.422826i		0		−1.72654	−	0.996819i		0		1.05011	−	2.42843i		0		2.64244	−	1.42040i		0
767.2		0		−1.65364	−	0.515254i		0		1.18190	+	0.682369i		0		−2.63670	−	0.218628i		0		2.46903	+	1.70409i		0
767.3		0		−1.56011	+	0.752368i		0		1.17582	+	0.678857i		0		1.81673	+	1.92340i		0		1.86789	−	2.34755i		0
767.4		0		−1.21604	−	1.23339i		0		−2.67963	−	1.54708i		0		1.60577	+	2.10274i		0		−0.0425024	+	2.99970i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
63.j	odd	6	1	inner
252.bb	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1008.2.cj.e	yes	32
3.b	odd	2	1		3024.2.cj.e		32
4.b	odd	2	1	inner	1008.2.cj.e	yes	32
7.c	even	3	1		1008.2.bh.e	✓	32
9.c	even	3	1		3024.2.bh.e		32
9.d	odd	6	1		1008.2.bh.e	✓	32
12.b	even	2	1		3024.2.cj.e		32
21.h	odd	6	1		3024.2.bh.e		32
28.g	odd	6	1		1008.2.bh.e	✓	32
36.f	odd	6	1		3024.2.bh.e		32
36.h	even	6	1		1008.2.bh.e	✓	32
63.h	even	3	1		3024.2.cj.e		32
63.j	odd	6	1	inner	1008.2.cj.e	yes	32
84.n	even	6	1		3024.2.bh.e		32
252.u	odd	6	1		3024.2.cj.e		32
252.bb	even	6	1	inner	1008.2.cj.e	yes	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.2.bh.e	✓	32	7.c	even	3	1
1008.2.bh.e	✓	32	9.d	odd	6	1
1008.2.bh.e	✓	32	28.g	odd	6	1
1008.2.bh.e	✓	32	36.h	even	6	1
1008.2.cj.e	yes	32	1.a	even	1	1	trivial
1008.2.cj.e	yes	32	4.b	odd	2	1	inner
1008.2.cj.e	yes	32	63.j	odd	6	1	inner
1008.2.cj.e	yes	32	252.bb	even	6	1	inner
3024.2.bh.e		32	9.c	even	3	1
3024.2.bh.e		32	21.h	odd	6	1
3024.2.bh.e		32	36.f	odd	6	1
3024.2.bh.e		32	84.n	even	6	1
3024.2.cj.e		32	3.b	odd	2	1
3024.2.cj.e		32	12.b	even	2	1
3024.2.cj.e		32	63.h	even	3	1
3024.2.cj.e		32	252.u	odd	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1008, [\chi])\):

T5^16 - 24*T5^14 + 411*T5^12 + 15*T5^11 - 3272*T5^10 + 453*T5^9 + 18801*T5^8 - 13347*T5^7 - 48705*T5^6 + 53778*T5^5 + 86773*T5^4 - 181506*T5^3 + 98151*T5^2 - 3222*T5 + 36

T11^32 + 102*T11^30 + 6525*T11^28 + 258772*T11^26 + 7484523*T11^24 + 149456847*T11^22 + 2188866369*T11^20 + 21086275755*T11^18 + 148683527142*T11^16 + 741634981477*T11^14 + 2766613443291*T11^12 + 7320127759608*T11^10 + 14147924674570*T11^8 + 17618434933752*T11^6 + 15765604893369*T11^4 + 8323335408384*T11^2 + 2821109907456