Newform orbit 1008.2.cx.i

• Label: 1008.2.cx.i
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.cx
• Analytic conductor: $8.049$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(8.04892052375\)
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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 24 * q - 6 * q^7 + 20 * q^9 + 24 * q^15 + 10 * q^21 + 18 * q^23 + 24 * q^25 - 6 * q^29 - 12 * q^37 - 12 * q^39 + 42 * q^43 + 12 * q^49 - 42 * q^51 + 96 * q^53 - 22 * q^57 + 18 * q^63 + 42 * q^65 + 36 * q^67 - 18 * q^77 - 60 * q^79 - 64 * q^81 - 6 * q^85 + 82 * q^93 - 126 * q^95 + 12 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
223.1		0		−1.71721	−	0.226267i		0		1.72020	−	0.993161i		0		1.81723	+	1.92293i		0		2.89761	+	0.777096i		0
223.2		0		−1.69365	+	0.362704i		0		−2.10269	+	1.21399i		0		1.15057	−	2.38247i		0		2.73689	−	1.22858i		0
223.3		0		−1.44146	+	0.960311i		0		0.675942	−	0.390255i		0		−1.89912	+	1.84210i		0		1.15560	−	2.76850i		0
223.4		0		−1.21473	−	1.23468i		0		−3.37919	+	1.95098i		0		0.667355	+	2.56020i		0		−0.0488500	+	2.99960i		0
223.5		0		−1.11570	−	1.32484i		0		−0.263424	+	0.152088i		0		−2.20588	−	1.46085i		0		−0.510411	+	2.95626i		0
223.6		0		−0.940521	+	1.45445i		0		3.48918	−	2.01448i		0		−1.90020	−	1.84099i		0		−1.23084	−	2.73588i		0
223.7		0		0.940521	−	1.45445i		0		−3.48918	+	2.01448i		0		−2.54444	−	0.725126i		0		−1.23084	−	2.73588i		0
223.8		0		1.11570	+	1.32484i		0		0.263424	−	0.152088i		0		−2.36807	−	1.17993i		0		−0.510411	+	2.95626i		0
223.9		0		1.21473	+	1.23468i		0		3.37919	−	1.95098i		0		2.55088	−	0.702155i		0		−0.0488500	+	2.99960i		0
223.10		0		1.44146	−	0.960311i		0		−0.675942	+	0.390255i		0		0.645750	−	2.56574i		0		1.15560	−	2.76850i		0
223.11		0		1.69365	−	0.362704i		0		2.10269	−	1.21399i		0		−1.48800	+	2.18766i		0		2.73689	−	1.22858i		0
223.12		0		1.71721	+	0.226267i		0		−1.72020	+	0.993161i		0		2.57392	+	0.612306i		0		2.89761	+	0.777096i		0
895.1		0		−1.71721	+	0.226267i		0		1.72020	+	0.993161i		0		1.81723	−	1.92293i		0		2.89761	−	0.777096i		0
895.2		0		−1.69365	−	0.362704i		0		−2.10269	−	1.21399i		0		1.15057	+	2.38247i		0		2.73689	+	1.22858i		0
895.3		0		−1.44146	−	0.960311i		0		0.675942	+	0.390255i		0		−1.89912	−	1.84210i		0		1.15560	+	2.76850i		0
895.4		0		−1.21473	+	1.23468i		0		−3.37919	−	1.95098i		0		0.667355	−	2.56020i		0		−0.0488500	−	2.99960i		0
895.5		0		−1.11570	+	1.32484i		0		−0.263424	−	0.152088i		0		−2.20588	+	1.46085i		0		−0.510411	−	2.95626i		0
895.6		0		−0.940521	−	1.45445i		0		3.48918	+	2.01448i		0		−1.90020	+	1.84099i		0		−1.23084	+	2.73588i		0
895.7		0		0.940521	+	1.45445i		0		−3.48918	−	2.01448i		0		−2.54444	+	0.725126i		0		−1.23084	+	2.73588i		0
895.8		0		1.11570	−	1.32484i		0		0.263424	+	0.152088i		0		−2.36807	+	1.17993i		0		−0.510411	−	2.95626i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
36.f	odd	6	1	inner
252.bi	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.cx.i	✓	24
3.b	odd	2	1		3024.2.cx.i		24
4.b	odd	2	1		1008.2.cx.j	yes	24
7.b	odd	2	1	inner	1008.2.cx.i	✓	24
9.c	even	3	1		1008.2.cx.j	yes	24
9.d	odd	6	1		3024.2.cx.j		24
12.b	even	2	1		3024.2.cx.j		24
21.c	even	2	1		3024.2.cx.i		24
28.d	even	2	1		1008.2.cx.j	yes	24
36.f	odd	6	1	inner	1008.2.cx.i	✓	24
36.h	even	6	1		3024.2.cx.i		24
63.l	odd	6	1		1008.2.cx.j	yes	24
63.o	even	6	1		3024.2.cx.j		24
84.h	odd	2	1		3024.2.cx.j		24
252.s	odd	6	1		3024.2.cx.i		24
252.bi	even	6	1	inner	1008.2.cx.i	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.2.cx.i	✓	24	1.a	even	1	1	trivial
1008.2.cx.i	✓	24	7.b	odd	2	1	inner
1008.2.cx.i	✓	24	36.f	odd	6	1	inner
1008.2.cx.i	✓	24	252.bi	even	6	1	inner
1008.2.cx.j	yes	24	4.b	odd	2	1
1008.2.cx.j	yes	24	9.c	even	3	1
1008.2.cx.j	yes	24	28.d	even	2	1
1008.2.cx.j	yes	24	63.l	odd	6	1
3024.2.cx.i		24	3.b	odd	2	1
3024.2.cx.i		24	21.c	even	2	1
3024.2.cx.i		24	36.h	even	6	1
3024.2.cx.i		24	252.s	odd	6	1
3024.2.cx.j		24	9.d	odd	6	1
3024.2.cx.j		24	12.b	even	2	1
3024.2.cx.j		24	63.o	even	6	1
3024.2.cx.j		24	84.h	odd	2	1

Hecke kernels

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

T5^24 - 42*T5^22 + 1155*T5^20 - 18432*T5^18 + 212814*T5^16 - 1508085*T5^14 + 7717464*T5^12 - 23470965*T5^10 + 48769209*T5^8 - 31384908*T5^6 + 15148620*T5^4 - 1364688*T5^2 + 104976

T11^12 - 42*T11^10 + 1455*T11^8 - 81*T11^7 - 12627*T11^6 + 2781*T11^5 + 87786*T11^4 - 91773*T11^3 - 20655*T11^2 + 48114*T11 + 26244