Newform orbit 1001.2.i.c

• Label: 1001.2.i.c
• Level: $1001$
• Weight: $2$
• Character orbit: 1001.i
• Analytic conductor: $7.993$
• Analytic rank: $0$
• Dimension: $30$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.99302524233\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(15\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 6 q^{2} + 2 q^{3} - 10 q^{4} + 3 q^{5} + 14 q^{6} + q^{7} - 30 q^{8} - 7 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
144.1	−1.07340	−	1.85919i	0.590698	−	1.02312i	−1.30438	+	2.25925i	−0.426156	−	0.738123i	−2.53623			1.86609	+	1.87556i	1.30689			0.802151	+	1.38937i	−0.914872	+	1.58461i
144.2	−1.03007	−	1.78413i	−0.206576	+	0.357800i	−1.12209	+	1.94352i	1.38101	+	2.39198i	0.851152			−1.25510	−	2.32911i	0.503049			1.41465	+	2.45025i	2.84508	−	4.92783i
144.3	−0.553376	−	0.958475i	−1.58833	+	2.75107i	0.387551	−	0.671258i	0.503027	+	0.871268i	3.51577			−0.887459	−	2.49247i	−3.07135			−3.54558	−	6.14112i	0.556726	−	0.964277i
144.4	−0.537998	−	0.931839i	−0.739637	+	1.28109i	0.421117	−	0.729396i	−0.447963	−	0.775894i	1.59169			−1.28075	+	2.31510i	−3.05823			0.405875	+	0.702997i	−0.482006	+	0.834858i
144.5	−0.447792	−	0.775599i	1.17397	−	2.03338i	0.598965	−	1.03744i	−0.781149	−	1.35299i	−2.10278			−2.50896	−	0.839724i	−2.86401			−1.25642	−	2.17619i	−0.699585	+	1.21172i
144.6	−0.319900	−	0.554083i	0.383574	−	0.664370i	0.795328	−	1.37755i	1.50896	+	2.61359i	−0.490822			2.61492	−	0.402729i	−2.29730			1.20574	+	2.08841i	0.965431	−	1.67218i
144.7	0.116639	+	0.202024i	−0.852036	+	1.47577i	0.972791	−	1.68492i	−0.677213	−	1.17297i	−0.397522			2.54707	−	0.715830i	0.920416			0.0480696	+	0.0832589i	0.157979	−	0.273627i
144.8	0.308098	+	0.533641i	1.59381	−	2.76057i	0.810151	−	1.40322i	−0.395666	−	0.685314i	1.96420			0.990245	+	2.45345i	2.23082			−3.58048	−	6.20158i	0.243808	−	0.422288i
144.9	0.562859	+	0.974901i	−0.134710	+	0.233325i	0.366378	−	0.634586i	1.20055	+	2.07942i	−0.303292			−0.102682	−	2.64376i	3.07632			1.46371	+	2.53521i	−1.35149	+	2.34084i
144.10	0.630467	+	1.09200i	−0.824485	+	1.42805i	0.205023	−	0.355110i	−1.25644	−	2.17621i	−2.07924			−2.61739	−	0.386363i	3.03891			0.140449	+	0.243264i	1.58429	−	2.74406i
144.11	0.636280	+	1.10207i	0.842866	−	1.45989i	0.190297	−	0.329603i	−0.220082	−	0.381193i	2.14519			2.41748	−	1.07507i	3.02945			0.0791540	+	0.137099i	0.280067	−	0.485091i
144.12	0.920551	+	1.59444i	−1.06605	+	1.84646i	−0.694827	+	1.20348i	1.11689	+	1.93452i	−3.92543			−0.920997	+	2.48028i	1.12371			−0.772944	−	1.33878i	−2.05631	+	3.56164i
144.13	1.13470	+	1.96536i	0.775053	−	1.34243i	−1.57509	+	2.72814i	1.30810	+	2.26569i	3.51781			−2.63722	−	0.212283i	−2.61022			0.298587	+	0.517168i	−2.96860	+	5.14176i
144.14	1.26924	+	2.19838i	1.24990	−	2.16489i	−2.22192	+	3.84847i	−1.29532	−	2.24356i	6.34567			2.15418	−	1.53607i	−6.20359			−1.62451	−	2.81373i	3.28813	−	5.69521i
144.15	1.38371	+	2.39665i	−0.198051	+	0.343034i	−2.82930	+	4.90048i	−0.0185554	−	0.0321388i	−1.09618			0.120564	+	2.64300i	−10.1248			1.42155	+	2.46220i	0.0513504	−	0.0889415i
716.1	−1.07340	+	1.85919i	0.590698	+	1.02312i	−1.30438	−	2.25925i	−0.426156	+	0.738123i	−2.53623			1.86609	−	1.87556i	1.30689			0.802151	−	1.38937i	−0.914872	−	1.58461i
716.2	−1.03007	+	1.78413i	−0.206576	−	0.357800i	−1.12209	−	1.94352i	1.38101	−	2.39198i	0.851152			−1.25510	+	2.32911i	0.503049			1.41465	−	2.45025i	2.84508	+	4.92783i
716.3	−0.553376	+	0.958475i	−1.58833	−	2.75107i	0.387551	+	0.671258i	0.503027	−	0.871268i	3.51577			−0.887459	+	2.49247i	−3.07135			−3.54558	+	6.14112i	0.556726	+	0.964277i
716.4	−0.537998	+	0.931839i	−0.739637	−	1.28109i	0.421117	+	0.729396i	−0.447963	+	0.775894i	1.59169			−1.28075	−	2.31510i	−3.05823			0.405875	−	0.702997i	−0.482006	−	0.834858i
716.5	−0.447792	+	0.775599i	1.17397	+	2.03338i	0.598965	+	1.03744i	−0.781149	+	1.35299i	−2.10278			−2.50896	+	0.839724i	−2.86401			−1.25642	+	2.17619i	−0.699585	−	1.21172i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1001.2.i.c	✓	30
7.c	even	3	1	inner	1001.2.i.c	✓	30
7.c	even	3	1		7007.2.a.z		15
7.d	odd	6	1		7007.2.a.ba		15

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1001.2.i.c	✓	30	1.a	even	1	1	trivial
1001.2.i.c	✓	30	7.c	even	3	1	inner
7007.2.a.z		15	7.c	even	3	1
7007.2.a.ba		15	7.d	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^30 - 6*T2^29 + 38*T2^28 - 130*T2^27 + 505*T2^26 - 1333*T2^25 + 4111*T2^24 - 8901*T2^23 + 22544*T2^22 - 40389*T2^21 + 87885*T2^20 - 132355*T2^19 + 248855*T2^18 - 307371*T2^17 + 509855*T2^16 - 522053*T2^15 + 789550*T2^14 - 658048*T2^13 + 916709*T2^12 - 614391*T2^11 + 813047*T2^10 - 426118*T2^9 + 526953*T2^8 - 211042*T2^7 + 248184*T2^6 - 76725*T2^5 + 72081*T2^4 - 17802*T2^3 + 13565*T2^2 - 2461*T2 + 529