Newform orbit 1001.2.i.b

• Label: 1001.2.i.b
• Level: $1001$
• Weight: $2$
• Character orbit: 1001.i
• Analytic conductor: $7.993$
• Analytic rank: $0$
• Dimension: $22$
• 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:	\(22\)
Relative dimension:	\(11\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
144.1	−1.20504	−	2.08720i	−0.407005	+	0.704953i	−1.90426	+	3.29827i	0.841551	+	1.45761i	1.96183			2.42416	−	1.05992i	4.35868			1.16869	+	2.02424i	2.02821	−	3.51297i
144.2	−0.888734	−	1.53933i	1.21685	−	2.10765i	−0.579698	+	1.00407i	−0.615526	−	1.06612i	−4.32583			−1.36894	−	2.26407i	−1.49415			−1.46146	−	2.53132i	−1.09408	+	1.89500i
144.3	−0.804599	−	1.39361i	−0.690951	+	1.19676i	−0.294760	+	0.510539i	−1.42043	−	2.46026i	2.22375			2.05528	+	1.66608i	−2.26974			0.545174	+	0.944269i	−2.28575	+	3.95904i
144.4	−0.270580	−	0.468659i	−0.551742	+	0.955645i	0.853573	−	1.47843i	−1.64274	−	2.84530i	0.597162			−2.51185	−	0.831024i	−2.00616			0.891162	+	1.54354i	−0.888984	+	1.53977i
144.5	−0.255862	−	0.443166i	0.600221	−	1.03961i	0.869069	−	1.50527i	0.151803	+	0.262931i	−0.614295			1.50410	+	2.17662i	−1.91289			0.779470	+	1.35008i	0.0776815	−	0.134548i
144.6	0.255576	+	0.442671i	1.21931	−	2.11190i	0.869362	−	1.50578i	1.12635	+	1.95089i	1.24651			2.61089	+	0.428094i	1.91106			−1.47343	−	2.55205i	−0.575736	+	0.997204i
144.7	0.433418	+	0.750701i	−0.161081	+	0.279000i	0.624298	−	1.08132i	−0.613490	−	1.06260i	−0.279261			2.39620	−	1.12171i	2.81600			1.44811	+	2.50819i	0.531794	−	0.921095i
144.8	0.639075	+	1.10691i	−0.0963266	+	0.166842i	0.183165	−	0.317251i	1.68734	+	2.92255i	−0.246240			−1.87102	−	1.87064i	3.02453			1.48144	+	2.56593i	−2.15667	+	3.73546i
144.9	0.788597	+	1.36589i	−1.39555	+	2.41716i	−0.243771	+	0.422225i	−0.840469	−	1.45573i	−4.40210			−0.225830	−	2.63610i	2.38544			−2.39510	−	4.14844i	1.32558	−	2.29598i
144.10	1.04293	+	1.80641i	1.10066	−	1.90639i	−1.17542	+	2.03588i	0.882491	+	1.52852i	4.59164			0.743157	−	2.53924i	−0.731784			−0.922890	−	1.59849i	−1.84076	+	3.18828i
144.11	1.26522	+	2.19143i	−1.33439	+	2.31123i	−2.20156	+	3.81322i	0.443121	+	0.767508i	−6.75317			1.74386	+	1.98971i	−6.08097			−2.06117	−	3.57006i	−1.12129	+	1.94213i
716.1	−1.20504	+	2.08720i	−0.407005	−	0.704953i	−1.90426	−	3.29827i	0.841551	−	1.45761i	1.96183			2.42416	+	1.05992i	4.35868			1.16869	−	2.02424i	2.02821	+	3.51297i
716.2	−0.888734	+	1.53933i	1.21685	+	2.10765i	−0.579698	−	1.00407i	−0.615526	+	1.06612i	−4.32583			−1.36894	+	2.26407i	−1.49415			−1.46146	+	2.53132i	−1.09408	−	1.89500i
716.3	−0.804599	+	1.39361i	−0.690951	−	1.19676i	−0.294760	−	0.510539i	−1.42043	+	2.46026i	2.22375			2.05528	−	1.66608i	−2.26974			0.545174	−	0.944269i	−2.28575	−	3.95904i
716.4	−0.270580	+	0.468659i	−0.551742	−	0.955645i	0.853573	+	1.47843i	−1.64274	+	2.84530i	0.597162			−2.51185	+	0.831024i	−2.00616			0.891162	−	1.54354i	−0.888984	−	1.53977i
716.5	−0.255862	+	0.443166i	0.600221	+	1.03961i	0.869069	+	1.50527i	0.151803	−	0.262931i	−0.614295			1.50410	−	2.17662i	−1.91289			0.779470	−	1.35008i	0.0776815	+	0.134548i
716.6	0.255576	−	0.442671i	1.21931	+	2.11190i	0.869362	+	1.50578i	1.12635	−	1.95089i	1.24651			2.61089	−	0.428094i	1.91106			−1.47343	+	2.55205i	−0.575736	−	0.997204i
716.7	0.433418	−	0.750701i	−0.161081	−	0.279000i	0.624298	+	1.08132i	−0.613490	+	1.06260i	−0.279261			2.39620	+	1.12171i	2.81600			1.44811	−	2.50819i	0.531794	+	0.921095i
716.8	0.639075	−	1.10691i	−0.0963266	−	0.166842i	0.183165	+	0.317251i	1.68734	−	2.92255i	−0.246240			−1.87102	+	1.87064i	3.02453			1.48144	−	2.56593i	−2.15667	−	3.73546i
716.9	0.788597	−	1.36589i	−1.39555	−	2.41716i	−0.243771	−	0.422225i	−0.840469	+	1.45573i	−4.40210			−0.225830	+	2.63610i	2.38544			−2.39510	+	4.14844i	1.32558	+	2.29598i

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.b	✓	22
7.c	even	3	1	inner	1001.2.i.b	✓	22
7.c	even	3	1		7007.2.a.v		11
7.d	odd	6	1		7007.2.a.u		11

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1001.2.i.b	✓	22	1.a	even	1	1	trivial
1001.2.i.b	✓	22	7.c	even	3	1	inner
7007.2.a.u		11	7.d	odd	6	1
7007.2.a.v		11	7.c	even	3	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^22 - 2*T2^21 + 16*T2^20 - 24*T2^19 + 146*T2^18 - 199*T2^17 + 816*T2^16 - 910*T2^15 + 3075*T2^14 - 3064*T2^13 + 7931*T2^12 - 6340*T2^11 + 13653*T2^10 - 9134*T2^9 + 15043*T2^8 - 5766*T2^7 + 7963*T2^6 - 1407*T2^5 + 3060*T2^4 - 234*T2^3 + 594*T2^2 + 81