Newform orbit 161.2.g.a

• Label: 161.2.g.a
• Level: $161$
• Weight: $2$
• Character orbit: 161.g
• Analytic conductor: $1.286$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.28559147254\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
45.1	−1.23299	−	2.13559i	0.854402	+	0.493289i	−2.04051	+	3.53426i	−1.24346	−	2.15373i		−	2.43287i	−2.57635	+	0.602017i	5.13171			−1.01333	−	1.75514i	−3.06632	+	5.31103i
45.2	−1.23299	−	2.13559i	0.854402	+	0.493289i	−2.04051	+	3.53426i	1.24346	+	2.15373i		−	2.43287i	2.57635	−	0.602017i	5.13171			−1.01333	−	1.75514i	3.06632	−	5.31103i
45.3	−1.06863	−	1.85092i	−2.39984	−	1.38555i	−1.28394	+	2.22386i	−1.92742	−	3.33839i			5.92256i	2.36835	−	1.17938i	1.21373			2.33949	+	4.05212i	−4.11940	+	7.13501i
45.4	−1.06863	−	1.85092i	−2.39984	−	1.38555i	−1.28394	+	2.22386i	1.92742	+	3.33839i			5.92256i	−2.36835	+	1.17938i	1.21373			2.33949	+	4.05212i	4.11940	−	7.13501i
45.5	−0.559952	−	0.969865i	2.13402	+	1.23207i	0.372908	−	0.645896i	−0.871219	−	1.50900i		−	2.75961i	−0.785854	−	2.52635i	−3.07505			1.53601	+	2.66045i	−0.975681	+	1.68993i
45.6	−0.559952	−	0.969865i	2.13402	+	1.23207i	0.372908	−	0.645896i	0.871219	+	1.50900i		−	2.75961i	0.785854	+	2.52635i	−3.07505			1.53601	+	2.66045i	0.975681	−	1.68993i
45.7	−0.304604	−	0.527589i	−1.12858	−	0.651588i	0.814433	−	1.41064i	−0.594638	−	1.02994i			0.793904i	−2.44810	+	1.00340i	−2.21073			−0.650867	−	1.12733i	−0.362258	+	0.627449i
45.8	−0.304604	−	0.527589i	−1.12858	−	0.651588i	0.814433	−	1.41064i	0.594638	+	1.02994i			0.793904i	2.44810	−	1.00340i	−2.21073			−0.650867	−	1.12733i	0.362258	−	0.627449i
45.9	0.292153	+	0.506024i	0.510598	+	0.294794i	0.829293	−	1.43638i	−1.76663	−	3.05989i			0.344500i	2.22044	+	1.43862i	2.13773			−1.32619	−	2.29703i	1.03225	−	1.78791i
45.10	0.292153	+	0.506024i	0.510598	+	0.294794i	0.829293	−	1.43638i	1.76663	+	3.05989i			0.344500i	−2.22044	−	1.43862i	2.13773			−1.32619	−	2.29703i	−1.03225	+	1.78791i
45.11	0.724735	+	1.25528i	−2.07526	−	1.19815i	−0.0504829	+	0.0874389i	−1.26781	−	2.19591i		−	3.47337i	−1.91509	−	1.82550i	2.75259			1.37113	+	2.37487i	1.83766	−	3.18291i
45.12	0.724735	+	1.25528i	−2.07526	−	1.19815i	−0.0504829	+	0.0874389i	1.26781	+	2.19591i		−	3.47337i	1.91509	+	1.82550i	2.75259			1.37113	+	2.37487i	−1.83766	+	3.18291i
45.13	1.14928	+	1.99062i	0.604669	+	0.349106i	−1.64170	+	2.84351i	−0.630826	−	1.09262i			1.60489i	−0.738016	+	2.54073i	−2.94999			−1.25625	−	2.17589i	1.44999	−	2.51146i
45.14	1.14928	+	1.99062i	0.604669	+	0.349106i	−1.64170	+	2.84351i	0.630826	+	1.09262i			1.60489i	0.738016	−	2.54073i	−2.94999			−1.25625	−	2.17589i	−1.44999	+	2.51146i
68.1	−1.23299	+	2.13559i	0.854402	−	0.493289i	−2.04051	−	3.53426i	−1.24346	+	2.15373i			2.43287i	−2.57635	−	0.602017i	5.13171			−1.01333	+	1.75514i	−3.06632	−	5.31103i
68.2	−1.23299	+	2.13559i	0.854402	−	0.493289i	−2.04051	−	3.53426i	1.24346	−	2.15373i			2.43287i	2.57635	+	0.602017i	5.13171			−1.01333	+	1.75514i	3.06632	+	5.31103i
68.3	−1.06863	+	1.85092i	−2.39984	+	1.38555i	−1.28394	−	2.22386i	−1.92742	+	3.33839i		−	5.92256i	2.36835	+	1.17938i	1.21373			2.33949	−	4.05212i	−4.11940	−	7.13501i
68.4	−1.06863	+	1.85092i	−2.39984	+	1.38555i	−1.28394	−	2.22386i	1.92742	−	3.33839i		−	5.92256i	−2.36835	−	1.17938i	1.21373			2.33949	−	4.05212i	4.11940	+	7.13501i
68.5	−0.559952	+	0.969865i	2.13402	−	1.23207i	0.372908	+	0.645896i	−0.871219	+	1.50900i			2.75961i	−0.785854	+	2.52635i	−3.07505			1.53601	−	2.66045i	−0.975681	−	1.68993i
68.6	−0.559952	+	0.969865i	2.13402	−	1.23207i	0.372908	+	0.645896i	0.871219	−	1.50900i			2.75961i	0.785854	−	2.52635i	−3.07505			1.53601	−	2.66045i	0.975681	+	1.68993i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
23.b	odd	2	1	inner
161.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	161.2.g.a	✓	28
7.c	even	3	1		1127.2.c.c		28
7.d	odd	6	1	inner	161.2.g.a	✓	28
7.d	odd	6	1		1127.2.c.c		28
23.b	odd	2	1	inner	161.2.g.a	✓	28
161.f	odd	6	1		1127.2.c.c		28
161.g	even	6	1	inner	161.2.g.a	✓	28
161.g	even	6	1		1127.2.c.c		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
161.2.g.a	✓	28	1.a	even	1	1	trivial
161.2.g.a	✓	28	7.d	odd	6	1	inner
161.2.g.a	✓	28	23.b	odd	2	1	inner
161.2.g.a	✓	28	161.g	even	6	1	inner
1127.2.c.c		28	7.c	even	3	1
1127.2.c.c		28	7.d	odd	6	1
1127.2.c.c		28	161.f	odd	6	1
1127.2.c.c		28	161.g	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(161, [\chi])\).