Newform orbit 241.2.g.a

• Label: 241.2.g.a
• Level: $241$
• Weight: $2$
• Character orbit: 241.g
• Analytic conductor: $1.924$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.g (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.92439468871\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(19\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{7} + 4 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
8.1	−1.80860	−	1.80860i	−2.21112	−	2.21112i			4.54209i	1.53247	−	1.53247i			7.99807i	1.47933	+	3.57143i	4.59763	−	4.59763i			6.77810i	−5.54327
8.2	−1.77101	−	1.77101i	0.109190	+	0.109190i			4.27293i	−0.769138	+	0.769138i		−	0.386754i	0.567425	+	1.36988i	4.02537	−	4.02537i		−	2.97615i	2.72430
8.3	−1.72022	−	1.72022i	2.26448	+	2.26448i			3.91833i	2.95672	−	2.95672i		−	7.79081i	0.525484	+	1.26863i	3.29995	−	3.29995i			7.25571i	−10.1724
8.4	−1.49799	−	1.49799i	1.61583	+	1.61583i			2.48797i	−2.16699	+	2.16699i		−	4.84100i	−0.692542	−	1.67194i	0.730982	−	0.730982i			2.22179i	6.49227
8.5	−1.24616	−	1.24616i	−1.19390	−	1.19390i			1.10583i	0.730449	−	0.730449i			2.97558i	−0.949818	−	2.29306i	−1.11428	+	1.11428i		−	0.149215i	−1.82051
8.6	−1.03988	−	1.03988i	0.399610	+	0.399610i			0.162692i	1.77057	−	1.77057i		−	0.831090i	−0.377344	−	0.910989i	−1.91058	+	1.91058i		−	2.68062i	−3.68236
8.7	−0.808360	−	0.808360i	−1.00052	−	1.00052i		−	0.693108i	−2.27761	+	2.27761i			1.61756i	1.02603	+	2.47705i	−2.17700	+	2.17700i		−	0.997932i	3.68226
8.8	−0.363669	−	0.363669i	2.00782	+	2.00782i		−	1.73549i	−0.640553	+	0.640553i		−	1.46036i	1.19239	+	2.87868i	−1.35848	+	1.35848i			5.06266i	0.465899
8.9	−0.291821	−	0.291821i	1.20513	+	1.20513i		−	1.82968i	1.44600	−	1.44600i		−	0.703366i	−0.856375	−	2.06747i	−1.11758	+	1.11758i		−	0.0953083i	−0.843945
8.10	−0.216287	−	0.216287i	−0.866933	−	0.866933i		−	1.90644i	2.22270	−	2.22270i			0.375013i	1.96394	+	4.74137i	−0.844912	+	0.844912i		−	1.49685i	−0.961481
8.11	0.0740795	+	0.0740795i	−0.0194080	−	0.0194080i		−	1.98902i	−1.74801	+	1.74801i		−	0.00287547i	−1.62455	−	3.92202i	0.295505	−	0.295505i		−	2.99925i	−0.258983
8.12	0.152268	+	0.152268i	−2.25454	−	2.25454i		−	1.95363i	−0.928424	+	0.928424i		−	0.686589i	−0.387444	−	0.935371i	0.602011	−	0.602011i			7.16592i	−0.282738
8.13	0.716618	+	0.716618i	0.713254	+	0.713254i		−	0.972918i	0.909141	−	0.909141i			1.02226i	0.285086	+	0.688260i	2.13045	−	2.13045i		−	1.98254i	1.30301
8.14	0.950718	+	0.950718i	−1.23253	−	1.23253i		−	0.192269i	0.210136	−	0.210136i		−	2.34358i	0.227215	+	0.548545i	2.08423	−	2.08423i			0.0382621i	0.399560
8.15	0.993872	+	0.993872i	0.813080	+	0.813080i		−	0.0244387i	−2.56710	+	2.56710i			1.61619i	1.58719	+	3.83183i	2.01203	−	2.01203i		−	1.67780i	−5.10274
8.16	1.06412	+	1.06412i	2.40062	+	2.40062i			0.264723i	−0.960866	+	0.960866i			5.10912i	−1.75089	−	4.22703i	1.84655	−	1.84655i			8.52598i	−2.04496
8.17	1.46619	+	1.46619i	−1.25390	−	1.25390i			2.29941i	2.33758	−	2.33758i		−	3.67691i	−1.17667	−	2.84073i	−0.438989	+	0.438989i			0.144538i	6.85467
8.18	1.80836	+	1.80836i	0.651931	+	0.651931i			4.54033i	0.633418	−	0.633418i			2.35785i	−0.151859	−	0.366620i	−4.59383	+	4.59383i		−	2.14997i	2.29090
8.19	1.83067	+	1.83067i	−1.73388	−	1.73388i			4.70269i	−0.862064	+	0.862064i		−	6.34832i	1.52761	+	3.68798i	−4.94774	+	4.94774i			3.01268i	−3.15631
30.1	−1.95816	+	1.95816i	−1.49026	+	1.49026i		−	5.66880i	−1.96106	−	1.96106i		−	5.83633i	−1.64506	−	0.681406i	7.18409	+	7.18409i		−	1.44174i	7.68015

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
241.g	even	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	241.2.g.a	✓	76
241.g	even	8	1	inner	241.2.g.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
241.2.g.a	✓	76	1.a	even	1	1	trivial
241.2.g.a	✓	76	241.g	even	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(241, [\chi])\).