Newform orbit 241.4.c.a

• Label: 241.4.c.a
• Level: $241$
• Weight: $4$
• Character orbit: 241.c
• Analytic conductor: $14.219$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	241.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.2194603114\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(60\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 120 q - q^{2} - 5 q^{3} - 235 q^{4} + 24 q^{5} + 13 q^{7} + 12 q^{8} - 585 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1	−2.79866	−	4.84742i	4.19931	−	7.27341i	−11.6650	+	20.2043i	−11.7610			−47.0097			15.0725	+	26.1064i	85.8065			−21.7683	−	37.7038i	32.9150	+	57.0104i
15.2	−2.67747	−	4.63751i	−3.28456	+	5.68902i	−10.3377	+	17.9054i	20.5169			35.1772			11.1433	+	19.3008i	67.8758			−8.07666	−	13.9892i	−54.9335	−	95.1476i
15.3	−2.65818	−	4.60411i	2.23001	−	3.86249i	−10.1319	+	17.5489i	12.4296			−23.7111			−6.05463	−	10.4869i	65.1985			3.55411	+	6.15590i	−33.0403	−	57.2274i
15.4	−2.64199	−	4.57607i	−3.75990	+	6.51233i	−9.96027	+	17.2517i	0.507671			39.7345			−16.9445	−	29.3488i	62.9880			−14.7736	−	25.5887i	−1.34126	−	2.32314i
15.5	−2.51505	−	4.35620i	−2.60656	+	4.51470i	−8.65098	+	14.9839i	−9.63211			26.2226			6.17466	+	10.6948i	46.7899			−0.0883573	−	0.153039i	24.2253	+	41.9594i
15.6	−2.46379	−	4.26740i	0.509220	−	0.881995i	−8.14048	+	14.0997i	−15.6845			−5.01844			−10.5896	−	18.3417i	40.8051			12.9814	+	22.4844i	38.6432	+	66.9320i
15.7	−2.31623	−	4.01183i	1.53923	−	2.66602i	−6.72986	+	11.6565i	6.87337			−14.2608			−0.357970	−	0.620022i	25.2919			8.76155	+	15.1755i	−15.9203	−	27.5748i
15.8	−2.26922	−	3.93040i	−0.666028	+	1.15360i	−6.29869	+	10.9096i	−4.46924			6.04545			15.0047	+	25.9888i	20.8649			12.6128	+	21.8460i	10.1417	+	17.5659i
15.9	−1.99327	−	3.45245i	3.94841	−	6.83884i	−3.94626	+	6.83513i	−10.9655			−31.4810			−5.99037	−	10.3756i	−0.428443			−17.6798	−	30.6224i	21.8572	+	37.8577i
15.10	−1.98063	−	3.43055i	4.71303	−	8.16321i	−3.84578	+	6.66109i	6.83714			−37.3391			−8.69317	−	15.0570i	−1.22180			−30.9253	−	53.5643i	−13.5418	−	23.4551i
15.11	−1.92566	−	3.33534i	−5.14699	+	8.91485i	−3.41631	+	5.91722i	0.456513			39.6454			0.826448	+	1.43145i	−4.49594			−39.4831	−	68.3867i	−0.879087	−	1.52262i
15.12	−1.81947	−	3.15142i	−2.16059	+	3.74225i	−2.62098	+	4.53966i	5.32814			15.7245			−11.6814	−	20.2328i	−10.0364			4.16371	+	7.21176i	−9.69442	−	16.7912i
15.13	−1.81680	−	3.14679i	−2.29104	+	3.96820i	−2.60154	+	4.50600i	18.8500			16.6495			−4.75600	−	8.23763i	−10.1629			3.00224	+	5.20003i	−34.2468	−	59.3172i
15.14	−1.77981	−	3.08272i	2.85538	−	4.94567i	−2.33544	+	4.04510i	13.8693			−20.3281			16.8834	+	29.2429i	−11.8504			−2.80643	−	4.86087i	−24.6847	−	42.7551i
15.15	−1.71322	−	2.96738i	−0.774772	+	1.34194i	−1.87023	+	3.23934i	8.10647			5.30941			3.00413	+	5.20330i	−14.5950			12.2995	+	21.3033i	−13.8882	−	24.0550i
15.16	−1.70908	−	2.96022i	−4.14300	+	7.17588i	−1.84193	+	3.19031i	−8.72976			28.3229			5.24883	+	9.09123i	−14.7533			−20.8289	−	36.0767i	14.9199	+	25.8420i
15.17	−1.49743	−	2.59363i	0.819740	−	1.41983i	−0.484619	+	0.839385i	−15.3472			−4.91003			5.11187	+	8.85401i	−21.0562			12.1561	+	21.0549i	22.9814	+	39.8050i
15.18	−1.39085	−	2.40902i	3.44745	−	5.97116i	0.131073	−	0.227024i	−10.3399			−19.1795			11.3611	+	19.6780i	−22.9828			−10.2698	−	17.7879i	14.3812	+	24.9090i
15.19	−1.30906	−	2.26736i	−2.91184	+	5.04346i	0.572724	−	0.991987i	−20.2461			15.2471			−6.19603	−	10.7318i	−23.9439			−3.45767	−	5.98886i	26.5034	+	45.9052i
15.20	−1.10704	−	1.91745i	0.852523	−	1.47661i	1.54893	−	2.68282i	−2.95332			−3.77510			−17.0149	−	29.4706i	−24.5715			12.0464	+	20.8650i	3.26944	+	5.66284i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	241.4.c.a	✓	120
241.c	even	3	1	inner	241.4.c.a	✓	120

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
241.4.c.a	✓	120	1.a	even	1	1	trivial
241.4.c.a	✓	120	241.c	even	3	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(241, [\chi])\).