Newform orbit 229.4.g.a

• Label: 229.4.g.a
• Level: $229$
• Weight: $4$
• Character orbit: 229.g
• Analytic conductor: $13.511$
• Analytic rank: $0$
• Dimension: $1026$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	229.g (of order \(19\), degree \(18\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.5114373913\)
Analytic rank:	\(0\)
Dimension:	\(1026\)
Relative dimension:	\(57\) over \(\Q(\zeta_{19})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{19}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1026 q - 15 q^{2} - 21 q^{3} - 257 q^{4} + 57 q^{5} + 3 q^{6} + 7 q^{7} + 23 q^{8} - 470 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
16.1	−3.73146	+	4.05345i	−2.74981	+	6.26892i	−1.84600	−	22.2779i	11.3405	+	3.89321i	−15.1500	−	34.5384i	5.48446	+	21.6577i	62.4086	+	48.5746i	−13.4514	−	14.6121i	−58.0977	+	31.4409i
16.2	−3.71275	+	4.03312i	2.13632	−	4.87032i	−1.82093	−	21.9753i	3.70548	+	1.27209i	11.7110	+	26.6983i	−1.61547	−	6.37936i	60.7822	+	47.3087i	−0.869528	−	0.944559i	−18.8880	+	10.2217i
16.3	−3.54340	+	3.84916i	−0.642373	+	1.46446i	−1.59970	−	19.3055i	−15.3330	−	5.26382i	−3.36076	−	7.66177i	−0.615535	−	2.43069i	46.9494	+	36.5422i	16.5546	+	17.9831i	74.5922	−	40.3673i
16.4	−3.25282	+	3.53350i	−0.120106	+	0.273815i	−1.24418	−	15.0150i	11.9544	+	4.10396i	−0.576842	−	1.31507i	−5.70335	−	22.5220i	26.7823	+	20.8455i	18.2261	+	19.7988i	−53.3869	+	28.8915i
16.5	−3.12247	+	3.39191i	−3.23307	+	7.37066i	−1.09458	−	13.2096i	2.42922	+	0.833951i	−14.9054	−	33.9810i	−6.62729	−	26.1706i	19.1181	+	14.8802i	−25.5873	−	27.7952i	−10.4138	+	5.63569i
16.6	−3.10100	+	3.36859i	2.21721	−	5.05472i	−1.07052	−	12.9193i	−4.71273	−	1.61788i	10.1517	+	23.1436i	7.35379	+	29.0394i	17.9342	+	13.9588i	−2.34763	−	2.55021i	20.0642	−	10.8582i
16.7	−3.05188	+	3.31522i	3.64392	−	8.30729i	−1.01611	−	12.2626i	−2.43674	−	0.836535i	16.4197	+	37.4332i	−2.64590	−	10.4484i	15.3070	+	11.9139i	−37.4464	−	40.6776i	10.2099	−	5.52535i
16.8	−2.97567	+	3.23244i	−0.505715	+	1.15291i	−0.933416	−	11.2647i	−7.34930	−	2.52302i	−2.22188	−	5.06538i	5.24902	+	20.7279i	11.4528	+	8.91409i	17.2131	+	18.6985i	30.0246	−	16.2485i
16.9	−2.92452	+	3.17687i	−2.94435	+	6.71244i	−0.879084	−	10.6090i	−12.6560	−	4.34481i	−12.7138	−	28.9845i	−0.589847	−	2.32925i	9.01402	+	7.01589i	−18.1010	−	19.6630i	50.8156	−	27.5001i
16.10	−2.88771	+	3.13688i	2.46240	−	5.61370i	−0.840566	−	10.1441i	19.9456	+	6.84734i	10.4988	+	23.9350i	5.25803	+	20.7635i	7.33118	+	5.70609i	−7.16362	−	7.78176i	−79.0764	+	42.7940i
16.11	−2.75753	+	2.99547i	−1.19095	+	2.71510i	−0.708268	−	8.54753i	13.2038	+	4.53287i	−4.84893	−	11.0544i	2.97623	+	11.7529i	1.85330	+	1.44248i	12.3332	+	13.3974i	−49.9879	+	27.0521i
16.12	−2.59770	+	2.82185i	2.00928	−	4.58069i	−0.554180	−	6.68796i	−16.4245	−	5.63854i	7.70654	+	17.5691i	−8.27532	−	32.6785i	−3.90180	−	3.03690i	1.34105	+	1.45677i	58.5770	−	31.7003i
16.13	−2.27592	+	2.47231i	−3.99263	+	9.10228i	−0.271859	−	3.28085i	−5.04118	−	1.73064i	−13.4167	−	30.5871i	7.99251	+	31.5617i	−12.4844	−	9.71703i	−48.6238	−	52.8196i	15.7520	−	8.52455i
16.14	−2.19838	+	2.38808i	1.33868	−	3.05188i	−0.209406	−	2.52716i	−5.92527	−	2.03415i	4.34521	+	9.90607i	1.41081	+	5.57117i	−13.9963	−	10.8938i	10.7647	+	11.6936i	17.8837	−	9.67819i
16.15	−2.13762	+	2.32207i	0.426314	−	0.971898i	−0.161972	−	1.95471i	10.7360	+	3.68569i	1.34552	+	3.06748i	−4.95132	−	19.5523i	−15.0401	−	11.7062i	17.5238	+	19.0359i	−31.5080	+	17.0513i
16.16	−1.98732	+	2.15880i	−1.88592	+	4.29947i	−0.0503605	−	0.607761i	5.50356	+	1.88937i	−5.53377	−	12.6157i	1.41395	+	5.58355i	−17.1122	−	13.3190i	3.35788	+	3.64763i	−15.0161	+	8.12630i
16.17	−1.66087	+	1.80418i	4.14560	−	9.45101i	0.164040	+	1.97967i	2.81340	+	0.965841i	10.1661	+	23.1763i	2.32401	+	9.17729i	−19.3255	−	15.0416i	−53.8490	−	58.4956i	−6.41523	+	3.47175i
16.18	−1.57437	+	1.71022i	−1.56995	+	3.57913i	0.214417	+	2.58763i	−9.54173	−	3.27568i	−3.64943	−	8.31986i	−4.96797	−	19.6181i	−19.4381	−	15.1293i	7.94115	+	8.62639i	20.6244	−	11.1613i
16.19	−1.45929	+	1.58521i	−3.13463	+	7.14624i	0.277268	+	3.34612i	16.9279	+	5.81135i	−6.75396	−	15.3975i	0.683761	+	2.70011i	−19.3113	−	15.0306i	−22.9562	−	24.9371i	−33.9149	+	18.3538i
16.20	−1.35201	+	1.46867i	2.39641	−	5.46328i	0.331562	+	4.00136i	7.26705	+	2.49478i	4.78379	+	10.9059i	−3.06207	−	12.0918i	−18.9274	−	14.7318i	−5.81797	−	6.32000i	−13.4891	+	7.29995i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
229.g	even	19	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	229.4.g.a	✓	1026
229.g	even	19	1	inner	229.4.g.a	✓	1026

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
229.4.g.a	✓	1026	1.a	even	1	1	trivial
229.4.g.a	✓	1026	229.g	even	19	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(229, [\chi])\).