Newform orbit 143.4.e.a

• Label: 143.4.e.a
• Level: $143$
• Weight: $4$
• Character orbit: 143.e
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 4 q^{2} + 6 q^{3} - 78 q^{4} + 32 q^{5} - 14 q^{6} + 6 q^{7} + 126 q^{8} - 135 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
100.1	−2.72586	+	4.72134i	−3.35776	+	5.81581i	−10.8607	−	18.8112i	3.97680			−18.3056	−	31.7062i	−5.48891	−	9.50707i	74.8051			−9.04908	−	15.6735i	−10.8402	+	18.7758i
100.2	−2.65028	+	4.59042i	1.29711	−	2.24666i	−10.0480	−	17.4036i	−4.49343			6.87541	+	11.9086i	16.6322	+	28.8078i	64.1151			10.1350	+	17.5543i	11.9088	−	20.6267i
100.3	−2.35333	+	4.07609i	5.09818	−	8.83032i	−7.07634	−	12.2566i	19.7628			23.9954	+	41.5613i	1.43260	+	2.48133i	28.9586			−38.4830	−	66.6545i	−46.5084	+	80.5548i
100.4	−1.99496	+	3.45536i	−0.837037	+	1.44979i	−3.95969	−	6.85839i	−20.8270			−3.33970	−	5.78454i	−4.98381	−	8.63221i	−0.321630			12.0987	+	20.9556i	41.5489	−	71.9649i
100.5	−1.39751	+	2.42056i	−5.07280	+	8.78635i	0.0939301	+	0.162692i	5.45712			−14.1786	−	24.5580i	−3.86797	−	6.69952i	−22.8852			−37.9666	−	65.7601i	−7.62638	+	13.2093i
100.6	−1.37242	+	2.37710i	2.09604	−	3.63045i	0.232916	+	0.403423i	5.57379			5.75330	+	9.96502i	3.44074	+	5.95954i	−23.2374			4.71323	+	8.16355i	−7.64959	+	13.2495i
100.7	−1.01173	+	1.75236i	3.73606	−	6.47104i	1.95282	+	3.38238i	−6.22433			7.55973	+	13.0938i	−14.2839	−	24.7405i	−24.0905			−14.4162	−	24.9696i	6.29732	−	10.9073i
100.8	−0.875485	+	1.51638i	−1.73778	+	3.00992i	2.46705	+	4.27306i	−8.23074			−3.04279	−	5.27028i	8.98252	+	15.5582i	−22.6472			7.46026	+	12.9216i	7.20589	−	12.4810i
100.9	0.0572303	−	0.0991258i	−2.90301	+	5.02816i	3.99345	+	6.91686i	11.2238			0.332281	+	0.575527i	7.98278	+	13.8266i	1.82987			−3.35494	−	5.81093i	0.642343	−	1.11257i
100.10	0.274609	−	0.475636i	0.280984	−	0.486679i	3.84918	+	6.66698i	16.1600			−0.154321	−	0.267292i	−15.5667	−	26.9624i	8.62181			13.3421	+	23.1092i	4.43769	−	7.68630i
100.11	0.535504	−	0.927520i	2.99596	−	5.18916i	3.42647	+	5.93482i	0.973634			−3.20870	−	5.55764i	14.1596	+	24.5251i	15.9076			−4.45160	−	7.71041i	0.521385	−	0.903066i
100.12	1.23624	−	2.14123i	−3.24665	+	5.62336i	0.943432	+	1.63407i	−10.7576			8.02726	+	13.9036i	−12.4880	−	21.6299i	24.4450			−7.58147	−	13.1315i	−13.2990	+	23.0345i
100.13	1.58741	−	2.74948i	−1.39720	+	2.42003i	−1.03977	−	1.80093i	−8.68483			4.43589	+	7.68318i	3.36772	+	5.83306i	18.7965			9.59564	+	16.6201i	−13.7864	+	23.8788i
100.14	1.60580	−	2.78133i	3.36970	−	5.83650i	−1.15719	−	2.00431i	9.24473			−10.8221	−	18.7445i	−4.28214	−	7.41689i	18.2600			−9.20981	−	15.9519i	14.8452	−	25.7126i
100.15	2.09463	−	3.62801i	4.10387	−	7.10811i	−4.77499	−	8.27053i	−18.8743			−17.1922	−	29.7778i	7.40609	+	12.8277i	−6.49330			−20.1835	−	34.9588i	−39.5349	+	68.4764i
100.16	2.30726	−	3.99630i	−1.84379	+	3.19354i	−6.64694	−	11.5128i	19.7910			8.50823	+	14.7367i	9.39345	+	16.2699i	−24.4287			6.70087	+	11.6062i	45.6630	−	79.0906i
100.17	2.68288	−	4.64689i	0.418116	−	0.724197i	−10.3957	−	18.0059i	1.92861			−2.24351	−	3.88587i	−8.83613	−	15.3046i	−68.6355			13.1504	+	22.7771i	5.17423	−	8.96203i
133.1	−2.72586	−	4.72134i	−3.35776	−	5.81581i	−10.8607	+	18.8112i	3.97680			−18.3056	+	31.7062i	−5.48891	+	9.50707i	74.8051			−9.04908	+	15.6735i	−10.8402	−	18.7758i
133.2	−2.65028	−	4.59042i	1.29711	+	2.24666i	−10.0480	+	17.4036i	−4.49343			6.87541	−	11.9086i	16.6322	−	28.8078i	64.1151			10.1350	−	17.5543i	11.9088	+	20.6267i
133.3	−2.35333	−	4.07609i	5.09818	+	8.83032i	−7.07634	+	12.2566i	19.7628			23.9954	−	41.5613i	1.43260	−	2.48133i	28.9586			−38.4830	+	66.6545i	−46.5084	−	80.5548i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.4.e.a	✓	34
13.c	even	3	1	inner	143.4.e.a	✓	34
13.c	even	3	1		1859.4.a.i		17
13.e	even	6	1		1859.4.a.f		17

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.e.a	✓	34	1.a	even	1	1	trivial
143.4.e.a	✓	34	13.c	even	3	1	inner
1859.4.a.f		17	13.e	even	6	1
1859.4.a.i		17	13.c	even	3	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^34 + 4*T2^33 + 115*T2^32 + 354*T2^31 + 7352*T2^30 + 19531*T2^29 + 312084*T2^28 + 696155*T2^27 + 9668086*T2^26 + 18624240*T2^25 + 226757301*T2^24 + 371002568*T2^23 + 4116675310*T2^22 + 5818922153*T2^21 + 58316032768*T2^20 + 70010350677*T2^19 + 645483943354*T2^18 + 665751631276*T2^17 + 5552513934451*T2^16 + 4716575929788*T2^15 + 36654408649812*T2^14 + 24897019167423*T2^13 + 181340545416258*T2^12 + 81681968639223*T2^11 + 643641412021731*T2^10 + 135482173045746*T2^9 + 1555286413119964*T2^8 - 284542580799920*T2^7 + 2210370238971440*T2^6 - 1144906292648448*T2^5 + 2434518882805568*T2^4 - 1204303636258816*T2^3 + 651292827065344*T2^2 - 71092926087168*T2 + 6744367448064