Newform orbit 43.6.g.a

• Label: 43.6.g.a
• Level: $43$
• Weight: $6$
• Character orbit: 43.g
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $204$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(204\)
Relative dimension:	\(17\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1	−6.52161	−	8.17784i	17.3296	+	2.61202i	−17.2250	+	75.4676i	2.46584	+	1.68118i	−91.6562	−	158.753i	94.8911	−	164.356i	427.928	−	206.079i	61.2883	+	18.9049i	−2.33281	−	31.1292i
9.2	−5.80705	−	7.28181i	−18.0713	−	2.72380i	−12.1822	+	53.3739i	−87.0006	−	59.3160i	85.1064	+	147.409i	−25.6945	+	44.5042i	190.876	−	91.9209i	86.9470	+	26.8196i	73.2889	+	977.972i
9.3	−5.47096	−	6.86037i	−18.4151	−	2.77564i	−10.0126	+	43.8679i	64.4216	+	43.9219i	81.7066	+	141.520i	8.11387	−	14.0536i	102.744	−	49.4787i	99.2091	+	30.6020i	−51.1277	−	682.251i
9.4	−5.14921	−	6.45690i	12.1966	+	1.83835i	−8.05656	+	35.2981i	6.56775	+	4.47782i	−50.9330	−	88.2185i	−125.151	+	216.768i	31.2951	−	15.0709i	−86.8258	−	26.7822i	−4.90589	−	65.4645i
9.5	−3.60873	−	4.52520i	−0.0525050	−	0.00791386i	−0.333852	+	1.46270i	−19.3143	−	13.1682i	0.153664	+	0.266155i	53.2202	−	92.1801i	−159.048	+	76.5937i	−232.201	−	71.6247i	10.1110	+	134.921i
9.6	−2.33890	−	2.93289i	28.6156	+	4.31311i	3.98929	−	17.4782i	−77.5461	−	52.8700i	−54.2792	−	94.0143i	35.5619	−	61.5951i	−168.746	+	81.2638i	568.046	+	175.219i	26.3107	+	351.092i
9.7	−1.80763	−	2.26670i	21.5746	+	3.25185i	5.25028	−	23.0030i	62.1654	+	42.3837i	−31.6280	−	54.7813i	1.33082	−	2.30504i	−145.219	+	69.9337i	222.685	+	68.6892i	−16.3012	−	217.525i
9.8	−1.23023	−	1.54266i	−24.9627	−	3.76252i	6.25434	−	27.4020i	−22.2688	−	15.1826i	24.9055	+	43.1377i	−4.12718	+	7.14849i	−106.854	+	51.4581i	376.774	+	116.219i	3.97415	+	53.0313i
9.9	−1.10270	−	1.38274i	−5.76893	−	0.869526i	6.42464	−	28.1482i	43.6641	+	29.7697i	5.15906	+	8.93576i	20.6505	−	35.7677i	−96.9964	+	46.7110i	−199.680	−	61.5931i	−6.98461	−	93.2031i
9.10	0.425286	+	0.533292i	2.86518	+	0.431857i	7.01714	−	30.7441i	−54.5646	−	37.2015i	0.988217	+	1.71164i	−110.445	+	191.296i	39.0457	−	18.8034i	−224.181	−	69.1508i	−3.36630	−	44.9201i
9.11	2.53765	+	3.18211i	2.05098	+	0.309135i	3.43451	−	15.0476i	−53.1952	−	36.2679i	4.22095	+	7.31090i	95.1032	−	164.724i	173.943	−	83.7664i	−228.093	−	70.3575i	−19.5823	−	261.308i
9.12	2.59848	+	3.25839i	17.4103	+	2.62418i	3.25566	−	14.2640i	30.9820	+	21.1232i	36.6897	+	63.5485i	16.4293	−	28.4563i	175.095	−	84.3211i	64.0287	+	19.7502i	11.6786	+	155.840i
9.13	2.92560	+	3.66858i	−13.3552	−	2.01297i	2.22129	−	9.73211i	69.6328	+	47.4749i	−31.6872	−	54.8838i	−99.9777	+	173.166i	177.485	−	85.4723i	−57.8948	−	17.8582i	29.5522	+	394.346i
9.14	3.93041	+	4.92858i	−23.5623	−	3.55144i	−1.72210	+	7.54503i	6.81244	+	4.64464i	−75.1059	−	130.087i	57.5727	−	99.7189i	137.793	−	66.3574i	310.364	+	95.7346i	3.88420	+	51.8310i
9.15	5.30682	+	6.65454i	23.7101	+	3.57372i	−8.99992	+	39.4312i	−24.4442	−	16.6658i	102.044	+	176.745i	−48.7498	+	84.4371i	−64.7633	+	31.1883i	317.192	+	97.8407i	−18.8179	−	251.108i
9.16	5.80897	+	7.28422i	−11.9998	−	1.80868i	−12.1950	+	53.4298i	−56.0782	−	38.2335i	−56.5318	−	97.9160i	−58.6801	+	101.637i	−191.420	+	92.1833i	−91.4795	−	28.2177i	−47.2556	−	630.582i
9.17	6.32555	+	7.93199i	2.21950	+	0.334535i	−15.7832	+	69.1506i	53.6893	+	36.6047i	11.3860	+	19.7211i	51.6195	−	89.4076i	−355.837	+	171.362i	−227.390	−	70.1405i	49.2659	+	657.407i
10.1	−2.36214	−	10.3492i	−5.75023	−	5.33543i	−72.6953	+	35.0082i	−7.82578	+	1.17955i	−41.6347	+	72.1133i	62.4925	+	108.240i	322.229	+	404.063i	−13.5611	−	180.961i	30.6929	+	78.2043i
10.2	−2.02425	−	8.86884i	20.8925	+	19.3854i	−45.7276	+	22.0213i	−27.6125	+	4.16191i	129.634	−	224.533i	100.934	+	174.822i	106.369	+	133.382i	42.5431	+	567.698i	92.8059	+	236.466i
10.3	−1.91263	−	8.37977i	7.67423	+	7.12065i	−37.7314	+	18.1705i	59.1521	−	8.91575i	44.9914	−	77.9274i	−90.2330	−	156.288i	52.9405	+	66.3853i	−9.96919	−	133.030i	−187.848	−	478.629i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
43.g	even	21	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	43.6.g.a	✓	204
43.g	even	21	1	inner	43.6.g.a	✓	204

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
43.6.g.a	✓	204	1.a	even	1	1	trivial
43.6.g.a	✓	204	43.g	even	21	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(43, [\chi])\).