Newform orbit 67.5.h.a

• Label: 67.5.h.a
• Level: $67$
• Weight: $5$
• Character orbit: 67.h
• Analytic conductor: $6.926$
• Analytic rank: $0$
• Dimension: $440$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	67.h (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.92578752662\)
Analytic rank:	\(0\)
Dimension:	\(440\)
Relative dimension:	\(22\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−7.67522	−	0.365616i	−4.26164	+	14.5138i	42.8478	+	4.09147i	−28.7699	−	24.9292i	38.0155	−	109.839i	4.03136	+	7.81975i	−205.679	−	29.5722i	−124.347	−	79.9132i	211.701	+	201.856i
2.2	−7.65772	−	0.364782i	2.51830	−	8.57655i	42.5800	+	4.06590i	3.47554	+	3.01157i	−22.4130	+	64.7582i	12.8998	+	25.0221i	−203.169	−	29.2113i	0.926113	+	0.595177i	−25.5161	−	24.3296i
2.3	−6.46537	−	0.307984i	−2.24527	+	7.64670i	25.7787	+	2.46156i	33.1321	+	28.7091i	16.8716	−	48.7473i	−36.8655	−	71.5091i	−63.4014	−	9.11574i	14.7107	+	9.45402i	−205.369	−	195.819i
2.4	−5.82885	−	0.277662i	0.215719	−	0.734670i	17.9709	+	1.71601i	−3.52021	−	3.05028i	−1.46138	+	4.22239i	−0.612184	−	1.18747i	−11.8561	−	1.70464i	67.6483	+	43.4749i	19.6719	+	18.7571i
2.5	−5.14762	−	0.245211i	4.28565	−	14.5956i	10.5103	+	1.00362i	−36.2663	−	31.4249i	−25.6399	+	74.0816i	−18.7117	−	36.2956i	27.7590	+	3.99113i	−126.522	−	81.3110i	178.979	+	170.657i
2.6	−4.58900	−	0.218601i	−3.62494	+	12.3454i	5.08355	+	0.485421i	17.7775	+	15.4043i	19.3336	−	55.8607i	42.2932	+	82.0374i	49.5367	+	7.12230i	−71.1278	−	45.7110i	−78.2134	−	74.5763i
2.7	−4.26920	−	0.203367i	3.68269	−	12.5421i	2.25715	+	0.215532i	25.1741	+	21.8135i	−18.2728	+	52.7958i	23.7317	+	46.0330i	58.0962	+	8.35297i	−75.6006	−	48.5855i	−103.037	−	98.2457i
2.8	−3.89658	−	0.185617i	−1.83274	+	6.24174i	−0.778653	−	0.0743523i	−19.2961	−	16.7201i	8.30000	−	23.9813i	−17.6765	−	34.2875i	64.8010	+	9.31698i	32.5412	+	20.9129i	72.0852	+	68.7331i
2.9	−2.01861	−	0.0961582i	3.16863	−	10.7914i	−11.8620	−	1.13268i	10.4874	+	9.08739i	−7.43391	+	21.4789i	−34.0692	−	66.0849i	55.8411	+	8.02874i	−38.2718	−	24.5958i	−20.2962	−	19.3523i
2.10	−1.31126	−	0.0624631i	0.858202	−	2.92277i	−14.2120	−	1.35709i	−23.1174	−	20.0313i	−1.30789	+	3.77890i	35.6530	+	69.1572i	39.3411	+	5.65640i	60.3355	+	38.7753i	29.0617	+	27.7103i
2.11	−1.12052	−	0.0533770i	0.463121	−	1.57725i	−14.6748	−	1.40128i	14.3099	+	12.3996i	−0.603125	+	1.74262i	−9.56384	−	18.5513i	34.1346	+	4.90782i	65.8683	+	42.3310i	−15.3727	−	14.6579i
2.12	−1.03118	−	0.0491214i	−3.83498	+	13.0607i	−14.8666	−	1.41959i	−11.8331	−	10.2534i	4.59613	−	13.2797i	−5.41428	−	10.5022i	31.6100	+	4.54484i	−87.7343	−	56.3834i	11.6985	+	11.1544i
2.13	0.600608	+	0.0286105i	−3.23175	+	11.0063i	−15.5676	−	1.48653i	23.3567	+	20.2387i	−2.25591	+	6.51803i	−15.7911	−	30.6305i	−18.8302	−	2.70738i	−42.5537	−	27.3476i	13.4492	+	12.8238i
2.14	1.79553	+	0.0855318i	3.76543	−	12.8239i	−12.7109	−	1.21375i	−9.46177	−	8.19867i	7.85780	−	22.7036i	9.51682	+	18.4601i	−51.1875	−	7.35965i	−82.1315	−	52.7827i	−16.2877	−	15.5303i
2.15	2.99695	+	0.142762i	−0.301492	+	1.02679i	−6.96623	−	0.665194i	20.3314	+	17.6172i	−1.05014	+	3.03419i	20.4478	+	39.6632i	−68.2994	−	9.81997i	67.1781	+	43.1728i	58.4170	+	55.7005i
2.16	3.57612	+	0.170351i	−2.51526	+	8.56618i	−3.16797	−	0.302504i	−28.5267	−	24.7185i	−10.4541	+	30.2052i	1.82066	+	3.53158i	−67.9772	−	9.77364i	1.08859	+	0.699595i	−97.8039	−	93.2558i
2.17	3.80072	+	0.181051i	1.10242	−	3.75449i	−1.51483	−	0.144649i	−14.6109	−	12.6604i	4.86973	−	14.0702i	−42.6315	−	82.6937i	−65.9921	−	9.48824i	55.2607	+	35.5139i	−53.2398	−	50.7641i
2.18	5.52885	+	0.263372i	3.68146	−	12.5379i	14.5713	+	1.39139i	32.4670	+	28.1328i	23.6564	−	68.3506i	−3.86851	−	7.50387i	−7.46446	−	1.07323i	−75.5043	−	48.5236i	172.096	+	164.093i
2.19	5.64013	+	0.268673i	−4.71637	+	16.0625i	15.8113	+	1.50980i	10.4042	+	9.01530i	−30.9165	+	89.3274i	−5.20271	−	10.0919i	−0.652485	−	0.0938132i	−167.618	−	107.721i	56.2589	+	53.6428i
2.20	6.51170	+	0.310190i	−1.49314	+	5.08517i	26.3784	+	2.51883i	−3.18168	−	2.75694i	−11.3002	+	32.6499i	29.2873	+	56.8095i	67.7433	+	9.74002i	44.5121	+	28.6062i	−19.8629	−	18.9393i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
67.h	odd	66	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	67.5.h.a	✓	440
67.h	odd	66	1	inner	67.5.h.a	✓	440

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
67.5.h.a	✓	440	1.a	even	1	1	trivial
67.5.h.a	✓	440	67.h	odd	66	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(67, [\chi])\).