Newform orbit 62.5.f.a

• Label: 62.5.f.a
• Level: $62$
• Weight: $5$
• Character orbit: 62.f
• Analytic conductor: $6.409$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.40893771120\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 96 q^{4} - 12 q^{5} - 12 q^{7} + 572 q^{9}+O(q^{10}) \)

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	−2.28825	+	1.66251i	−9.67143	+	13.3116i	2.47214	−	7.60845i	−19.2288				−	46.5390i	−27.0287	+	83.1858i	6.99226	+	21.5200i	−58.6312	−	180.448i	44.0001	−	31.9679i
15.2	−2.28825	+	1.66251i	−5.67014	+	7.80428i	2.47214	−	7.60845i	48.0160				−	27.2848i	7.01456	−	21.5886i	6.99226	+	21.5200i	−3.72590	−	11.4671i	−109.872	+	79.8270i
15.3	−2.28825	+	1.66251i	−3.23361	+	4.45068i	2.47214	−	7.60845i	−21.6905				−	15.5601i	22.3746	−	68.8620i	6.99226	+	21.5200i	15.6781	+	48.2521i	49.6332	−	36.0606i
15.4	−2.28825	+	1.66251i	−0.384536	+	0.529268i	2.47214	−	7.60845i	0.771017				−	1.85039i	−7.59103	+	23.3628i	6.99226	+	21.5200i	24.8981	+	76.6285i	−1.76428	+	1.28182i
15.5	−2.28825	+	1.66251i	4.81807	−	6.63151i	2.47214	−	7.60845i	−34.4670					23.1846i	−15.0893	+	46.4400i	6.99226	+	21.5200i	4.26728	+	13.1333i	78.8690	−	57.3017i
15.6	−2.28825	+	1.66251i	8.55147	−	11.7701i	2.47214	−	7.60845i	18.2490					41.1497i	4.39838	−	13.5368i	6.99226	+	21.5200i	−40.3769	−	124.267i	−41.7582	+	30.3391i
15.7	2.28825	−	1.66251i	−9.55339	+	13.1491i	2.47214	−	7.60845i	−14.9657					45.9710i	17.0534	−	52.4850i	−6.99226	−	21.5200i	−56.6016	−	174.202i	−34.2452	+	24.8806i
15.8	2.28825	−	1.66251i	−5.37791	+	7.40205i	2.47214	−	7.60845i	13.5475					25.8785i	−20.9669	+	64.5295i	−6.99226	−	21.5200i	−0.838136	−	2.57952i	31.0001	−	22.5229i
15.9	2.28825	−	1.66251i	−2.58811	+	3.56223i	2.47214	−	7.60845i	17.9178					12.4540i	18.2766	−	56.2496i	−6.99226	−	21.5200i	19.0392	+	58.5967i	41.0003	−	29.7885i
15.10	2.28825	−	1.66251i	−1.11265	+	1.53144i	2.47214	−	7.60845i	−47.5642					5.35410i	−18.0916	+	55.6802i	−6.99226	−	21.5200i	23.9231	+	73.6277i	−108.839	+	79.0759i
15.11	2.28825	−	1.66251i	6.26076	−	8.61720i	2.47214	−	7.60845i	44.4534				−	30.1268i	−17.2165	+	52.9870i	−6.99226	−	21.5200i	−10.0286	−	30.8649i	101.720	−	73.9042i
15.12	2.28825	−	1.66251i	6.78113	−	9.33343i	2.47214	−	7.60845i	−14.7468				−	32.6309i	11.5057	−	35.4110i	−6.99226	−	21.5200i	−16.0987	−	49.5468i	−33.7442	+	24.5166i
23.1	−0.874032	+	2.68999i	−15.7161	+	5.10647i	−6.47214	−	4.70228i	−39.6789				−	46.7394i	50.4810	+	36.6766i	18.3060	−	13.3001i	155.389	−	112.897i	34.6806	−	106.736i
23.2	−0.874032	+	2.68999i	−7.69734	+	2.50102i	−6.47214	−	4.70228i	4.55763				−	22.8918i	−27.7167	−	20.1374i	18.3060	−	13.3001i	−12.5364	+	9.10820i	−3.98352	+	12.2600i
23.3	−0.874032	+	2.68999i	−4.14951	+	1.34826i	−6.47214	−	4.70228i	32.5411				−	12.3406i	35.7419	+	25.9680i	18.3060	−	13.3001i	−50.1297	+	36.4214i	−28.4419	+	87.5353i
23.4	−0.874032	+	2.68999i	6.55254	−	2.12905i	−6.47214	−	4.70228i	−24.5818					19.4871i	−54.5451	−	39.6293i	18.3060	−	13.3001i	−27.1275	+	19.7093i	21.4853	−	66.1249i
23.5	−0.874032	+	2.68999i	12.7672	−	4.14833i	−6.47214	−	4.70228i	−18.2473					37.9696i	75.3789	+	54.7660i	18.3060	−	13.3001i	80.2636	−	58.3149i	15.9488	−	49.0852i
23.6	−0.874032	+	2.68999i	13.8333	−	4.49472i	−6.47214	−	4.70228i	38.1105					41.1401i	−47.4449	−	34.4707i	18.3060	−	13.3001i	105.628	−	76.7433i	−33.3098	+	102.517i
23.7	0.874032	−	2.68999i	−14.7882	+	4.80499i	−6.47214	−	4.70228i	10.2977					43.9800i	26.8331	+	19.4954i	−18.3060	+	13.3001i	130.073	−	94.5039i	9.00053	−	27.7008i
23.8	0.874032	−	2.68999i	−5.14386	+	1.67134i	−6.47214	−	4.70228i	11.2606					15.2977i	−48.1930	−	35.0143i	−18.3060	+	13.3001i	−41.8645	+	30.4163i	9.84212	−	30.2909i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.f	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	62.5.f.a	✓	48
31.f	odd	10	1	inner	62.5.f.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
62.5.f.a	✓	48	1.a	even	1	1	trivial
62.5.f.a	✓	48	31.f	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(62, [\chi])\).