Newform orbit 62.3.h.a

• Label: 62.3.h.a
• Level: $62$
• Weight: $3$
• Character orbit: 62.h
• Analytic conductor: $1.689$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	62.h (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.68937763903\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(6\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 6 q^{3} - 24 q^{4} + 6 q^{5} + 18 q^{7} - 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.14412	+	0.831254i	−2.72490	−	0.286398i	0.618034	−	1.90211i	2.55607	−	4.42725i	3.35568	−	1.93741i	11.5829	−	2.46202i	0.874032	+	2.68999i	−1.46030	−	0.310396i	0.755706	+	7.19006i
3.2	−1.14412	+	0.831254i	−1.73477	−	0.182331i	0.618034	−	1.90211i	−2.54757	+	4.41252i	2.13635	−	1.23342i	−9.72036	+	2.06613i	0.874032	+	2.68999i	−5.82715	−	1.23860i	−0.753192	−	7.16614i
3.3	−1.14412	+	0.831254i	4.29053	+	0.450953i	0.618034	−	1.90211i	1.85810	−	3.21833i	−5.28375	+	3.05058i	−1.89983	+	0.403821i	0.874032	+	2.68999i	9.40198	+	1.99845i	0.549350	+	5.22671i
3.4	1.14412	−	0.831254i	−4.29464	−	0.451385i	0.618034	−	1.90211i	4.65646	−	8.06523i	−5.28881	+	3.05349i	−6.98294	+	1.48427i	−0.874032	−	2.68999i	9.43683	+	2.00586i	−1.37669	−	13.0983i
3.5	1.14412	−	0.831254i	0.427629	+	0.0449456i	0.618034	−	1.90211i	0.263285	−	0.456023i	0.526621	−	0.304045i	11.1409	−	2.36807i	−0.874032	−	2.68999i	−8.62248	−	1.83277i	−0.0778406	−	0.740604i
3.6	1.14412	−	0.831254i	3.69788	+	0.388663i	0.618034	−	1.90211i	−1.30508	+	2.26046i	4.55390	−	2.62920i	−9.60759	+	2.04216i	−0.874032	−	2.68999i	4.71991	+	1.00325i	0.385848	+	3.67110i
11.1	−0.437016	−	1.34500i	−2.55630	+	2.30170i	−1.61803	+	1.17557i	2.12476	+	3.68018i	4.21292	+	2.43233i	0.717825	+	6.82965i	2.28825	+	1.66251i	0.296073	−	2.81694i	4.02129	−	4.46609i
11.2	−0.437016	−	1.34500i	−1.36657	+	1.23046i	−1.61803	+	1.17557i	−4.33815	−	7.51390i	2.25218	+	1.30030i	−1.19735	−	11.3920i	2.28825	+	1.66251i	−0.587288	+	5.58767i	−8.21033	+	9.11849i
11.3	−0.437016	−	1.34500i	3.50932	−	3.15980i	−1.61803	+	1.17557i	−3.00929	−	5.21225i	−5.78355	−	3.33914i	1.44405	+	13.7393i	2.28825	+	1.66251i	1.39019	−	13.2268i	−5.69535	+	6.32533i
11.4	0.437016	+	1.34500i	−3.57045	+	3.21485i	−1.61803	+	1.17557i	−3.26484	−	5.65487i	−5.88431	−	3.39731i	0.973704	+	9.26418i	−2.28825	−	1.66251i	1.47211	−	14.0062i	6.17900	−	6.86247i
11.5	0.437016	+	1.34500i	−0.426688	+	0.384192i	−1.61803	+	1.17557i	2.75524	+	4.77222i	−0.703206	−	0.405996i	0.186434	+	1.77380i	−2.28825	−	1.66251i	−0.906297	+	8.62284i	−5.21454	+	5.79133i
11.6	0.437016	+	1.34500i	3.58359	−	3.22668i	−1.61803	+	1.17557i	−0.136597	−	0.236594i	5.90597	+	3.40981i	−0.133803	−	1.27305i	−2.28825	−	1.66251i	1.48991	−	14.1755i	0.258522	−	0.287118i
13.1	−1.14412	+	0.831254i	−0.368929	−	0.828629i	0.618034	−	1.90211i	−4.73666	−	8.20413i	1.11090	+	0.641379i	1.75890	+	1.95345i	0.874032	+	2.68999i	5.47166	−	6.07689i	12.2390	+	5.44917i
13.2	−1.14412	+	0.831254i	−0.297611	−	0.668445i	0.618034	−	1.90211i	3.04757	+	5.27854i	0.896151	+	0.517393i	3.96158	+	4.39978i	0.874032	+	2.68999i	5.66393	−	6.29043i	−7.87459	−	3.50600i
13.3	−1.14412	+	0.831254i	2.14469	+	4.81705i	0.618034	−	1.90211i	0.501474	+	0.868579i	−6.45798	−	3.72851i	−2.25571	−	2.50522i	0.874032	+	2.68999i	−12.5821	+	13.9738i	−1.29576	−	0.576909i
13.4	1.14412	−	0.831254i	−1.14843	−	2.57943i	0.618034	−	1.90211i	−1.15365	−	1.99818i	−3.45811	−	1.99654i	1.42640	+	1.58417i	−0.874032	−	2.68999i	0.687638	−	0.763699i	−2.98092	−	1.32719i
13.5	1.14412	−	0.831254i	0.750095	+	1.68474i	0.618034	−	1.90211i	4.26853	+	7.39331i	2.25865	+	1.30403i	−6.71028	−	7.45252i	−0.874032	−	2.68999i	3.74647	−	4.16087i	11.0294	+	4.91062i
13.6	1.14412	−	0.831254i	1.87649	+	4.21466i	0.618034	−	1.90211i	−2.55443	−	4.42440i	5.65038	+	3.26225i	6.21587	+	6.90342i	−0.874032	−	2.68999i	−8.21998	+	9.12921i	−6.60039	−	2.93868i
17.1	−0.437016	+	1.34500i	−2.55630	−	2.30170i	−1.61803	−	1.17557i	2.12476	−	3.68018i	4.21292	−	2.43233i	0.717825	−	6.82965i	2.28825	−	1.66251i	0.296073	+	2.81694i	4.02129	+	4.46609i
17.2	−0.437016	+	1.34500i	−1.36657	−	1.23046i	−1.61803	−	1.17557i	−4.33815	+	7.51390i	2.25218	−	1.30030i	−1.19735	+	11.3920i	2.28825	−	1.66251i	−0.587288	−	5.58767i	−8.21033	−	9.11849i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.h	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	62.3.h.a	✓	48
31.h	odd	30	1	inner	62.3.h.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
62.3.h.a	✓	48	1.a	even	1	1	trivial
62.3.h.a	✓	48	31.h	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(62, [\chi])\).