Newform orbit 79.2.g.a

• Label: 79.2.g.a
• Level: $79$
• Weight: $2$
• Character orbit: 79.g
• Analytic conductor: $0.631$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	79.g (of order \(39\), degree \(24\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.630818175968\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(6\) over \(\Q(\zeta_{39})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q - 24 q^{2} - 26 q^{3} - 22 q^{4} - 25 q^{5} - 35 q^{6} - 26 q^{7} - 18 q^{9}+O(q^{10}) \)

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	−2.10490	−	1.58173i	1.85532	+	0.301518i	1.37229	+	4.73771i	2.57284	+	1.62696i	−3.42833	−	3.56927i	−1.29513	+	1.58625i	2.73791	−	7.21926i	0.505680	+	0.168821i	−2.84214	−	7.49412i
2.2	−1.44720	−	1.08750i	−0.0244783	−	0.00397811i	0.355293	+	1.22661i	−3.07133	−	1.94219i	0.0310988	+	0.0323772i	1.69466	−	2.07559i	−0.464092	+	1.22371i	−2.84503	−	0.949809i	2.33269	+	6.15080i
2.3	−0.118685	−	0.0891862i	−0.451502	−	0.0733762i	−0.550303	−	1.89987i	2.91732	+	1.84480i	0.0470425	+	0.0489764i	2.07689	−	2.54373i	−0.209418	+	0.552191i	−2.64714	−	0.883745i	−0.181712	−	0.479136i
2.4	0.142230	+	0.106879i	−3.18278	−	0.517252i	−0.547629	−	1.89063i	−1.39244	−	0.880524i	−0.397402	−	0.413740i	−1.33913	+	1.64014i	0.250356	−	0.660133i	7.01692	+	2.34259i	−0.103937	−	0.274058i
2.5	1.16578	+	0.876027i	0.664133	+	0.107932i	0.0351849	+	0.121472i	−0.932917	−	0.589941i	0.679681	+	0.707623i	−1.80538	+	2.21119i	0.968803	−	2.55452i	−2.41619	−	0.806641i	−0.570772	−	1.50500i
2.6	2.09576	+	1.57486i	−1.79628	−	0.291924i	1.35559	+	4.68003i	−1.52217	−	0.962562i	−3.30483	−	3.44069i	2.90591	−	3.55910i	−2.67020	+	7.04073i	0.295788	+	0.0987485i	−1.67420	−	4.41450i
4.1	−0.758695	−	2.61932i	−1.58803	−	0.530161i	−4.59484	+	2.90560i	0.436980	+	0.920916i	−0.183833	+	4.56178i	−0.918394	−	4.49859i	7.01442	+	6.21423i	−0.157574	−	0.118409i	2.08064	−	1.84329i
4.2	−0.542829	−	1.87406i	2.02394	+	0.675691i	−1.52707	+	0.965659i	−0.341471	−	0.719635i	0.167633	−	4.15978i	0.582601	+	2.85377i	−0.282191	−	0.249999i	1.24146	+	0.932895i	−1.16328	+	1.03058i
4.3	−0.295732	−	1.02099i	−1.31421	−	0.438749i	0.735425	−	0.465054i	−0.824411	−	1.73741i	−0.0593013	+	1.47155i	0.138386	+	0.677860i	−2.28357	−	2.02306i	−0.863669	−	0.649005i	−1.53007	+	1.35552i
4.4	0.221436	+	0.764487i	−0.462297	−	0.154338i	1.15497	−	0.730361i	0.460287	+	0.970035i	0.0156196	−	0.387597i	0.195988	+	0.960014i	2.00560	+	1.77681i	−2.20843	−	1.65953i	−0.639655	+	0.566685i
4.5	0.621386	+	2.14527i	1.38249	+	0.461545i	−2.52570	+	1.59715i	−1.20761	−	2.54498i	−0.131076	+	3.25263i	−0.510981	−	2.50295i	−1.65223	−	1.46375i	−0.700060	−	0.526061i	4.70928	−	4.17206i
4.6	0.710925	+	2.45440i	−2.78988	−	0.931399i	−3.82828	+	2.42086i	1.10867	+	2.33647i	0.302628	−	7.50963i	−0.0153079	−	0.0749828i	−4.83805	−	4.28614i	4.51760	+	3.39475i	−4.94644	+	4.38216i
5.1	−2.29207	−	1.44941i	−1.00890	+	0.758139i	2.29538	+	4.83740i	0.144326	+	0.176767i	3.41132	−	0.275390i	1.92310	+	0.819356i	1.09648	−	9.03035i	−0.391548	+	1.35178i	−0.0745954	−	0.614349i
5.2	−1.54110	−	0.974530i	2.19889	−	1.65236i	0.567882	+	1.19679i	0.675406	+	0.827222i	−4.99896	+	0.403558i	−0.686450	−	0.292469i	−0.148423	+	1.22237i	1.27017	−	4.38512i	−0.234713	−	1.93303i
5.3	−0.859173	−	0.543308i	−1.92366	+	1.44554i	−0.414390	−	0.873309i	−0.988037	−	1.21013i	2.43813	−	0.196826i	−4.22790	−	1.80134i	−0.363505	+	2.99373i	0.776238	−	2.67988i	0.191424	+	1.57652i
5.4	−0.311788	−	0.197163i	0.623033	−	0.468179i	−0.799047	−	1.68395i	−2.43101	−	2.97744i	−0.286562	+	0.0231336i	4.51355	+	1.92304i	−0.171811	+	1.41499i	−0.665674	+	2.29817i	0.170918	+	1.40764i
5.5	0.559108	+	0.353559i	0.537733	−	0.404080i	−0.669787	−	1.41155i	1.52906	+	1.87276i	0.443517	−	0.0358044i	−1.38118	−	0.588467i	0.284055	−	2.33941i	−0.708776	+	2.44698i	0.192780	+	1.58769i
5.6	1.46121	+	0.924011i	−2.50475	+	1.88220i	0.423942	+	0.893439i	0.270277	+	0.331029i	−5.39913	+	0.435863i	2.74734	+	1.17053i	0.210699	−	1.73526i	1.89646	−	6.54733i	0.0890558	+	0.733440i
9.1	−2.56704	−	0.857004i	−0.246562	−	0.0199045i	4.25636	+	3.19845i	0.540434	−	1.86580i	0.615876	+	0.262400i	−1.16481	−	2.45479i	−5.11044	−	7.40375i	−2.90075	−	0.471418i	−2.98631	+	4.32642i
9.2	−1.47908	−	0.493788i	−1.24000	−	0.100103i	0.344956	+	0.259218i	−1.05987	+	3.65909i	1.78462	+	0.760355i	0.347713	+	0.732789i	1.38938	+	2.01286i	−1.43358	−	0.232980i	3.37444	−	4.88873i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.g	even	39	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.2.g.a	✓	144
3.b	odd	2	1		711.2.ba.c		144
79.g	even	39	1	inner	79.2.g.a	✓	144
79.g	even	39	1		6241.2.a.v		72
79.h	odd	78	1		6241.2.a.w		72
237.o	odd	78	1		711.2.ba.c		144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.2.g.a	✓	144	1.a	even	1	1	trivial
79.2.g.a	✓	144	79.g	even	39	1	inner
711.2.ba.c		144	3.b	odd	2	1
711.2.ba.c		144	237.o	odd	78	1
6241.2.a.v		72	79.g	even	39	1
6241.2.a.w		72	79.h	odd	78	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(79, [\chi])\).