Newform orbit 65.4.m.a

• Label: 65.4.m.a
• Level: $65$
• Weight: $4$
• Character orbit: 65.m
• Analytic conductor: $3.835$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.83512415037\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 12 q^{3} + 56 q^{4} + 90 q^{6} - 36 q^{7} - 110 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
36.1	−4.49968	+	2.59789i	−0.587925	−	1.01832i	9.49807	−	16.4511i			5.00000i	5.29094	+	3.05473i	17.4040	+	10.0482i			57.1335i	12.8087	−	22.1853i	−12.9895	−	22.4984i
36.2	−4.08243	+	2.35699i	1.46795	+	2.54256i	7.11080	−	12.3163i		−	5.00000i	−11.9856	−	6.91987i	−21.6101	−	12.4766i			29.3285i	9.19026	−	15.9180i	11.7849	+	20.4121i
36.3	−3.89666	+	2.24974i	−4.84320	−	8.38867i	6.12264	−	10.6047i		−	5.00000i	37.7446	+	21.7919i	−6.75342	−	3.89909i			19.1016i	−33.4132	+	57.8734i	11.2487	+	19.4833i
36.4	−2.63330	+	1.52034i	−1.55006	−	2.68478i	0.622842	−	1.07879i			5.00000i	8.16353	+	4.71322i	−6.56940	−	3.79285i		−	20.5377i	8.69464	−	15.0596i	−7.60168	−	13.1665i
36.5	−1.25672	+	0.725566i	3.34475	+	5.79327i	−2.94711	+	5.10454i			5.00000i	−8.40680	−	4.85367i	−11.9975	−	6.92678i		−	20.1623i	−8.87467	+	15.3714i	−3.62783	−	6.28359i
36.6	−1.24847	+	0.720803i	−1.96169	−	3.39774i	−2.96089	+	5.12841i		−	5.00000i	4.89820	+	2.82798i	30.0697	+	17.3607i		−	20.0697i	5.80357	−	10.0521i	3.60401	+	6.24234i
36.7	−0.820466	+	0.473696i	−0.791418	−	1.37078i	−3.55122	+	6.15090i		−	5.00000i	1.29866	+	0.749783i	−19.3982	−	11.1996i		−	14.3079i	12.2473	−	21.2130i	2.36848	+	4.10233i
36.8	0.172266	−	0.0994581i	−4.74220	−	8.21373i	−3.98022	+	6.89394i			5.00000i	−1.63384	−	0.943301i	0.235193	+	0.135788i			3.17479i	−31.4769	+	54.5196i	0.497291	+	0.861332i
36.9	1.39179	−	0.803549i	3.99752	+	6.92391i	−2.70862	+	4.69146i		−	5.00000i	11.1274	+	6.42441i	−0.762443	−	0.440197i			21.5628i	−18.4604	+	31.9743i	−4.01775	−	6.95894i
36.10	1.72463	−	0.995715i	1.16747	+	2.02212i	−2.01710	+	3.49372i			5.00000i	4.02691	+	2.32494i	21.2579	+	12.2733i			23.9653i	10.7740	−	18.6612i	4.97858	+	8.62315i
36.11	3.00893	−	1.73720i	−3.70380	−	6.41516i	2.03576	−	3.52604i		−	5.00000i	−22.2889	−	12.8685i	−9.41534	−	5.43595i			13.6491i	−13.9362	+	24.1382i	−8.68602	−	15.0446i
36.12	3.91525	−	2.26047i	1.10258	+	1.90973i	6.21947	−	10.7724i		−	5.00000i	8.63378	+	4.98471i	5.87946	+	3.39451i		−	20.0682i	11.0686	−	19.1714i	−11.3024	−	19.5763i
36.13	4.04428	−	2.33497i	3.91214	+	6.77603i	6.90415	−	11.9583i			5.00000i	31.6436	+	18.2694i	−22.0294	−	12.7187i		−	27.1244i	−17.1097	+	29.6348i	11.6748	+	20.2214i
36.14	4.18057	−	2.41365i	−2.81212	−	4.87074i	7.65142	−	13.2527i			5.00000i	−23.5125	−	13.5750i	5.68967	+	3.28493i		−	35.2530i	−2.31608	+	4.01156i	12.0683	+	20.9028i
56.1	−4.49968	−	2.59789i	−0.587925	+	1.01832i	9.49807	+	16.4511i		−	5.00000i	5.29094	−	3.05473i	17.4040	−	10.0482i		−	57.1335i	12.8087	+	22.1853i	−12.9895	+	22.4984i
56.2	−4.08243	−	2.35699i	1.46795	−	2.54256i	7.11080	+	12.3163i			5.00000i	−11.9856	+	6.91987i	−21.6101	+	12.4766i		−	29.3285i	9.19026	+	15.9180i	11.7849	−	20.4121i
56.3	−3.89666	−	2.24974i	−4.84320	+	8.38867i	6.12264	+	10.6047i			5.00000i	37.7446	−	21.7919i	−6.75342	+	3.89909i		−	19.1016i	−33.4132	−	57.8734i	11.2487	−	19.4833i
56.4	−2.63330	−	1.52034i	−1.55006	+	2.68478i	0.622842	+	1.07879i		−	5.00000i	8.16353	−	4.71322i	−6.56940	+	3.79285i			20.5377i	8.69464	+	15.0596i	−7.60168	+	13.1665i
56.5	−1.25672	−	0.725566i	3.34475	−	5.79327i	−2.94711	−	5.10454i		−	5.00000i	−8.40680	+	4.85367i	−11.9975	+	6.92678i			20.1623i	−8.87467	−	15.3714i	−3.62783	+	6.28359i
56.6	−1.24847	−	0.720803i	−1.96169	+	3.39774i	−2.96089	−	5.12841i			5.00000i	4.89820	−	2.82798i	30.0697	−	17.3607i			20.0697i	5.80357	+	10.0521i	3.60401	−	6.24234i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.e	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	65.4.m.a	✓	28
13.e	even	6	1	inner	65.4.m.a	✓	28
13.f	odd	12	1		845.4.a.m		14
13.f	odd	12	1		845.4.a.n		14

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
65.4.m.a	✓	28	1.a	even	1	1	trivial
65.4.m.a	✓	28	13.e	even	6	1	inner
845.4.a.m		14	13.f	odd	12	1
845.4.a.n		14	13.f	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(65, [\chi])\).