Newform orbit 927.2.p.a

• Label: 927.2.p.a
• Level: $927$
• Weight: $2$
• Character orbit: 927.p
• Analytic conductor: $7.402$
• Analytic rank: $0$
• Dimension: $204$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.40213226737\)
Analytic rank:	\(0\)
Dimension:	\(204\)
Relative dimension:	\(102\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 204 q - 3 q^{2} + 3 q^{3} + 101 q^{4} - 3 q^{5} + 3 q^{6} - 11 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1	−2.41995	+	1.39716i	1.13595	−	1.30752i	2.90410	−	5.03005i	0.838636	−	1.45256i	−0.922126	+	4.75124i	−0.893491					10.6413i	−0.419233	−	2.97056i			4.68683i
47.2	−2.39944	+	1.38532i	−1.38047	−	1.04609i	2.83820	−	4.91590i	1.82809	−	3.16635i	4.76151	+	0.597631i	−1.59422					10.1859i	0.811404	+	2.88819i			10.1300i
47.3	−2.32190	+	1.34055i	−1.31934	−	1.12221i	2.59416	−	4.49322i	−1.58934	+	2.75283i	4.56775	+	0.837027i	4.08705					8.54822i	0.481290	+	2.96114i		−	8.52240i
47.4	−2.27171	+	1.31157i	−1.00881	+	1.40794i	2.44046	−	4.22699i	−1.51146	+	2.61792i	0.445115	−	4.52157i	−3.93121					7.55706i	−0.964593	−	2.84070i		−	7.92956i
47.5	−2.23691	+	1.29148i	0.222800	+	1.71766i	2.33586	−	4.04583i	−0.520524	+	0.901574i	−2.71672	−	3.55452i	2.58965					6.90096i	−2.90072	+	0.765391i		−	2.68899i
47.6	−2.23003	+	1.28751i	−0.130006	−	1.72716i	2.31536	−	4.01033i	−1.72477	+	2.98738i	2.51366	+	3.68425i	−4.65829					6.77418i	−2.96620	+	0.449083i		−	8.88262i
47.7	−2.20175	+	1.27118i	−1.68852	+	0.385871i	2.23180	−	3.86559i	−0.424880	+	0.735913i	3.22719	−	2.99601i	0.736879					6.26337i	2.70221	−	1.30310i		−	2.16040i
47.8	−2.19381	+	1.26660i	1.03315	+	1.39018i	2.20854	−	3.82530i	1.16679	−	2.02093i	−4.02733	−	1.74121i	−3.59236					6.12294i	−0.865209	+	2.87253i			5.91140i
47.9	−2.12574	+	1.22729i	0.504134	−	1.65706i	2.01250	−	3.48576i	0.103484	−	0.179240i	0.962046	+	4.14119i	1.77658					4.97056i	−2.49170	−	1.67076i			0.508022i
47.10	−2.09145	+	1.20750i	−0.881524	+	1.49094i	1.91611	−	3.31880i	1.07592	−	1.86354i	0.0433492	−	4.18268i	−0.776503					4.42482i	−1.44583	−	2.62861i			5.19668i
47.11	−2.07307	+	1.19689i	1.54558	+	0.781777i	1.86508	−	3.23041i	1.55616	−	2.69535i	−4.13980	+	0.229209i	4.58609					4.14160i	1.77765	+	2.41660i			7.45018i
47.12	−2.03568	+	1.17530i	1.66808	−	0.466390i	1.76267	−	3.05303i	0.139036	−	0.240817i	−2.84752	+	2.90991i	1.04452					3.58545i	2.56496	−	1.55595i			0.653635i
47.13	−1.99089	+	1.14944i	1.33887	−	1.09883i	1.64242	−	2.84475i	−1.77654	+	3.07707i	−1.40249	+	3.72660i	3.84031					2.95368i	0.585125	−	2.94238i		−	8.16812i
47.14	−1.95795	+	1.13042i	1.61761	+	0.619144i	1.55571	−	2.69458i	−1.81873	+	3.15013i	−3.86710	+	0.616331i	−1.79388					2.51277i	2.23332	+	2.00307i		−	8.22373i
47.15	−1.85617	+	1.07166i	−0.353197	−	1.69566i	1.29692	−	2.24633i	0.566135	−	0.980574i	2.47277	+	2.76893i	−1.70338					1.27280i	−2.75050	+	1.19780i			2.42682i
47.16	−1.83997	+	1.06231i	1.69027	−	0.378146i	1.25700	−	2.17719i	−0.235364	+	0.407662i	−2.70834	+	2.49137i	−4.05371					1.09205i	2.71401	−	1.27834i		−	1.00012i
47.17	−1.81727	+	1.04920i	−1.73200	+	0.0128649i	1.20166	−	2.08133i	1.44254	−	2.49854i	3.13403	−	1.84060i	2.48222					0.846317i	2.99967	−	0.0445639i			6.05405i
47.18	−1.69941	+	0.981153i	−1.05140	+	1.37643i	0.925321	−	1.60270i	1.68632	−	2.92078i	0.436278	−	3.37070i	−2.31645				−	0.293088i	−0.789100	−	2.89436i			6.61813i
47.19	−1.68647	+	0.973681i	−1.71933	−	0.209552i	0.896110	−	1.55211i	−0.466252	+	0.807572i	3.10362	−	1.32068i	−3.31669				−	0.404622i	2.91218	+	0.720577i		−	1.81592i
47.20	−1.67972	+	0.969787i	0.588132	+	1.62914i	0.880975	−	1.52589i	−2.07062	+	3.58642i	−2.56782	−	2.16614i	−0.419794				−	0.461716i	−2.30820	+	1.91630i		−	8.03224i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
927.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	927.2.p.a	yes	204
9.d	odd	6	1		927.2.j.a	✓	204
103.d	odd	6	1		927.2.j.a	✓	204
927.p	even	6	1	inner	927.2.p.a	yes	204

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
927.2.j.a	✓	204	9.d	odd	6	1
927.2.j.a	✓	204	103.d	odd	6	1
927.2.p.a	yes	204	1.a	even	1	1	trivial
927.2.p.a	yes	204	927.p	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(927, [\chi])\).