Newform orbit 145.2.t.a

• Label: 145.2.t.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.t
• Analytic conductor: $1.158$
• Analytic rank: $0$
• Dimension: $156$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.t (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.15783082931\)
Analytic rank:	\(0\)
Dimension:	\(156\)
Relative dimension:	\(13\) over \(\Q(\zeta_{28})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 156 q - 14 q^{2} - 10 q^{3} + 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} - 14 q^{8} - 10 q^{9}+O(q^{10}) \)

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	−2.43135	+	0.554939i	1.81404	+	0.873594i	3.80156	−	1.83074i	−0.151265	+	2.23095i	−4.89535	−	1.11733i	3.00411	−	1.05118i	−4.32739	+	3.45098i	0.657093	+	0.823969i	−0.870262	−	5.50815i
3.2	−2.31914	+	0.529329i	−1.77490	−	0.854745i	3.29630	−	1.58741i	−2.07065	−	0.844052i	4.56868	+	1.04277i	0.698030	−	0.244251i	−3.08471	+	2.45997i	0.549197	+	0.688671i	5.24891	+	0.861425i
3.3	−2.02391	+	0.461944i	−1.48024	−	0.712845i	2.08088	−	1.00210i	1.88201	+	1.20750i	3.32516	+	0.758947i	−3.33902	+	1.16837i	−0.502501	+	0.400731i	−0.187511	−	0.235132i	−4.36681	−	1.57449i
3.4	−1.62317	+	0.370478i	1.59768	+	0.769400i	0.695489	−	0.334930i	1.95368	−	1.08773i	−2.87835	−	0.656964i	0.649579	−	0.227298i	1.59855	−	1.27480i	0.0901230	+	0.113011i	−2.76817	+	2.48936i
3.5	−0.718317	+	0.163951i	−0.427973	−	0.206101i	−1.31284	+	0.632230i	−0.265444	−	2.22026i	0.341211	+	0.0778792i	1.22364	−	0.428169i	1.99147	−	1.58814i	−1.72979	−	2.16908i	0.554686	+	1.55133i
3.6	−0.469443	+	0.107147i	0.197855	+	0.0952819i	−1.59304	+	0.767168i	−1.09670	+	1.94865i	−0.103091	−	0.0235298i	−3.11661	+	1.09055i	1.41857	−	1.13127i	−1.84040	−	2.30779i	0.306044	−	1.03229i
3.7	−0.426538	+	0.0973546i	−2.42758	−	1.16906i	−1.62948	+	0.784717i	1.36135	+	1.77390i	1.14927	+	0.262313i	4.53036	−	1.58524i	1.30275	−	1.03891i	2.65596	+	3.33047i	−0.753366	−	0.624102i
3.8	0.0671767	−	0.0153326i	2.71909	+	1.30944i	−1.79766	+	0.865707i	−2.19083	+	0.447510i	0.202737	+	0.0462733i	3.00352	−	1.05098i	−0.215230	+	0.171640i	3.80833	+	4.77549i	−0.140311	+	0.0636534i
3.9	0.898066	−	0.204978i	−2.27912	−	1.09757i	−1.03743	+	0.499601i	−2.08580	−	0.805888i	−2.27178	−	0.518518i	−0.941288	+	0.329371i	−2.26966	+	1.80999i	2.11927	+	2.65748i	−2.03837	−	0.296199i
3.10	1.40869	−	0.321524i	0.596213	+	0.287121i	0.0790869	−	0.0380862i	1.12791	+	1.93076i	0.932195	+	0.212767i	0.878334	−	0.307342i	−2.16020	+	1.72270i	−1.59744	−	2.00312i	2.20966	+	2.35718i
3.11	1.68122	−	0.383728i	1.75904	+	0.847111i	0.877317	−	0.422494i	−0.646560	−	2.14055i	3.28240	+	0.749187i	−2.98844	+	1.04570i	−1.38363	+	1.10341i	0.506171	+	0.634719i	−1.90840	−	3.35064i
3.12	2.15407	−	0.491652i	−2.28313	−	1.09950i	2.59634	−	1.25033i	2.11300	−	0.731603i	−5.45857	−	1.24588i	−0.579985	+	0.202945i	1.52312	−	1.21464i	2.13330	+	2.67508i	4.19184	−	2.61478i
3.13	2.44273	−	0.557537i	−0.416303	−	0.200481i	3.85413	−	1.85605i	−1.91761	+	1.15012i	−1.12869	−	0.257616i	−0.222008	+	0.0776841i	4.46194	−	3.55828i	−1.73735	−	2.17857i	−4.04296	+	3.87857i
27.1	−2.03189	+	1.62038i	0.433809	+	1.90064i	1.05791	−	4.63499i	0.920670	+	2.03774i	−3.96120	−	3.15895i	−1.75507	+	2.79318i	3.10566	+	6.44896i	−0.721337	+	0.347377i	−5.17260	−	2.64862i
27.2	−1.72889	+	1.37874i	0.0324304	+	0.142087i	0.643081	−	2.81752i	1.02293	−	1.98837i	−0.251970	−	0.200939i	0.555045	−	0.883349i	0.853902	+	1.77315i	2.68377	−	1.29244i	0.972925	+	4.84802i
27.3	−1.49240	+	1.19015i	−0.343037	−	1.50294i	0.365759	−	1.60249i	−1.92139	+	1.14380i	2.30068	+	1.83473i	1.10422	−	1.75735i	−0.295090	−	0.612760i	0.561738	−	0.270519i	1.50618	−	3.99374i
27.4	−0.892134	+	0.711453i	−0.324743	−	1.42279i	−0.155304	+	0.680432i	1.31414	+	1.80916i	1.30196	+	1.03828i	−0.495384	+	0.788400i	−1.33574	−	2.77369i	0.784033	−	0.377570i	−2.45952	−	0.679062i
27.5	−0.554273	+	0.442018i	0.339722	+	1.48842i	−0.333203	+	1.45986i	−1.82434	−	1.29297i	−0.846207	−	0.674828i	−2.04713	+	3.25799i	−1.07579	−	2.23391i	0.602920	−	0.290351i	1.58270	−	0.0897329i
27.6	−0.553028	+	0.441025i	0.668619	+	2.92941i	−0.333705	+	1.46206i	2.21821	−	0.282015i	−1.66171	−	1.32517i	1.47214	−	2.34289i	−1.07407	−	2.23033i	−5.43148	+	2.61566i	−1.10236	+	1.13425i
27.7	−0.0214476	+	0.0171039i	−0.243851	−	1.06838i	−0.444874	+	1.94912i	−0.0575944	−	2.23533i	0.0235034	+	0.0187434i	2.24458	−	3.57223i	−0.0476010	−	0.0988446i	1.62093	−	0.780601i	0.0394680	+	0.0469572i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
145.t	even	28	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	145.2.t.a	yes	156
5.b	even	2	1		725.2.bd.b		156
5.c	odd	4	1		145.2.o.a	✓	156
5.c	odd	4	1		725.2.y.b		156
29.f	odd	28	1		145.2.o.a	✓	156
145.o	even	28	1		725.2.bd.b		156
145.s	odd	28	1		725.2.y.b		156
145.t	even	28	1	inner	145.2.t.a	yes	156

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.2.o.a	✓	156	5.c	odd	4	1
145.2.o.a	✓	156	29.f	odd	28	1
145.2.t.a	yes	156	1.a	even	1	1	trivial
145.2.t.a	yes	156	145.t	even	28	1	inner
725.2.y.b		156	5.c	odd	4	1
725.2.y.b		156	145.s	odd	28	1
725.2.bd.b		156	5.b	even	2	1
725.2.bd.b		156	145.o	even	28	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(145, [\chi])\).