Newform orbit 145.2.o.a

• Label: 145.2.o.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.o
• 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.o (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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−1.60543	−	2.01315i	2.77645	−	0.633706i	−1.03031	+	4.51409i	0.618631	+	2.14879i	−5.73314	−	4.57203i	1.73798	−	2.76598i	6.10180	−	2.93847i	4.60418	−	2.21725i	3.33266	−	4.69513i
2.2	−1.59286	−	1.99739i	−3.00453	+	0.685765i	−1.00730	+	4.41327i	−2.20621	−	0.364215i	6.15555	+	4.90889i	1.16508	−	1.85421i	5.81600	−	2.80084i	5.85404	−	2.81916i	2.78671	+	4.98679i
2.3	−1.24856	−	1.56564i	−0.857117	+	0.195631i	−0.447295	+	1.95973i	0.789952	+	2.09188i	1.37645	+	1.09768i	−2.04306	+	3.25151i	0.0182701	−	0.00879841i	−2.00653	+	0.966293i	2.28884	−	3.84862i
2.4	−1.12498	−	1.41068i	−0.839422	+	0.191593i	−0.279397	+	1.22412i	1.76332	−	1.37503i	1.21461	+	0.968619i	1.72814	−	2.75032i	−1.21013	+	0.582769i	−2.03498	+	0.979997i	−3.92343	−	0.940595i
2.5	−0.816077	−	1.02333i	1.87585	−	0.428151i	0.0638227	−	0.279625i	−1.93268	−	1.12460i	−1.96898	−	1.57021i	0.790080	−	1.25741i	−2.69676	+	1.29869i	0.632594	−	0.304641i	0.426380	+	2.89553i
2.6	−0.508232	−	0.637303i	2.29753	−	0.524396i	0.297187	−	1.30206i	2.16962	−	0.541078i	−1.50188	−	1.19771i	−1.94097	+	3.08903i	−2.44968	+	1.17970i	2.30073	−	1.10797i	−1.44750	−	1.10771i
2.7	−0.224434	−	0.281431i	−1.73122	+	0.395140i	0.416209	−	1.82353i	−2.17449	−	0.521141i	0.499749	+	0.398537i	−1.92899	+	3.06996i	−1.25524	+	0.604492i	0.138091	−	0.0665011i	0.341364	+	0.728930i
2.8	0.0656308	+	0.0822985i	−3.27186	+	0.746782i	0.442576	−	1.93905i	1.95685	+	1.08201i	−0.276194	−	0.220258i	0.857209	−	1.36424i	0.378306	−	0.182183i	7.44450	−	3.58508i	0.0393814	+	0.232059i
2.9	0.377899	+	0.473871i	−0.369693	+	0.0843800i	0.363296	−	1.59171i	0.322290	−	2.21272i	−0.179692	−	0.143299i	0.549671	−	0.874796i	1.98371	−	0.955305i	−2.57335	+	1.23926i	1.17034	−	0.683461i
2.10	0.418034	+	0.524198i	1.64797	−	0.376139i	0.345011	−	1.51159i	−0.885244	+	2.05337i	0.886079	+	0.706625i	−0.0716415	+	0.114017i	2.14475	−	1.03286i	−0.128580	+	0.0619209i	−1.44644	+	0.394337i
2.11	1.03166	+	1.29366i	−0.387798	+	0.0885124i	−0.164193	+	0.719377i	2.13823	+	0.654186i	−0.514581	−	0.410364i	0.219801	−	0.349812i	1.88156	−	0.906112i	−2.56035	+	1.23300i	1.35963	+	3.44104i
2.12	1.33080	+	1.66877i	−1.91674	+	0.437482i	−0.568723	+	2.49174i	−1.61953	+	1.54180i	−3.28085	−	2.61639i	−0.455070	+	0.724240i	−1.06887	+	0.514741i	0.779576	−	0.375424i	−4.72817	−	0.650797i
2.13	1.52066	+	1.90684i	1.44574	−	0.329980i	−0.878611	+	3.84945i	−2.05609	−	0.878907i	2.82769	+	2.25501i	2.07965	−	3.30974i	−4.28153	+	2.06187i	−0.721637	+	0.347522i	−1.45067	−	5.25716i
8.1	−2.41902	+	1.16494i	−1.19864	+	0.955884i	3.24760	−	4.07236i	1.34856	+	1.78364i	1.78599	−	3.70865i	3.42286	+	0.385664i	−1.91706	+	8.39918i	−0.144537	+	0.633260i	−5.34003	−	2.74367i
8.2	−1.81951	+	0.876230i	−1.14803	+	0.915523i	1.29586	−	1.62496i	−0.422003	−	2.19589i	1.28664	−	2.67174i	−1.46192	−	0.164719i	−0.0352304	+	0.154354i	−0.187773	+	0.822687i	2.69194	+	3.62566i
8.3	−1.79891	+	0.866310i	2.14192	−	1.70812i	1.23861	−	1.55317i	2.22906	+	0.176869i	−2.37336	+	4.92833i	−2.13346	−	0.240384i	0.00596311	−	0.0261261i	1.00257	−	4.39254i	−4.16311	+	1.61289i
8.4	−1.67680	+	0.807503i	0.475210	−	0.378967i	0.912610	−	1.14438i	−1.84867	+	1.25795i	−0.490814	+	1.01919i	−1.84555	−	0.207943i	0.222095	−	0.973061i	−0.585354	+	2.56461i	2.08405	−	3.60213i
8.5	−0.822356	+	0.396026i	−2.53662	+	2.02289i	−0.727547	+	0.912315i	2.07441	+	0.834755i	1.28489	−	2.66810i	−3.14014	−	0.353808i	0.643212	−	2.81810i	1.67481	−	7.33780i	−2.03649	+	0.135055i
8.6	−0.686283	+	0.330496i	1.81501	−	1.44742i	−0.885224	+	1.11004i	−1.21127	−	1.87958i	−0.767242	+	1.59319i	4.23694	+	0.477389i	0.579647	−	2.53960i	0.531668	−	2.32939i	1.45247	+	0.889604i
8.7	−0.209045	+	0.100671i	0.462135	−	0.368540i	−1.21341	+	1.52157i	0.659820	+	2.13650i	−0.0595056	+	0.123565i	0.526961	+	0.0593743i	0.203740	−	0.892641i	−0.589816	+	2.58415i	−0.353015	−	0.380200i

Inner twists

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

    

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

Hecke kernels

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