Newform orbit 145.3.i.a

• Label: 145.3.i.a
• Level: $145$
• Weight: $3$
• Character orbit: 145.i
• Analytic conductor: $3.951$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	145.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.95096383322\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 4 q^{3} + 4 q^{5} - 24 q^{6} + 12 q^{7} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
88.1	−2.74357	+	2.74357i	1.94586	+	1.94586i		−	11.0543i	3.67630	−	3.38892i	−10.6772			−2.86202	+	2.86202i	19.3539	+	19.3539i		−	1.42722i	−0.788453	+	19.3839i
88.2	−2.51708	+	2.51708i	−3.18753	−	3.18753i		−	8.67141i	3.55563	+	3.51532i	16.0465			0.462406	−	0.462406i	11.7583	+	11.7583i			11.3207i	−17.7982	+	0.101477i
88.3	−2.47063	+	2.47063i	1.18308	+	1.18308i		−	8.20807i	−3.55198	+	3.51902i	−5.84592			−0.746658	+	0.746658i	10.3966	+	10.3966i		−	6.20064i	0.0814340	−	17.4698i
88.4	−2.05512	+	2.05512i	−2.24530	−	2.24530i		−	4.44700i	−4.97941	−	0.453264i	9.22871			−2.57716	+	2.57716i	0.918641	+	0.918641i			1.08277i	11.1648	−	9.30176i
88.5	−1.90045	+	1.90045i	1.54098	+	1.54098i		−	3.22341i	−2.09602	−	4.53946i	−5.85711			8.61655	−	8.61655i	−1.47588	−	1.47588i		−	4.25075i	12.6104	+	4.64364i
88.6	−1.82450	+	1.82450i	3.71731	+	3.71731i		−	2.65761i	1.42689	+	4.79208i	−13.5645			−0.0502145	+	0.0502145i	−2.44920	−	2.44920i			18.6368i	−11.3465	−	6.13979i
88.7	−1.69670	+	1.69670i	−0.382922	−	0.382922i		−	1.75758i	4.70818	+	1.68318i	1.29941			7.91408	−	7.91408i	−3.80471	−	3.80471i		−	8.70674i	−10.8442	+	5.13252i
88.8	−1.62127	+	1.62127i	−1.06507	−	1.06507i		−	1.25703i	3.75028	−	3.30688i	3.45352			−7.13269	+	7.13269i	−4.44709	−	4.44709i		−	6.73127i	−0.718868	+	11.4415i
88.9	−1.35643	+	1.35643i	3.34873	+	3.34873i			0.320219i	−2.59767	−	4.27225i	−9.08461			−6.53447	+	6.53447i	−5.86006	−	5.86006i			13.4280i	9.31854	+	2.27143i
88.10	−0.952939	+	0.952939i	−4.05907	−	4.05907i			2.18381i	1.02907	−	4.89296i	7.73610			2.81315	−	2.81315i	−5.89280	−	5.89280i			23.9522i	3.68205	+	5.64333i
88.11	−0.803514	+	0.803514i	−2.94165	−	2.94165i			2.70873i	−2.46726	+	4.34887i	4.72731			5.84636	−	5.84636i	−5.39056	−	5.39056i			8.30662i	−1.51190	−	5.47685i
88.12	−0.774385	+	0.774385i	0.333962	+	0.333962i			2.80066i	0.728880	+	4.94659i	−0.517230			−4.05932	+	4.05932i	−5.26632	−	5.26632i		−	8.77694i	−4.39499	−	3.26613i
88.13	−0.238667	+	0.238667i	−0.735639	−	0.735639i			3.88608i	−4.40148	−	2.37213i	0.351146			−0.877322	+	0.877322i	−1.88215	−	1.88215i		−	7.91767i	1.61664	−	0.484339i
88.14	−0.0951356	+	0.0951356i	2.59152	+	2.59152i			3.98190i	4.86451	−	1.15609i	−0.493092			0.437976	−	0.437976i	−0.759362	−	0.759362i			4.43200i	−0.352803	+	0.572773i
88.15	0.0969176	−	0.0969176i	3.23623	+	3.23623i			3.98121i	−4.17207	+	2.75570i	0.627296			9.52384	−	9.52384i	0.773520	+	0.773520i			11.9464i	−0.137271	+	0.671422i
88.16	0.324573	−	0.324573i	−0.415091	−	0.415091i			3.78930i	0.00662345	−	5.00000i	−0.269455			3.42686	−	3.42686i	2.52820	+	2.52820i		−	8.65540i	−1.62071	−	1.62501i
88.17	0.416345	−	0.416345i	−3.15013	−	3.15013i			3.65331i	4.59462	+	1.97217i	−2.62308			−6.64071	+	6.64071i	3.18642	+	3.18642i			10.8466i	2.73405	−	1.09185i
88.18	0.963305	−	0.963305i	2.35204	+	2.35204i			2.14409i	−4.89995	+	0.995210i	4.53146			−7.10852	+	7.10852i	5.91863	+	5.91863i			2.06418i	−3.76146	+	5.67884i
88.19	1.03150	−	1.03150i	−2.64167	−	2.64167i			1.87201i	−3.83799	+	3.20466i	−5.44977			−3.60858	+	3.60858i	6.05699	+	6.05699i			4.95685i	−0.653272	+	7.26450i
88.20	1.36711	−	1.36711i	−1.79931	−	1.79931i			0.262040i	4.52295	−	2.13142i	−4.91969			5.29311	−	5.29311i	5.82666	+	5.82666i		−	2.52499i	3.26947	−	9.09723i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	145.3.i.a	✓	56
5.c	odd	4	1	inner	145.3.i.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.3.i.a	✓	56	1.a	even	1	1	trivial
145.3.i.a	✓	56	5.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(145, [\chi])\).