Newform orbit 145.3.f.a

• Label: 145.3.f.a
• Level: $145$
• Weight: $3$
• Character orbit: 145.f
• Analytic conductor: $3.951$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	145.f (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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
99.1	−2.75207	+	2.75207i	−0.458586	+	0.458586i		−	11.1478i	−4.99943	+	0.0756853i		−	2.52412i		−	8.28559i	19.6712	+	19.6712i			8.57940i	13.5505	−	13.9671i
99.2	−2.44924	+	2.44924i	3.96463	−	3.96463i		−	7.99756i	−2.03731	−	4.56611i			19.4206i			6.75696i	9.79098	+	9.79098i		−	22.4365i	16.1734	+	6.19362i
99.3	−2.30756	+	2.30756i	−0.479391	+	0.479391i		−	6.64962i	3.45042	−	3.61865i		−	2.21244i			5.07665i	6.11415	+	6.11415i			8.54037i	0.388208	+	16.3123i
99.4	−2.25084	+	2.25084i	−3.77509	+	3.77509i		−	6.13256i	4.55114	+	2.07053i		−	16.9942i		−	11.7956i	4.80006	+	4.80006i		−	19.5026i	−14.9043	+	5.58346i
99.5	−2.17830	+	2.17830i	−1.62861	+	1.62861i		−	5.48996i	−0.268037	+	4.99281i		−	7.09518i			11.0456i	3.24558	+	3.24558i			3.69528i	−10.2920	−	11.4597i
99.6	−2.01791	+	2.01791i	2.80954	−	2.80954i		−	4.14394i	0.954221	+	4.90810i			11.3388i		−	1.42693i	0.290453	+	0.290453i		−	6.78702i	−11.8297	−	7.97858i
99.7	−1.54543	+	1.54543i	1.34392	−	1.34392i		−	0.776725i	−4.79207	+	1.42690i			4.15387i		−	2.18145i	−4.98135	−	4.98135i			5.38777i	5.20064	−	9.61101i
99.8	−1.44561	+	1.44561i	−2.28830	+	2.28830i		−	0.179596i	−1.92508	−	4.61455i		−	6.61599i		−	1.81631i	−5.52283	−	5.52283i		−	1.47261i	9.45378	+	3.88793i
99.9	−1.43501	+	1.43501i	1.94244	−	1.94244i		−	0.118508i	4.10095	−	2.86046i			5.57484i		−	11.8275i	−5.56998	−	5.56998i			1.45386i	−1.78011	+	9.98969i
99.10	−0.702280	+	0.702280i	−3.35259	+	3.35259i			3.01361i	−3.47698	+	3.59313i		−	4.70891i			3.11086i	−4.92551	−	4.92551i		−	13.4797i	−0.0815733	−	4.96520i
99.11	−0.685034	+	0.685034i	2.61026	−	2.61026i			3.06146i	4.95502	−	0.669150i			3.57623i			12.4543i	−4.83734	−	4.83734i		−	4.62690i	−2.93597	+	3.85275i
99.12	−0.605792	+	0.605792i	−0.878690	+	0.878690i			3.26603i	3.27471	+	3.77839i		−	1.06461i		−	3.05930i	−4.40171	−	4.40171i			7.45581i	−4.27272	−	0.305124i
99.13	−0.593380	+	0.593380i	1.07917	−	1.07917i			3.29580i	−3.37869	−	3.68571i			1.28071i			8.16487i	−4.32918	−	4.32918i			6.67080i	4.19187	+	0.182175i
99.14	−0.0178136	+	0.0178136i	−3.63854	+	3.63854i			3.99937i	4.12139	−	2.83093i		−	0.129631i			9.48607i	−0.142497	−	0.142497i		−	17.4780i	−0.0229876	+	0.123846i
99.15	0.0178136	−	0.0178136i	3.63854	−	3.63854i			3.99937i	−4.12139	−	2.83093i		−	0.129631i		−	9.48607i	0.142497	+	0.142497i		−	17.4780i	−0.123846	+	0.0229876i
99.16	0.593380	−	0.593380i	−1.07917	+	1.07917i			3.29580i	3.37869	−	3.68571i			1.28071i		−	8.16487i	4.32918	+	4.32918i			6.67080i	−0.182175	−	4.19187i
99.17	0.605792	−	0.605792i	0.878690	−	0.878690i			3.26603i	−3.27471	+	3.77839i		−	1.06461i			3.05930i	4.40171	+	4.40171i			7.45581i	0.305124	+	4.27272i
99.18	0.685034	−	0.685034i	−2.61026	+	2.61026i			3.06146i	−4.95502	−	0.669150i			3.57623i		−	12.4543i	4.83734	+	4.83734i		−	4.62690i	−3.85275	+	2.93597i
99.19	0.702280	−	0.702280i	3.35259	−	3.35259i			3.01361i	3.47698	+	3.59313i		−	4.70891i		−	3.11086i	4.92551	+	4.92551i		−	13.4797i	4.96520	+	0.0815733i
99.20	1.43501	−	1.43501i	−1.94244	+	1.94244i		−	0.118508i	−4.10095	−	2.86046i			5.57484i			11.8275i	5.56998	+	5.56998i			1.45386i	−9.98969	+	1.78011i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
29.c	odd	4	1	inner
145.f	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.f.a	✓	56
5.b	even	2	1	inner	145.3.f.a	✓	56
29.c	odd	4	1	inner	145.3.f.a	✓	56
145.f	odd	4	1	inner	145.3.f.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.3.f.a	✓	56	1.a	even	1	1	trivial
145.3.f.a	✓	56	5.b	even	2	1	inner
145.3.f.a	✓	56	29.c	odd	4	1	inner
145.3.f.a	✓	56	145.f	odd	4	1	inner

Hecke kernels

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