Newform orbit 145.2.l.a

• Label: 145.2.l.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.l
• Analytic conductor: $1.158$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.l (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.15783082931\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(12\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 18 q^{4} - 9 q^{5} + 4 q^{6} - 14 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−0.584262	+	2.55982i	−1.84827	+	0.890080i	−4.40937	−	2.12344i	0.258362	+	2.22109i	−1.19857	−	5.25128i	−0.0881466	−	0.183038i	4.73773	−	5.94092i	0.753390	−	0.944721i	−5.83654	−	0.636340i
4.2	−0.500388	+	2.19235i	1.36712	−	0.658372i	−2.75405	−	1.32628i	1.91493	−	1.15457i	0.759286	+	3.32665i	0.927353	+	1.92567i	1.48165	−	1.85793i	−0.434894	+	0.545340i	1.57300	+	4.77593i
4.3	−0.351585	+	1.54039i	−0.278885	+	0.134304i	−0.447265	−	0.215391i	−2.22028	+	0.265265i	−0.108829	−	0.476812i	0.934317	+	1.94013i	−1.48120	+	1.85736i	−1.81073	+	2.27058i	0.372003	−	3.51337i
4.4	−0.334116	+	1.46386i	2.46599	−	1.18756i	−0.229312	−	0.110431i	−0.141142	+	2.23161i	0.914491	+	4.00665i	−1.71394	−	3.55903i	−1.63407	+	2.04906i	2.80035	−	3.51153i	−3.21960	−	0.952229i
4.5	−0.201954	+	0.884818i	−1.84663	+	0.889290i	1.05982	+	0.510383i	2.13173	+	0.675083i	−0.413926	−	1.81353i	−0.303433	−	0.630084i	−1.79736	+	2.25381i	0.748734	−	0.938883i	−1.02784	+	1.74986i
4.6	−0.117010	+	0.512653i	1.21246	−	0.583890i	1.55282	+	0.747797i	0.338714	−	2.21027i	0.157463	+	0.689892i	−1.17080	−	2.43120i	−1.22076	+	1.53079i	−0.741336	+	0.929606i	1.09347	+	0.432265i
4.7	0.117010	−	0.512653i	−1.21246	+	0.583890i	1.55282	+	0.747797i	0.653828	−	2.13834i	0.157463	+	0.689892i	1.17080	+	2.43120i	1.22076	−	1.53079i	−0.741336	+	0.929606i	−1.01972	−	0.585394i
4.8	0.201954	−	0.884818i	1.84663	−	0.889290i	1.05982	+	0.510383i	−2.21353	−	0.316694i	−0.413926	−	1.81353i	0.303433	+	0.630084i	1.79736	−	2.25381i	0.748734	−	0.938883i	−0.727247	+	1.89461i
4.9	0.334116	−	1.46386i	−2.46599	+	1.18756i	−0.229312	−	0.110431i	−0.841094	+	2.07185i	0.914491	+	4.00665i	1.71394	+	3.55903i	1.63407	−	2.04906i	2.80035	−	3.51153i	2.75187	+	1.92348i
4.10	0.351585	−	1.54039i	0.278885	−	0.134304i	−0.447265	−	0.215391i	1.88531	+	1.20234i	−0.108829	−	0.476812i	−0.934317	−	1.94013i	1.48120	−	1.85736i	−1.81073	+	2.27058i	2.51492	−	2.48139i
4.11	0.500388	−	2.19235i	−1.36712	+	0.658372i	−2.75405	−	1.32628i	−1.22435	−	1.87109i	0.759286	+	3.32665i	−0.927353	−	1.92567i	−1.48165	+	1.85793i	−0.434894	+	0.545340i	−4.71472	+	1.74792i
4.12	0.584262	−	2.55982i	1.84827	−	0.890080i	−4.40937	−	2.12344i	−1.19647	+	1.88904i	−1.19857	−	5.25128i	0.0881466	+	0.183038i	−4.73773	+	5.94092i	0.753390	−	0.944721i	4.13654	+	4.16644i
9.1	−2.06579	+	0.994830i	0.965193	+	1.21031i	2.03081	−	2.54655i	0.723461	−	2.11580i	−3.19794	−	1.54005i	3.67018	−	2.92687i	−0.641411	+	2.81021i	0.134301	−	0.588412i	0.610344	+	5.09051i
9.2	−2.05985	+	0.991973i	−0.625691	−	0.784592i	2.01201	−	2.52298i	−1.76973	+	1.36676i	2.06713	+	0.995475i	0.674382	−	0.537802i	−0.624230	+	2.73493i	0.443468	−	1.94296i	2.28960	−	4.57086i
9.3	−1.36351	+	0.656630i	1.26647	+	1.58810i	0.181009	−	0.226978i	1.55038	+	1.61131i	−2.76963	−	1.33378i	−1.32760	+	1.05873i	0.575751	−	2.52253i	−0.250556	+	1.09776i	−3.17199	−	1.17901i
9.4	−1.06063	+	0.510773i	−0.171630	−	0.215217i	−0.382930	+	0.480179i	−1.37063	−	1.76674i	0.291963	+	0.140602i	−3.21095	+	2.56064i	0.684794	−	3.00028i	0.650701	−	2.85091i	2.35614	+	1.17378i
9.5	−0.689886	+	0.332232i	−1.07769	−	1.35138i	−0.881415	+	1.10526i	2.23606	−	0.00463917i	1.19245	+	0.574255i	0.918299	−	0.732319i	0.581649	−	2.54837i	0.00275115	−	0.0120536i	−1.54109	+	0.746091i
9.6	−0.0720204	+	0.0346832i	1.62624	+	2.03925i	−1.24300	+	1.55867i	−2.22923	+	0.174753i	−0.187850	−	0.0904640i	0.986722	−	0.786885i	0.0710366	−	0.311232i	−0.846291	+	3.70784i	0.154489	−	0.0899026i
9.7	0.0720204	−	0.0346832i	−1.62624	−	2.03925i	−1.24300	+	1.55867i	−1.52653	+	1.63392i	−0.187850	−	0.0904640i	−0.986722	+	0.786885i	−0.0710366	+	0.311232i	−0.846291	+	3.70784i	−0.0532715	+	0.170621i
9.8	0.689886	−	0.332232i	1.07769	+	1.35138i	−0.881415	+	1.10526i	1.39779	−	1.74533i	1.19245	+	0.574255i	−0.918299	+	0.732319i	−0.581649	+	2.54837i	0.00275115	−	0.0120536i	0.384461	−	1.66847i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
29.e	even	14	1	inner
145.l	even	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	145.2.l.a	✓	72
5.b	even	2	1	inner	145.2.l.a	✓	72
5.c	odd	4	2		725.2.q.f		72
29.e	even	14	1	inner	145.2.l.a	✓	72
145.l	even	14	1	inner	145.2.l.a	✓	72
145.q	odd	28	2		725.2.q.f		72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.2.l.a	✓	72	1.a	even	1	1	trivial
145.2.l.a	✓	72	5.b	even	2	1	inner
145.2.l.a	✓	72	29.e	even	14	1	inner
145.2.l.a	✓	72	145.l	even	14	1	inner
725.2.q.f		72	5.c	odd	4	2
725.2.q.f		72	145.q	odd	28	2

Hecke kernels

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