Newform orbit 120.3.p.a

• Label: 120.3.p.a
• Level: $120$
• Weight: $3$
• Character orbit: 120.p
• Analytic conductor: $3.270$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.p (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.26976317232\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{4} - 6 q^{6} - 72 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.97451	−	0.318295i			1.73205i	3.79738	+	1.25695i	−0.371139	−	4.98621i	0.551302	−	3.41995i	1.20123			−7.09788	−	3.69055i	−3.00000			−0.854264	+	9.96344i
19.2	−1.97451	+	0.318295i		−	1.73205i	3.79738	−	1.25695i	−0.371139	+	4.98621i	0.551302	+	3.41995i	1.20123			−7.09788	+	3.69055i	−3.00000			−0.854264	−	9.96344i
19.3	−1.83348	−	0.798974i		−	1.73205i	2.72328	+	2.92980i	−4.00162	−	2.99784i	−1.38386	+	3.17568i	0.116466			−2.65225	−	7.54756i	−3.00000			4.94169	+	8.69366i
19.4	−1.83348	+	0.798974i			1.73205i	2.72328	−	2.92980i	−4.00162	+	2.99784i	−1.38386	−	3.17568i	0.116466			−2.65225	+	7.54756i	−3.00000			4.94169	−	8.69366i
19.5	−1.71329	−	1.03181i			1.73205i	1.87075	+	3.53557i	3.24023	+	3.80801i	1.78714	−	2.96751i	−13.5060			0.442871	−	7.98773i	−3.00000			−1.62234	−	9.86752i
19.6	−1.71329	+	1.03181i		−	1.73205i	1.87075	−	3.53557i	3.24023	−	3.80801i	1.78714	+	2.96751i	−13.5060			0.442871	+	7.98773i	−3.00000			−1.62234	+	9.86752i
19.7	−1.35826	−	1.46803i		−	1.73205i	−0.310252	+	3.98795i	4.79248	+	1.42554i	−2.54271	+	2.35258i	5.41487			6.27585	−	4.96122i	−3.00000			−4.41669	−	8.97178i
19.8	−1.35826	+	1.46803i			1.73205i	−0.310252	−	3.98795i	4.79248	−	1.42554i	−2.54271	−	2.35258i	5.41487			6.27585	+	4.96122i	−3.00000			−4.41669	+	8.97178i
19.9	−0.452908	−	1.94804i		−	1.73205i	−3.58975	+	1.76457i	−1.72202	+	4.69411i	−3.37411	+	0.784460i	−9.26960			5.06329	+	6.19380i	−3.00000			9.92424	+	1.22857i
19.10	−0.452908	+	1.94804i			1.73205i	−3.58975	−	1.76457i	−1.72202	−	4.69411i	−3.37411	−	0.784460i	−9.26960			5.06329	−	6.19380i	−3.00000			9.92424	−	1.22857i
19.11	−0.0655209	−	1.99893i			1.73205i	−3.99141	+	0.261943i	4.40648	+	2.36283i	3.46224	−	0.113485i	6.07322			0.785125	+	7.96138i	−3.00000			4.43441	−	8.96304i
19.12	−0.0655209	+	1.99893i		−	1.73205i	−3.99141	−	0.261943i	4.40648	−	2.36283i	3.46224	+	0.113485i	6.07322			0.785125	−	7.96138i	−3.00000			4.43441	+	8.96304i
19.13	0.0655209	−	1.99893i			1.73205i	−3.99141	−	0.261943i	−4.40648	−	2.36283i	3.46224	+	0.113485i	−6.07322			−0.785125	+	7.96138i	−3.00000			−5.01184	+	8.65341i
19.14	0.0655209	+	1.99893i		−	1.73205i	−3.99141	+	0.261943i	−4.40648	+	2.36283i	3.46224	−	0.113485i	−6.07322			−0.785125	−	7.96138i	−3.00000			−5.01184	−	8.65341i
19.15	0.452908	−	1.94804i		−	1.73205i	−3.58975	−	1.76457i	1.72202	−	4.69411i	−3.37411	−	0.784460i	9.26960			−5.06329	+	6.19380i	−3.00000			−8.36441	−	5.48057i
19.16	0.452908	+	1.94804i			1.73205i	−3.58975	+	1.76457i	1.72202	+	4.69411i	−3.37411	+	0.784460i	9.26960			−5.06329	−	6.19380i	−3.00000			−8.36441	+	5.48057i
19.17	1.35826	−	1.46803i		−	1.73205i	−0.310252	−	3.98795i	−4.79248	−	1.42554i	−2.54271	−	2.35258i	−5.41487			−6.27585	−	4.96122i	−3.00000			−8.60218	+	5.09926i
19.18	1.35826	+	1.46803i			1.73205i	−0.310252	+	3.98795i	−4.79248	+	1.42554i	−2.54271	+	2.35258i	−5.41487			−6.27585	+	4.96122i	−3.00000			−8.60218	−	5.09926i
19.19	1.71329	−	1.03181i			1.73205i	1.87075	−	3.53557i	−3.24023	−	3.80801i	1.78714	+	2.96751i	13.5060			−0.442871	−	7.98773i	−3.00000			−9.48059	−	3.18095i
19.20	1.71329	+	1.03181i		−	1.73205i	1.87075	+	3.53557i	−3.24023	+	3.80801i	1.78714	−	2.96751i	13.5060			−0.442871	+	7.98773i	−3.00000			−9.48059	+	3.18095i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.d	odd	2	1	inner
40.e	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	120.3.p.a	✓	24
3.b	odd	2	1		360.3.p.i		24
4.b	odd	2	1		480.3.p.a		24
5.b	even	2	1	inner	120.3.p.a	✓	24
5.c	odd	4	2		600.3.g.e		24
8.b	even	2	1		480.3.p.a		24
8.d	odd	2	1	inner	120.3.p.a	✓	24
12.b	even	2	1		1440.3.p.i		24
15.d	odd	2	1		360.3.p.i		24
20.d	odd	2	1		480.3.p.a		24
20.e	even	4	2		2400.3.g.e		24
24.f	even	2	1		360.3.p.i		24
24.h	odd	2	1		1440.3.p.i		24
40.e	odd	2	1	inner	120.3.p.a	✓	24
40.f	even	2	1		480.3.p.a		24
40.i	odd	4	2		2400.3.g.e		24
40.k	even	4	2		600.3.g.e		24
60.h	even	2	1		1440.3.p.i		24
120.i	odd	2	1		1440.3.p.i		24
120.m	even	2	1		360.3.p.i		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.3.p.a	✓	24	1.a	even	1	1	trivial
120.3.p.a	✓	24	5.b	even	2	1	inner
120.3.p.a	✓	24	8.d	odd	2	1	inner
120.3.p.a	✓	24	40.e	odd	2	1	inner
360.3.p.i		24	3.b	odd	2	1
360.3.p.i		24	15.d	odd	2	1
360.3.p.i		24	24.f	even	2	1
360.3.p.i		24	120.m	even	2	1
480.3.p.a		24	4.b	odd	2	1
480.3.p.a		24	8.b	even	2	1
480.3.p.a		24	20.d	odd	2	1
480.3.p.a		24	40.f	even	2	1
600.3.g.e		24	5.c	odd	4	2
600.3.g.e		24	40.k	even	4	2
1440.3.p.i		24	12.b	even	2	1
1440.3.p.i		24	24.h	odd	2	1
1440.3.p.i		24	60.h	even	2	1
1440.3.p.i		24	120.i	odd	2	1
2400.3.g.e		24	20.e	even	4	2
2400.3.g.e		24	40.i	odd	4	2

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(120, [\chi])\).