Newform orbit 105.4.m.a

• Label: 105.4.m.a
• Level: $105$
• Weight: $4$
• Character orbit: 105.m
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1	−3.58711	+	3.58711i	−2.12132	+	2.12132i		−	17.7347i	10.0305	−	4.93863i		−	15.2188i	2.02215	+	18.4095i	34.9193	+	34.9193i		−	9.00000i	−18.2649	+	53.6957i
13.2	−3.58711	+	3.58711i	2.12132	−	2.12132i		−	17.7347i	−10.0305	+	4.93863i			15.2188i	−18.4095	−	2.02215i	34.9193	+	34.9193i		−	9.00000i	18.2649	−	53.6957i
13.3	−2.96540	+	2.96540i	−2.12132	+	2.12132i		−	9.58718i	−8.64856	+	7.08536i		−	12.5811i	−4.10485	+	18.0596i	4.70662	+	4.70662i		−	9.00000i	4.63550	−	46.6574i
13.4	−2.96540	+	2.96540i	2.12132	−	2.12132i		−	9.58718i	8.64856	−	7.08536i			12.5811i	−18.0596	+	4.10485i	4.70662	+	4.70662i		−	9.00000i	−4.63550	+	46.6574i
13.5	−2.50091	+	2.50091i	−2.12132	+	2.12132i		−	4.50911i	−9.59495	−	5.73906i		−	10.6105i	16.0890	−	9.17301i	−8.73040	−	8.73040i		−	9.00000i	38.3490	−	9.64324i
13.6	−2.50091	+	2.50091i	2.12132	−	2.12132i		−	4.50911i	9.59495	+	5.73906i			10.6105i	9.17301	−	16.0890i	−8.73040	−	8.73040i		−	9.00000i	−38.3490	+	9.64324i
13.7	−2.16465	+	2.16465i	−2.12132	+	2.12132i		−	1.37142i	9.30469	−	6.19861i		−	9.18383i	−8.45914	−	16.4755i	−14.3486	−	14.3486i		−	9.00000i	−6.72356	+	33.5592i
13.8	−2.16465	+	2.16465i	2.12132	−	2.12132i		−	1.37142i	−9.30469	+	6.19861i			9.18383i	16.4755	+	8.45914i	−14.3486	−	14.3486i		−	9.00000i	6.72356	−	33.5592i
13.9	−0.817511	+	0.817511i	−2.12132	+	2.12132i			6.66335i	8.83013	+	6.85775i		−	3.46841i	18.0193	+	4.27846i	−11.9875	−	11.9875i		−	9.00000i	−12.8250	+	1.61244i
13.10	−0.817511	+	0.817511i	2.12132	−	2.12132i			6.66335i	−8.83013	−	6.85775i			3.46841i	−4.27846	−	18.0193i	−11.9875	−	11.9875i		−	9.00000i	12.8250	−	1.61244i
13.11	−0.811442	+	0.811442i	−2.12132	+	2.12132i			6.68312i	−4.54645	+	10.2142i		−	3.44266i	−15.2496	−	10.5095i	−11.9145	−	11.9145i		−	9.00000i	−4.59905	−	11.9774i
13.12	−0.811442	+	0.811442i	2.12132	−	2.12132i			6.68312i	4.54645	−	10.2142i			3.44266i	10.5095	+	15.2496i	−11.9145	−	11.9145i		−	9.00000i	4.59905	+	11.9774i
13.13	−0.216837	+	0.216837i	−2.12132	+	2.12132i			7.90596i	−1.17774	−	11.1181i		−	0.919960i	−3.57938	+	18.1711i	−3.44900	−	3.44900i		−	9.00000i	2.66620	+	2.15544i
13.14	−0.216837	+	0.216837i	2.12132	−	2.12132i			7.90596i	1.17774	+	11.1181i			0.919960i	−18.1711	+	3.57938i	−3.44900	−	3.44900i		−	9.00000i	−2.66620	−	2.15544i
13.15	1.52903	−	1.52903i	−2.12132	+	2.12132i			3.32413i	−1.55846	−	11.0712i			6.48713i	15.0664	−	10.7705i	17.3149	+	17.3149i		−	9.00000i	−19.3111	−	14.5453i
13.16	1.52903	−	1.52903i	2.12132	−	2.12132i			3.32413i	1.55846	+	11.0712i		−	6.48713i	10.7705	−	15.0664i	17.3149	+	17.3149i		−	9.00000i	19.3111	+	14.5453i
13.17	1.79945	−	1.79945i	−2.12132	+	2.12132i			1.52398i	−11.1587	−	0.695951i			7.63441i	−12.8255	−	13.3607i	17.1379	+	17.1379i		−	9.00000i	−21.3317	+	18.8271i
13.18	1.79945	−	1.79945i	2.12132	−	2.12132i			1.52398i	11.1587	+	0.695951i		−	7.63441i	13.3607	+	12.8255i	17.1379	+	17.1379i		−	9.00000i	21.3317	−	18.8271i
13.19	2.53770	−	2.53770i	−2.12132	+	2.12132i		−	4.87986i	−2.35304	+	10.9299i			10.7666i	8.62377	+	16.3900i	7.91797	+	7.91797i		−	9.00000i	21.7656	+	33.7082i
13.20	2.53770	−	2.53770i	2.12132	−	2.12132i		−	4.87986i	2.35304	−	10.9299i		−	10.7666i	−16.3900	−	8.62377i	7.91797	+	7.91797i		−	9.00000i	−21.7656	−	33.7082i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.b	odd	2	1	inner
35.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.4.m.a	✓	48
5.c	odd	4	1	inner	105.4.m.a	✓	48
7.b	odd	2	1	inner	105.4.m.a	✓	48
35.f	even	4	1	inner	105.4.m.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.4.m.a	✓	48	1.a	even	1	1	trivial
105.4.m.a	✓	48	5.c	odd	4	1	inner
105.4.m.a	✓	48	7.b	odd	2	1	inner
105.4.m.a	✓	48	35.f	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(105, [\chi])\).