Newform orbit 105.3.k.d

• Label: 105.3.k.d
• Level: $105$
• Weight: $3$
• Character orbit: 105.k
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
62.1	−2.63482	+	2.63482i	−2.54097	−	1.59482i		−	9.88460i	−4.15332	−	2.78387i	10.8971	−	2.49295i	2.39850	+	6.57626i	15.5049	+	15.5049i	3.91310	+	8.10479i	18.2783	−	3.60824i
62.2	−2.63482	+	2.63482i	2.54097	+	1.59482i		−	9.88460i	4.15332	+	2.78387i	−10.8971	+	2.49295i	6.57626	+	2.39850i	15.5049	+	15.5049i	3.91310	+	8.10479i	−18.2783	+	3.60824i
62.3	−2.28094	+	2.28094i	−1.07458	+	2.80094i		−	6.40541i	1.80941	−	4.66112i	−3.93772	−	8.83986i	−6.22100	−	3.20922i	5.48661	+	5.48661i	−6.69054	−	6.01969i	6.50460	+	14.7589i
62.4	−2.28094	+	2.28094i	1.07458	−	2.80094i		−	6.40541i	−1.80941	+	4.66112i	3.93772	+	8.83986i	−3.20922	−	6.22100i	5.48661	+	5.48661i	−6.69054	−	6.01969i	−6.50460	−	14.7589i
62.5	−1.88692	+	1.88692i	−2.65373	−	1.39918i		−	3.12092i	4.96950	+	0.551428i	7.64751	−	2.36725i	2.09055	−	6.68054i	−1.65875	−	1.65875i	5.08462	+	7.42608i	−10.4175	+	8.33654i
62.6	−1.88692	+	1.88692i	2.65373	+	1.39918i		−	3.12092i	−4.96950	−	0.551428i	−7.64751	+	2.36725i	−6.68054	+	2.09055i	−1.65875	−	1.65875i	5.08462	+	7.42608i	10.4175	−	8.33654i
62.7	−1.67168	+	1.67168i	−2.55943	+	1.56503i		−	1.58906i	0.529219	+	4.97191i	1.66231	−	6.89480i	−1.73590	+	6.78135i	−4.03033	−	4.03033i	4.10134	−	8.01118i	−9.19616	−	7.42678i
62.8	−1.67168	+	1.67168i	2.55943	−	1.56503i		−	1.58906i	−0.529219	−	4.97191i	−1.66231	+	6.89480i	6.78135	−	1.73590i	−4.03033	−	4.03033i	4.10134	−	8.01118i	9.19616	+	7.42678i
62.9	1.67168	−	1.67168i	−1.56503	+	2.55943i		−	1.58906i	0.529219	+	4.97191i	1.66231	+	6.89480i	6.78135	−	1.73590i	4.03033	+	4.03033i	−4.10134	−	8.01118i	9.19616	+	7.42678i
62.10	1.67168	−	1.67168i	1.56503	−	2.55943i		−	1.58906i	−0.529219	−	4.97191i	−1.66231	−	6.89480i	−1.73590	+	6.78135i	4.03033	+	4.03033i	−4.10134	−	8.01118i	−9.19616	−	7.42678i
62.11	1.88692	−	1.88692i	−1.39918	−	2.65373i		−	3.12092i	−4.96950	−	0.551428i	−7.64751	−	2.36725i	2.09055	−	6.68054i	1.65875	+	1.65875i	−5.08462	+	7.42608i	−10.4175	+	8.33654i
62.12	1.88692	−	1.88692i	1.39918	+	2.65373i		−	3.12092i	4.96950	+	0.551428i	7.64751	+	2.36725i	−6.68054	+	2.09055i	1.65875	+	1.65875i	−5.08462	+	7.42608i	10.4175	−	8.33654i
62.13	2.28094	−	2.28094i	−2.80094	+	1.07458i		−	6.40541i	1.80941	−	4.66112i	−3.93772	+	8.83986i	−3.20922	−	6.22100i	−5.48661	−	5.48661i	6.69054	−	6.01969i	−6.50460	−	14.7589i
62.14	2.28094	−	2.28094i	2.80094	−	1.07458i		−	6.40541i	−1.80941	+	4.66112i	3.93772	−	8.83986i	−6.22100	−	3.20922i	−5.48661	−	5.48661i	6.69054	−	6.01969i	6.50460	+	14.7589i
62.15	2.63482	−	2.63482i	−1.59482	−	2.54097i		−	9.88460i	4.15332	+	2.78387i	−10.8971	−	2.49295i	2.39850	+	6.57626i	−15.5049	−	15.5049i	−3.91310	+	8.10479i	18.2783	−	3.60824i
62.16	2.63482	−	2.63482i	1.59482	+	2.54097i		−	9.88460i	−4.15332	−	2.78387i	10.8971	+	2.49295i	6.57626	+	2.39850i	−15.5049	−	15.5049i	−3.91310	+	8.10479i	−18.2783	+	3.60824i
83.1	−2.63482	−	2.63482i	−2.54097	+	1.59482i			9.88460i	−4.15332	+	2.78387i	10.8971	+	2.49295i	2.39850	−	6.57626i	15.5049	−	15.5049i	3.91310	−	8.10479i	18.2783	+	3.60824i
83.2	−2.63482	−	2.63482i	2.54097	−	1.59482i			9.88460i	4.15332	−	2.78387i	−10.8971	−	2.49295i	6.57626	−	2.39850i	15.5049	−	15.5049i	3.91310	−	8.10479i	−18.2783	−	3.60824i
83.3	−2.28094	−	2.28094i	−1.07458	−	2.80094i			6.40541i	1.80941	+	4.66112i	−3.93772	+	8.83986i	−6.22100	+	3.20922i	5.48661	−	5.48661i	−6.69054	+	6.01969i	6.50460	−	14.7589i
83.4	−2.28094	−	2.28094i	1.07458	+	2.80094i			6.40541i	−1.80941	−	4.66112i	3.93772	−	8.83986i	−3.20922	+	6.22100i	5.48661	−	5.48661i	−6.69054	+	6.01969i	−6.50460	+	14.7589i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.b	odd	2	1	inner
15.e	even	4	1	inner
21.c	even	2	1	inner
35.f	even	4	1	inner
105.k	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.3.k.d	✓	32
3.b	odd	2	1	inner	105.3.k.d	✓	32
5.c	odd	4	1	inner	105.3.k.d	✓	32
7.b	odd	2	1	inner	105.3.k.d	✓	32
15.e	even	4	1	inner	105.3.k.d	✓	32
21.c	even	2	1	inner	105.3.k.d	✓	32
35.f	even	4	1	inner	105.3.k.d	✓	32
105.k	odd	4	1	inner	105.3.k.d	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.3.k.d	✓	32	1.a	even	1	1	trivial
105.3.k.d	✓	32	3.b	odd	2	1	inner
105.3.k.d	✓	32	5.c	odd	4	1	inner
105.3.k.d	✓	32	7.b	odd	2	1	inner
105.3.k.d	✓	32	15.e	even	4	1	inner
105.3.k.d	✓	32	21.c	even	2	1	inner
105.3.k.d	✓	32	35.f	even	4	1	inner
105.3.k.d	✓	32	105.k	odd	4	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(105, [\chi])\):

\( T_{2}^{16} + 383T_{2}^{12} + 47127T_{2}^{8} + 2187309T_{2}^{4} + 33062500 \)

\( T_{11}^{8} + 497T_{11}^{6} + 63614T_{11}^{4} + 2343020T_{11}^{2} + 25047000 \)

\( T_{13}^{16} + 66241T_{13}^{12} + 288088400T_{13}^{8} + 17091165504T_{13}^{4} + 253806379264 \)