Newform orbit 152.3.g.c

• Label: 152.3.g.c
• Level: $152$
• Weight: $3$
• Character orbit: 152.g
• Analytic conductor: $4.142$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.14170001828\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 22 q^{4} - 22 q^{6} - 4 q^{7} + 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−1.87828	−	0.687069i	0.551655			3.05587	+	2.58102i			8.19843i	−1.03616	−	0.379025i	−4.38598			−3.96645	−	6.94747i	−8.69568			5.63289	−	15.3990i
37.2	−1.87828	+	0.687069i	0.551655			3.05587	−	2.58102i		−	8.19843i	−1.03616	+	0.379025i	−4.38598			−3.96645	+	6.94747i	−8.69568			5.63289	+	15.3990i
37.3	−1.71548	−	1.02816i	−2.73525			1.88577	+	3.52759i		−	6.27390i	4.69229	+	2.81228i	4.40827			0.391919	−	7.99039i	−1.51838			−6.45058	+	10.7628i
37.4	−1.71548	+	1.02816i	−2.73525			1.88577	−	3.52759i			6.27390i	4.69229	−	2.81228i	4.40827			0.391919	+	7.99039i	−1.51838			−6.45058	−	10.7628i
37.5	−1.57472	−	1.23299i	2.81361			0.959455	+	3.88323i			1.92387i	−4.43063	−	3.46916i	5.15988			3.27712	−	7.29798i	−1.08361			2.37212	−	3.02955i
37.6	−1.57472	+	1.23299i	2.81361			0.959455	−	3.88323i		−	1.92387i	−4.43063	+	3.46916i	5.15988			3.27712	+	7.29798i	−1.08361			2.37212	+	3.02955i
37.7	−1.56379	−	1.24682i	3.79824			0.890862	+	3.89953i		−	7.25711i	−5.93964	−	4.73573i	−10.3770			3.46891	−	7.20879i	5.42661			−9.04834	+	11.3486i
37.8	−1.56379	+	1.24682i	3.79824			0.890862	−	3.89953i			7.25711i	−5.93964	+	4.73573i	−10.3770			3.46891	+	7.20879i	5.42661			−9.04834	−	11.3486i
37.9	−1.08315	−	1.68131i	−4.18220			−1.65357	+	3.64221i			2.72392i	4.52995	+	7.03156i	−0.0477399			7.91473	−	1.16490i	8.49082			4.57974	−	2.95041i
37.10	−1.08315	+	1.68131i	−4.18220			−1.65357	−	3.64221i		−	2.72392i	4.52995	−	7.03156i	−0.0477399			7.91473	+	1.16490i	8.49082			4.57974	+	2.95041i
37.11	−0.630874	−	1.89789i	0.442869			−3.20400	+	2.39466i			1.54280i	−0.279395	−	0.840519i	−7.23381			6.56613	+	4.57011i	−8.80387			2.92806	−	0.973310i
37.12	−0.630874	+	1.89789i	0.442869			−3.20400	−	2.39466i		−	1.54280i	−0.279395	+	0.840519i	−7.23381			6.56613	−	4.57011i	−8.80387			2.92806	+	0.973310i
37.13	−0.411805	−	1.95714i	5.43834			−3.66083	+	1.61193i			7.56221i	−2.23954	−	10.6436i	−0.579999			4.66232	+	6.50098i	20.5756			14.8003	−	3.11416i
37.14	−0.411805	+	1.95714i	5.43834			−3.66083	−	1.61193i		−	7.56221i	−2.23954	+	10.6436i	−0.579999			4.66232	−	6.50098i	20.5756			14.8003	+	3.11416i
37.15	−0.336484	−	1.97149i	2.36824			−3.77356	+	1.32675i		−	6.78748i	−0.796874	−	4.66896i	12.0564			3.88542	+	6.99311i	−3.39144			−13.3815	+	2.28388i
37.16	−0.336484	+	1.97149i	2.36824			−3.77356	−	1.32675i			6.78748i	−0.796874	+	4.66896i	12.0564			3.88542	−	6.99311i	−3.39144			−13.3815	−	2.28388i
37.17	0.336484	−	1.97149i	−2.36824			−3.77356	−	1.32675i			6.78748i	−0.796874	+	4.66896i	12.0564			−3.88542	+	6.99311i	−3.39144			13.3815	+	2.28388i
37.18	0.336484	+	1.97149i	−2.36824			−3.77356	+	1.32675i		−	6.78748i	−0.796874	−	4.66896i	12.0564			−3.88542	−	6.99311i	−3.39144			13.3815	−	2.28388i
37.19	0.411805	−	1.95714i	−5.43834			−3.66083	−	1.61193i		−	7.56221i	−2.23954	+	10.6436i	−0.579999			−4.66232	+	6.50098i	20.5756			−14.8003	−	3.11416i
37.20	0.411805	+	1.95714i	−5.43834			−3.66083	+	1.61193i			7.56221i	−2.23954	−	10.6436i	−0.579999			−4.66232	−	6.50098i	20.5756			−14.8003	+	3.11416i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
19.b	odd	2	1	inner
152.g	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	152.3.g.c	✓	32
4.b	odd	2	1		608.3.g.c		32
8.b	even	2	1	inner	152.3.g.c	✓	32
8.d	odd	2	1		608.3.g.c		32
19.b	odd	2	1	inner	152.3.g.c	✓	32
76.d	even	2	1		608.3.g.c		32
152.b	even	2	1		608.3.g.c		32
152.g	odd	2	1	inner	152.3.g.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.3.g.c	✓	32	1.a	even	1	1	trivial
152.3.g.c	✓	32	8.b	even	2	1	inner
152.3.g.c	✓	32	19.b	odd	2	1	inner
152.3.g.c	✓	32	152.g	odd	2	1	inner
608.3.g.c		32	4.b	odd	2	1
608.3.g.c		32	8.d	odd	2	1
608.3.g.c		32	76.d	even	2	1
608.3.g.c		32	152.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^16 - 83*T3^14 + 2675*T3^12 - 43201*T3^10 + 372480*T3^8 - 1662240*T3^6 + 3242624*T3^4 - 1329216*T3^2 + 147968