Newform orbit 161.4.c.c

• Label: 161.4.c.c
• Level: $161$
• Weight: $4$
• Character orbit: 161.c
• Analytic conductor: $9.499$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$161 = 7 \cdot 23$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	161.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 36 * q - 8 * q^2 + 184 * q^4 - 228 * q^8 - 436 * q^9 + 168 * q^16 - 404 * q^18 + 204 * q^23 - 140 * q^25 + 256 * q^29 + 1008 * q^32 - 2040 * q^35 - 4412 * q^36 + 1296 * q^39 - 888 * q^46 + 1916 * q^49 + 4080 * q^50 + 6020 * q^58 + 3988 * q^64 - 1712 * q^70 - 5040 * q^71 - 8636 * q^72 - 2864 * q^77 + 8820 * q^78 + 9380 * q^81 - 5032 * q^85 - 3672 * q^92 - 5352 * q^93 - 3840 * q^95 + 6884 * q^98

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
160.1	−5.29875				−	6.28001i	20.0768			−10.4216					33.2762i	11.5274	−	14.4955i	−63.9920			−12.4385			55.2216
160.2	−5.29875				−	6.28001i	20.0768			10.4216					33.2762i	−11.5274	+	14.4955i	−63.9920			−12.4385			−55.2216
160.3	−5.29875					6.28001i	20.0768			−10.4216				−	33.2762i	11.5274	+	14.4955i	−63.9920			−12.4385			55.2216
160.4	−5.29875					6.28001i	20.0768			10.4216				−	33.2762i	−11.5274	−	14.4955i	−63.9920			−12.4385			−55.2216
160.5	−4.42537				−	3.10698i	11.5839			−13.0444					13.7495i	−12.3048	+	13.8417i	−15.8600			17.3467			57.7264
160.6	−4.42537				−	3.10698i	11.5839			13.0444					13.7495i	12.3048	−	13.8417i	−15.8600			17.3467			−57.7264
160.7	−4.42537					3.10698i	11.5839			−13.0444				−	13.7495i	−12.3048	−	13.8417i	−15.8600			17.3467			57.7264
160.8	−4.42537					3.10698i	11.5839			13.0444				−	13.7495i	12.3048	+	13.8417i	−15.8600			17.3467			−57.7264
160.9	−3.36931				−	9.90574i	3.35226			−8.06501					33.3755i	16.4867	+	8.43733i	15.6597			−71.1238			27.1735
160.10	−3.36931				−	9.90574i	3.35226			8.06501					33.3755i	−16.4867	−	8.43733i	15.6597			−71.1238			−27.1735
160.11	−3.36931					9.90574i	3.35226			−8.06501				−	33.3755i	16.4867	−	8.43733i	15.6597			−71.1238			27.1735
160.12	−3.36931					9.90574i	3.35226			8.06501				−	33.3755i	−16.4867	+	8.43733i	15.6597			−71.1238			−27.1735
160.13	−2.89408				−	3.10338i	0.375694			−8.39365					8.98142i	13.9217	+	12.2141i	22.0653			17.3690			24.2919
160.14	−2.89408				−	3.10338i	0.375694			8.39365					8.98142i	−13.9217	−	12.2141i	22.0653			17.3690			−24.2919
160.15	−2.89408					3.10338i	0.375694			−8.39365				−	8.98142i	13.9217	−	12.2141i	22.0653			17.3690			24.2919
160.16	−2.89408					3.10338i	0.375694			8.39365				−	8.98142i	−13.9217	+	12.2141i	22.0653			17.3690			−24.2919
160.17	0.765757				−	0.826637i	−7.41362			−5.17868				−	0.633003i	15.9670	+	9.38369i	−11.8031			26.3167			−3.96561
160.18	0.765757				−	0.826637i	−7.41362			5.17868				−	0.633003i	−15.9670	−	9.38369i	−11.8031			26.3167			3.96561
160.19	0.765757					0.826637i	−7.41362			−5.17868					0.633003i	15.9670	−	9.38369i	−11.8031			26.3167			−3.96561
160.20	0.765757					0.826637i	−7.41362			5.17868					0.633003i	−15.9670	+	9.38369i	−11.8031			26.3167			3.96561

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
23.b	odd	2	1	inner
161.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	161.4.c.c	✓	36
7.b	odd	2	1	inner	161.4.c.c	✓	36
23.b	odd	2	1	inner	161.4.c.c	✓	36
161.c	even	2	1	inner	161.4.c.c	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
161.4.c.c	✓	36	1.a	even	1	1	trivial
161.4.c.c	✓	36	7.b	odd	2	1	inner
161.4.c.c	✓	36	23.b	odd	2	1	inner
161.4.c.c	✓	36	161.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{9} + 2T_{2}^{8} - 57T_{2}^{7} - 87T_{2}^{6} + 1108T_{2}^{5} + 1005T_{2}^{4} - 8880T_{2}^{3} - 1572T_{2}^{2} + 25504T_{2} - 15232$ acting on $S_{4}^{\mathrm{new}}(161, [\chi])$.