Newform orbit 140.4.c.b

• Label: 140.4.c.b
• Level: $140$
• Weight: $4$
• Character orbit: 140.c
• Analytic conductor: $8.260$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	140.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.26026740080\)
Analytic rank:	\(0\)
Dimension:	\(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 36 q^{4} - 616 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−2.72523	−	0.757045i		−	5.87136i	6.85377	+	4.12624i	−7.09042	+	8.64442i	−4.44488	+	16.0008i	17.7914	−	5.14452i	−15.5543	−	16.4336i	−7.47290			25.8672	−	18.1903i
139.2	−2.72523	−	0.757045i			5.87136i	6.85377	+	4.12624i	7.09042	−	8.64442i	4.44488	−	16.0008i	17.7914	+	5.14452i	−15.5543	−	16.4336i	−7.47290			−25.8672	+	18.1903i
139.3	−2.72523	+	0.757045i		−	5.87136i	6.85377	−	4.12624i	7.09042	+	8.64442i	4.44488	+	16.0008i	17.7914	−	5.14452i	−15.5543	+	16.4336i	−7.47290			−25.8672	−	18.1903i
139.4	−2.72523	+	0.757045i			5.87136i	6.85377	−	4.12624i	−7.09042	−	8.64442i	−4.44488	−	16.0008i	17.7914	+	5.14452i	−15.5543	+	16.4336i	−7.47290			25.8672	+	18.1903i
139.5	−2.57257	−	1.17553i		−	2.89403i	5.23628	+	6.04825i	−10.0191	−	4.96158i	−3.40200	+	7.44510i	−3.85882	+	18.1138i	−6.36085	−	21.7150i	18.6246			19.9425	+	24.5418i
139.6	−2.57257	−	1.17553i			2.89403i	5.23628	+	6.04825i	10.0191	+	4.96158i	3.40200	−	7.44510i	−3.85882	−	18.1138i	−6.36085	−	21.7150i	18.6246			−19.9425	−	24.5418i
139.7	−2.57257	+	1.17553i		−	2.89403i	5.23628	−	6.04825i	10.0191	−	4.96158i	3.40200	+	7.44510i	−3.85882	+	18.1138i	−6.36085	+	21.7150i	18.6246			−19.9425	+	24.5418i
139.8	−2.57257	+	1.17553i			2.89403i	5.23628	−	6.04825i	−10.0191	+	4.96158i	−3.40200	−	7.44510i	−3.85882	−	18.1138i	−6.36085	+	21.7150i	18.6246			19.9425	−	24.5418i
139.9	−2.57205	−	1.17668i		−	9.04401i	5.23084	+	6.05296i	10.8006	+	2.88919i	−10.6419	+	23.2616i	−18.0011	+	4.35430i	−6.33156	−	21.7235i	−54.7941			−24.3799	−	20.1400i
139.10	−2.57205	−	1.17668i			9.04401i	5.23084	+	6.05296i	−10.8006	−	2.88919i	10.6419	−	23.2616i	−18.0011	−	4.35430i	−6.33156	−	21.7235i	−54.7941			24.3799	+	20.1400i
139.11	−2.57205	+	1.17668i		−	9.04401i	5.23084	−	6.05296i	−10.8006	+	2.88919i	10.6419	+	23.2616i	−18.0011	+	4.35430i	−6.33156	+	21.7235i	−54.7941			24.3799	−	20.1400i
139.12	−2.57205	+	1.17668i			9.04401i	5.23084	−	6.05296i	10.8006	−	2.88919i	−10.6419	−	23.2616i	−18.0011	−	4.35430i	−6.33156	+	21.7235i	−54.7941			−24.3799	+	20.1400i
139.13	−1.95963	−	2.03957i		−	4.50506i	−0.319725	+	7.99361i	9.17326	−	6.39150i	−9.18840	+	8.82823i	16.5451	+	8.32223i	16.9301	−	15.0124i	6.70447			−31.0121	−	6.18459i
139.14	−1.95963	−	2.03957i			4.50506i	−0.319725	+	7.99361i	−9.17326	+	6.39150i	9.18840	−	8.82823i	16.5451	−	8.32223i	16.9301	−	15.0124i	6.70447			31.0121	+	6.18459i
139.15	−1.95963	+	2.03957i		−	4.50506i	−0.319725	−	7.99361i	−9.17326	−	6.39150i	9.18840	+	8.82823i	16.5451	+	8.32223i	16.9301	+	15.0124i	6.70447			31.0121	−	6.18459i
139.16	−1.95963	+	2.03957i			4.50506i	−0.319725	−	7.99361i	9.17326	+	6.39150i	−9.18840	−	8.82823i	16.5451	−	8.32223i	16.9301	+	15.0124i	6.70447			−31.0121	+	6.18459i
139.17	−1.55248	−	2.36427i		−	8.63759i	−3.17959	+	7.34099i	−7.85914	−	7.95197i	−20.4216	+	13.4097i	4.27322	−	18.0205i	22.2924	−	3.87934i	−47.6079			−6.59946	+	30.9265i
139.18	−1.55248	−	2.36427i			8.63759i	−3.17959	+	7.34099i	7.85914	+	7.95197i	20.4216	−	13.4097i	4.27322	+	18.0205i	22.2924	−	3.87934i	−47.6079			6.59946	−	30.9265i
139.19	−1.55248	+	2.36427i		−	8.63759i	−3.17959	−	7.34099i	7.85914	−	7.95197i	20.4216	+	13.4097i	4.27322	−	18.0205i	22.2924	+	3.87934i	−47.6079			6.59946	+	30.9265i
139.20	−1.55248	+	2.36427i			8.63759i	−3.17959	−	7.34099i	−7.85914	+	7.95197i	−20.4216	−	13.4097i	4.27322	+	18.0205i	22.2924	+	3.87934i	−47.6079			−6.59946	−	30.9265i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
7.b	odd	2	1	inner
20.d	odd	2	1	inner
28.d	even	2	1	inner
35.c	odd	2	1	inner
140.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	140.4.c.b	✓	64
4.b	odd	2	1	inner	140.4.c.b	✓	64
5.b	even	2	1	inner	140.4.c.b	✓	64
7.b	odd	2	1	inner	140.4.c.b	✓	64
20.d	odd	2	1	inner	140.4.c.b	✓	64
28.d	even	2	1	inner	140.4.c.b	✓	64
35.c	odd	2	1	inner	140.4.c.b	✓	64
140.c	even	2	1	inner	140.4.c.b	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.4.c.b	✓	64	1.a	even	1	1	trivial
140.4.c.b	✓	64	4.b	odd	2	1	inner
140.4.c.b	✓	64	5.b	even	2	1	inner
140.4.c.b	✓	64	7.b	odd	2	1	inner
140.4.c.b	✓	64	20.d	odd	2	1	inner
140.4.c.b	✓	64	28.d	even	2	1	inner
140.4.c.b	✓	64	35.c	odd	2	1	inner
140.4.c.b	✓	64	140.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^16 + 293*T3^14 + 33995*T3^12 + 1993751*T3^10 + 63000376*T3^8 + 1074903088*T3^6 + 9597221440*T3^4 + 41891797136*T3^2 + 70412888000