Newform orbit 140.6.u.a

• Label: 140.6.u.a
• Level: $140$
• Weight: $6$
• Character orbit: 140.u
• Analytic conductor: $22.454$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	140.u (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.4537347738\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(20\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 66 q^{5} + 42 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−28.6620	+	7.67995i		0		−13.6014	−	54.2218i		0		50.0114	+	119.607i		0		552.082	−	318.745i		0
17.2		0		−24.6561	+	6.60658i		0		−19.7185	+	52.3085i		0		64.2899	−	112.578i		0		353.832	−	204.285i		0
17.3		0		−22.2853	+	5.97133i		0		53.5816	+	15.9377i		0		−117.100	−	55.6299i		0		250.534	−	144.646i		0
17.4		0		−20.9799	+	5.62155i		0		51.4012	+	21.9754i		0		57.9611	+	115.963i		0		198.110	−	114.379i		0
17.5		0		−18.3680	+	4.92170i		0		−39.4305	−	39.6262i		0		−96.7282	−	86.3172i		0		102.718	−	59.3042i		0
17.6		0		−12.9666	+	3.47439i		0		−44.5380	+	33.7842i		0		−38.3124	+	123.851i		0		−54.3827	+	31.3979i		0
17.7		0		−10.6528	+	2.85441i		0		34.5582	−	43.9401i		0		103.391	−	78.2127i		0		−105.110	+	60.6851i		0
17.8		0		−6.20483	+	1.66258i		0		−55.5692	−	6.08830i		0		125.167	−	33.7685i		0		−174.708	+	100.868i		0
17.9		0		−4.43646	+	1.18874i		0		28.2223	−	48.2546i		0		−123.898	+	38.1621i		0		−192.175	+	110.952i		0
17.10		0		−1.99232	+	0.533841i		0		6.14036	+	55.5634i		0		−128.841	+	14.3832i		0		−206.760	+	119.373i		0
17.11		0		2.31849	−	0.621237i		0		48.7507	+	27.3563i		0		106.437	+	74.0153i		0		−205.455	+	118.619i		0
17.12		0		5.29788	−	1.41956i		0		7.00534	+	55.4610i		0		19.4867	−	128.169i		0		−184.392	+	106.459i		0
17.13		0		10.1216	−	2.71208i		0		−37.9182	−	41.0757i		0		41.6858	+	122.757i		0		−115.352	+	66.5987i		0
17.14		0		10.7276	−	2.87444i		0		15.7664	−	53.6323i		0		−49.9716	+	119.624i		0		−103.626	+	59.8284i		0
17.15		0		11.3735	−	3.04752i		0		−52.9864	−	17.8170i		0		−77.0457	−	104.264i		0		−90.3752	+	52.1781i		0
17.16		0		15.9912	−	4.28483i		0		55.2109	−	8.76112i		0		−43.0553	−	122.283i		0		26.9144	−	15.5391i		0
17.17		0		20.8037	−	5.57433i		0		−24.0852	+	50.4470i		0		124.416	+	36.4360i		0		191.276	−	110.434i		0
17.18		0		23.8722	−	6.39654i		0		−47.9860	+	28.6765i		0		−128.825	+	14.5325i		0		318.523	−	183.899i		0
17.19		0		25.2191	−	6.75744i		0		52.8316	+	18.2707i		0		−69.8174	+	109.236i		0		379.897	−	219.334i		0
17.20		0		25.4790	−	6.82708i		0		−1.13527	−	55.8902i		0		107.244	−	72.8407i		0		392.127	−	226.395i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.d	odd	6	1	inner
35.k	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	140.6.u.a	✓	80
5.c	odd	4	1	inner	140.6.u.a	✓	80
7.d	odd	6	1	inner	140.6.u.a	✓	80
35.k	even	12	1	inner	140.6.u.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.6.u.a	✓	80	1.a	even	1	1	trivial
140.6.u.a	✓	80	5.c	odd	4	1	inner
140.6.u.a	✓	80	7.d	odd	6	1	inner
140.6.u.a	✓	80	35.k	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(140, [\chi])\).