Newform orbit 833.2.j.e

• Label: 833.2.j.e
• Level: $833$
• Weight: $2$
• Character orbit: 833.j
• Analytic conductor: $6.652$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.65153848837\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	−1.17642	−	2.03762i	−1.71513	−	0.990229i	−1.76793	+	3.06215i	1.84854	−	1.06726i			4.65970i		0		3.61366			0.461105	+	0.798658i	−4.34934	−	2.51109i
67.2	−1.17642	−	2.03762i	−1.71513	−	0.990229i	−1.76793	+	3.06215i	1.84854	−	1.06726i			4.65970i		0		3.61366			0.461105	+	0.798658i	−4.34934	−	2.51109i
67.3	−1.17642	−	2.03762i	1.71513	+	0.990229i	−1.76793	+	3.06215i	−1.84854	+	1.06726i		−	4.65970i		0		3.61366			0.461105	+	0.798658i	4.34934	+	2.51109i
67.4	−1.17642	−	2.03762i	1.71513	+	0.990229i	−1.76793	+	3.06215i	−1.84854	+	1.06726i		−	4.65970i		0		3.61366			0.461105	+	0.798658i	4.34934	+	2.51109i
67.5	−0.580136	−	1.00483i	−2.19522	−	1.26741i	0.326884	−	0.566179i	−3.12891	+	1.80647i			2.94109i		0		−3.07909			1.71266	+	2.96642i	3.63038	+	2.09600i
67.6	−0.580136	−	1.00483i	−2.19522	−	1.26741i	0.326884	−	0.566179i	−3.12891	+	1.80647i			2.94109i		0		−3.07909			1.71266	+	2.96642i	3.63038	+	2.09600i
67.7	−0.580136	−	1.00483i	2.19522	+	1.26741i	0.326884	−	0.566179i	3.12891	−	1.80647i		−	2.94109i		0		−3.07909			1.71266	+	2.96642i	−3.63038	−	2.09600i
67.8	−0.580136	−	1.00483i	2.19522	+	1.26741i	0.326884	−	0.566179i	3.12891	−	1.80647i		−	2.94109i		0		−3.07909			1.71266	+	2.96642i	−3.63038	−	2.09600i
67.9	0.281864	+	0.488204i	−0.426048	−	0.245979i	0.841105	−	1.45684i	2.02713	−	1.17036i		−	0.277331i		0		2.07577			−1.37899	−	2.38848i	1.14275	+	0.659767i
67.10	0.281864	+	0.488204i	−0.426048	−	0.245979i	0.841105	−	1.45684i	2.02713	−	1.17036i		−	0.277331i		0		2.07577			−1.37899	−	2.38848i	1.14275	+	0.659767i
67.11	0.281864	+	0.488204i	0.426048	+	0.245979i	0.841105	−	1.45684i	−2.02713	+	1.17036i			0.277331i		0		2.07577			−1.37899	−	2.38848i	−1.14275	−	0.659767i
67.12	0.281864	+	0.488204i	0.426048	+	0.245979i	0.841105	−	1.45684i	−2.02713	+	1.17036i			0.277331i		0		2.07577			−1.37899	−	2.38848i	−1.14275	−	0.659767i
67.13	0.974693	+	1.68822i	−2.01441	−	1.16302i	−0.900054	+	1.55894i	−0.826794	+	0.477350i		−	4.53434i		0		0.389667			1.20522	+	2.08750i	−1.61174	−	0.930540i
67.14	0.974693	+	1.68822i	−2.01441	−	1.16302i	−0.900054	+	1.55894i	−0.826794	+	0.477350i		−	4.53434i		0		0.389667			1.20522	+	2.08750i	−1.61174	−	0.930540i
67.15	0.974693	+	1.68822i	2.01441	+	1.16302i	−0.900054	+	1.55894i	0.826794	−	0.477350i			4.53434i		0		0.389667			1.20522	+	2.08750i	1.61174	+	0.930540i
67.16	0.974693	+	1.68822i	2.01441	+	1.16302i	−0.900054	+	1.55894i	0.826794	−	0.477350i			4.53434i		0		0.389667			1.20522	+	2.08750i	1.61174	+	0.930540i
373.1	−1.17642	+	2.03762i	−1.71513	+	0.990229i	−1.76793	−	3.06215i	1.84854	+	1.06726i		−	4.65970i		0		3.61366			0.461105	−	0.798658i	−4.34934	+	2.51109i
373.2	−1.17642	+	2.03762i	−1.71513	+	0.990229i	−1.76793	−	3.06215i	1.84854	+	1.06726i		−	4.65970i		0		3.61366			0.461105	−	0.798658i	−4.34934	+	2.51109i
373.3	−1.17642	+	2.03762i	1.71513	−	0.990229i	−1.76793	−	3.06215i	−1.84854	−	1.06726i			4.65970i		0		3.61366			0.461105	−	0.798658i	4.34934	−	2.51109i
373.4	−1.17642	+	2.03762i	1.71513	−	0.990229i	−1.76793	−	3.06215i	−1.84854	−	1.06726i			4.65970i		0		3.61366			0.461105	−	0.798658i	4.34934	−	2.51109i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
7.c	even	3	1	inner
7.d	odd	6	1	inner
17.b	even	2	1	inner
119.d	odd	2	1	inner
119.h	odd	6	1	inner
119.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	833.2.j.e		32
7.b	odd	2	1	inner	833.2.j.e		32
7.c	even	3	1		833.2.b.e	✓	16
7.c	even	3	1	inner	833.2.j.e		32
7.d	odd	6	1		833.2.b.e	✓	16
7.d	odd	6	1	inner	833.2.j.e		32
17.b	even	2	1	inner	833.2.j.e		32
119.d	odd	2	1	inner	833.2.j.e		32
119.h	odd	6	1		833.2.b.e	✓	16
119.h	odd	6	1	inner	833.2.j.e		32
119.j	even	6	1		833.2.b.e	✓	16
119.j	even	6	1	inner	833.2.j.e		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
833.2.b.e	✓	16	7.c	even	3	1
833.2.b.e	✓	16	7.d	odd	6	1
833.2.b.e	✓	16	119.h	odd	6	1
833.2.b.e	✓	16	119.j	even	6	1
833.2.j.e		32	1.a	even	1	1	trivial
833.2.j.e		32	7.b	odd	2	1	inner
833.2.j.e		32	7.c	even	3	1	inner
833.2.j.e		32	7.d	odd	6	1	inner
833.2.j.e		32	17.b	even	2	1	inner
833.2.j.e		32	119.d	odd	2	1	inner
833.2.j.e		32	119.h	odd	6	1	inner
833.2.j.e		32	119.j	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{8} + T_{2}^{7} + 6T_{2}^{6} + T_{2}^{5} + 25T_{2}^{4} + 9T_{2}^{3} + 24T_{2}^{2} - 9T_{2} + 9 \)

\( T_{13}^{8} - 50T_{13}^{6} + 600T_{13}^{4} - 1472T_{13}^{2} + 784 \)