Newform orbit 1764.2.j.i

• Label: 1764.2.j.i
• Level: $1764$
• Weight: $2$
• Character orbit: 1764.j
• Analytic conductor: $14.086$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.0856109166\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
589.1		0		−1.72754	+	0.124883i		0		−1.73981	+	3.01343i		0			0			0		2.96881	−	0.431481i		0
589.2		0		−1.69569	+	0.353059i		0		0.469227	−	0.812725i		0			0			0		2.75070	−	1.19736i		0
589.3		0		−1.47192	−	0.912932i		0		1.94623	−	3.37097i		0			0			0		1.33311	+	2.68753i		0
589.4		0		−1.05155	+	1.37631i		0		0.736933	−	1.27640i		0			0			0		−0.788484	−	2.89453i		0
589.5		0		−0.899846	−	1.47996i		0		1.19243	−	2.06535i		0			0			0		−1.38055	+	2.66347i		0
589.6		0		−0.241270	+	1.71516i		0		−0.0111913	+	0.0193839i		0			0			0		−2.88358	−	0.827636i		0
589.7		0		0.241270	−	1.71516i		0		0.0111913	−	0.0193839i		0			0			0		−2.88358	−	0.827636i		0
589.8		0		0.899846	+	1.47996i		0		−1.19243	+	2.06535i		0			0			0		−1.38055	+	2.66347i		0
589.9		0		1.05155	−	1.37631i		0		−0.736933	+	1.27640i		0			0			0		−0.788484	−	2.89453i		0
589.10		0		1.47192	+	0.912932i		0		−1.94623	+	3.37097i		0			0			0		1.33311	+	2.68753i		0
589.11		0		1.69569	−	0.353059i		0		−0.469227	+	0.812725i		0			0			0		2.75070	−	1.19736i		0
589.12		0		1.72754	−	0.124883i		0		1.73981	−	3.01343i		0			0			0		2.96881	−	0.431481i		0
1177.1		0		−1.72754	−	0.124883i		0		−1.73981	−	3.01343i		0			0			0		2.96881	+	0.431481i		0
1177.2		0		−1.69569	−	0.353059i		0		0.469227	+	0.812725i		0			0			0		2.75070	+	1.19736i		0
1177.3		0		−1.47192	+	0.912932i		0		1.94623	+	3.37097i		0			0			0		1.33311	−	2.68753i		0
1177.4		0		−1.05155	−	1.37631i		0		0.736933	+	1.27640i		0			0			0		−0.788484	+	2.89453i		0
1177.5		0		−0.899846	+	1.47996i		0		1.19243	+	2.06535i		0			0			0		−1.38055	−	2.66347i		0
1177.6		0		−0.241270	−	1.71516i		0		−0.0111913	−	0.0193839i		0			0			0		−2.88358	+	0.827636i		0
1177.7		0		0.241270	+	1.71516i		0		0.0111913	+	0.0193839i		0			0			0		−2.88358	+	0.827636i		0
1177.8		0		0.899846	−	1.47996i		0		−1.19243	−	2.06535i		0			0			0		−1.38055	−	2.66347i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
9.c	even	3	1	inner
63.l	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1764.2.j.i	✓	24
3.b	odd	2	1		5292.2.j.i		24
7.b	odd	2	1	inner	1764.2.j.i	✓	24
7.c	even	3	1		1764.2.i.j		24
7.c	even	3	1		1764.2.l.j		24
7.d	odd	6	1		1764.2.i.j		24
7.d	odd	6	1		1764.2.l.j		24
9.c	even	3	1	inner	1764.2.j.i	✓	24
9.d	odd	6	1		5292.2.j.i		24
21.c	even	2	1		5292.2.j.i		24
21.g	even	6	1		5292.2.i.j		24
21.g	even	6	1		5292.2.l.j		24
21.h	odd	6	1		5292.2.i.j		24
21.h	odd	6	1		5292.2.l.j		24
63.g	even	3	1		1764.2.i.j		24
63.h	even	3	1		1764.2.l.j		24
63.i	even	6	1		5292.2.l.j		24
63.j	odd	6	1		5292.2.l.j		24
63.k	odd	6	1		1764.2.i.j		24
63.l	odd	6	1	inner	1764.2.j.i	✓	24
63.n	odd	6	1		5292.2.i.j		24
63.o	even	6	1		5292.2.j.i		24
63.s	even	6	1		5292.2.i.j		24
63.t	odd	6	1		1764.2.l.j		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1764.2.i.j		24	7.c	even	3	1
1764.2.i.j		24	7.d	odd	6	1
1764.2.i.j		24	63.g	even	3	1
1764.2.i.j		24	63.k	odd	6	1
1764.2.j.i	✓	24	1.a	even	1	1	trivial
1764.2.j.i	✓	24	7.b	odd	2	1	inner
1764.2.j.i	✓	24	9.c	even	3	1	inner
1764.2.j.i	✓	24	63.l	odd	6	1	inner
1764.2.l.j		24	7.c	even	3	1
1764.2.l.j		24	7.d	odd	6	1
1764.2.l.j		24	63.h	even	3	1
1764.2.l.j		24	63.t	odd	6	1
5292.2.i.j		24	21.g	even	6	1
5292.2.i.j		24	21.h	odd	6	1
5292.2.i.j		24	63.n	odd	6	1
5292.2.i.j		24	63.s	even	6	1
5292.2.j.i		24	3.b	odd	2	1
5292.2.j.i		24	9.d	odd	6	1
5292.2.j.i		24	21.c	even	2	1
5292.2.j.i		24	63.o	even	6	1
5292.2.l.j		24	21.g	even	6	1
5292.2.l.j		24	21.h	odd	6	1
5292.2.l.j		24	63.i	even	6	1
5292.2.l.j		24	63.j	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 36*T5^22 + 855*T5^20 + 11596*T5^18 + 113607*T5^16 + 669690*T5^14 + 2816880*T5^12 + 6442560*T5^10 + 10423395*T5^8 + 7656052*T5^6 + 3988170*T5^4 + 1998*T5^2 + 1