Newform orbit 2700.3.p.f

• Label: 2700.3.p.f
• Level: $2700$
• Weight: $3$
• Character orbit: 2700.p
• Analytic conductor: $73.570$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2700.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(73.5696713773\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 180)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1601.1		0			0			0			0			0		−6.19003	+	10.7214i		0			0			0
1601.2		0			0			0			0			0		−5.75148	+	9.96186i		0			0			0
1601.3		0			0			0			0			0		−3.67363	+	6.36292i		0			0			0
1601.4		0			0			0			0			0		−1.36039	+	2.35627i		0			0			0
1601.5		0			0			0			0			0		−0.382345	+	0.662241i		0			0			0
1601.6		0			0			0			0			0		−0.333962	+	0.578439i		0			0			0
1601.7		0			0			0			0			0		0.333962	−	0.578439i		0			0			0
1601.8		0			0			0			0			0		0.382345	−	0.662241i		0			0			0
1601.9		0			0			0			0			0		1.36039	−	2.35627i		0			0			0
1601.10		0			0			0			0			0		3.67363	−	6.36292i		0			0			0
1601.11		0			0			0			0			0		5.75148	−	9.96186i		0			0			0
1601.12		0			0			0			0			0		6.19003	−	10.7214i		0			0			0
2501.1		0			0			0			0			0		−6.19003	−	10.7214i		0			0			0
2501.2		0			0			0			0			0		−5.75148	−	9.96186i		0			0			0
2501.3		0			0			0			0			0		−3.67363	−	6.36292i		0			0			0
2501.4		0			0			0			0			0		−1.36039	−	2.35627i		0			0			0
2501.5		0			0			0			0			0		−0.382345	−	0.662241i		0			0			0
2501.6		0			0			0			0			0		−0.333962	−	0.578439i		0			0			0
2501.7		0			0			0			0			0		0.333962	+	0.578439i		0			0			0
2501.8		0			0			0			0			0		0.382345	+	0.662241i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
9.d	odd	6	1	inner
45.h	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2700.3.p.f		24
3.b	odd	2	1		900.3.p.f		24
5.b	even	2	1	inner	2700.3.p.f		24
5.c	odd	4	2		540.3.t.a		24
9.c	even	3	1		900.3.p.f		24
9.d	odd	6	1	inner	2700.3.p.f		24
15.d	odd	2	1		900.3.p.f		24
15.e	even	4	2		180.3.t.a	✓	24
45.h	odd	6	1	inner	2700.3.p.f		24
45.j	even	6	1		900.3.p.f		24
45.k	odd	12	2		180.3.t.a	✓	24
45.k	odd	12	2		1620.3.b.b		24
45.l	even	12	2		540.3.t.a		24
45.l	even	12	2		1620.3.b.b		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
180.3.t.a	✓	24	15.e	even	4	2
180.3.t.a	✓	24	45.k	odd	12	2
540.3.t.a		24	5.c	odd	4	2
540.3.t.a		24	45.l	even	12	2
900.3.p.f		24	3.b	odd	2	1
900.3.p.f		24	9.c	even	3	1
900.3.p.f		24	15.d	odd	2	1
900.3.p.f		24	45.j	even	6	1
1620.3.b.b		24	45.k	odd	12	2
1620.3.b.b		24	45.l	even	12	2
2700.3.p.f		24	1.a	even	1	1	trivial
2700.3.p.f		24	5.b	even	2	1	inner
2700.3.p.f		24	9.d	odd	6	1	inner
2700.3.p.f		24	45.h	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^24 + 348*T7^22 + 82536*T7^20 + 10624700*T7^18 + 991303875*T7^16 + 47322913536*T7^14 + 1585750445988*T7^12 + 12635547508746*T7^10 + 78274823934825*T7^8 + 76951314990680*T7^6 + 55727495557356*T7^4 + 18411430333728*T7^2 + 4469486461456