Newform orbit 540.3.t.a

• Label: 540.3.t.a
• Level: $540$
• Weight: $3$
• Character orbit: 540.t
• Analytic conductor: $14.714$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	540.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7139342755\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 9 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1		0			0			0		−4.95655	+	0.657734i		0		−0.662241	−	0.382345i		0			0			0
89.2		0			0			0		−4.40486	−	2.36585i		0		2.35627	+	1.36039i		0			0			0
89.3		0			0			0		−3.29926	−	3.75697i		0		−6.36292	−	3.67363i		0			0			0
89.4		0			0			0		−3.04789	+	3.96363i		0		0.662241	+	0.382345i		0			0			0
89.5		0			0			0		−1.19554	−	4.85497i		0		10.7214	+	6.19003i		0			0			0
89.6		0			0			0		−0.153546	+	4.99764i		0		−2.35627	−	1.36039i		0			0			0
89.7		0			0			0		1.60400	+	4.73573i		0		6.36292	+	3.67363i		0			0			0
89.8		0			0			0		2.98105	−	4.01414i		0		−0.578439	−	0.333962i		0			0			0
89.9		0			0			0		3.59000	−	3.48021i		0		−9.96186	−	5.75148i		0			0			0
89.10		0			0			0		3.60676	+	3.46285i		0		−10.7214	−	6.19003i		0			0			0
89.11		0			0			0		4.80895	−	1.36893i		0		9.96186	+	5.75148i		0			0			0
89.12		0			0			0		4.96687	−	0.574598i		0		0.578439	+	0.333962i		0			0			0
449.1		0			0			0		−4.95655	−	0.657734i		0		−0.662241	+	0.382345i		0			0			0
449.2		0			0			0		−4.40486	+	2.36585i		0		2.35627	−	1.36039i		0			0			0
449.3		0			0			0		−3.29926	+	3.75697i		0		−6.36292	+	3.67363i		0			0			0
449.4		0			0			0		−3.04789	−	3.96363i		0		0.662241	−	0.382345i		0			0			0
449.5		0			0			0		−1.19554	+	4.85497i		0		10.7214	−	6.19003i		0			0			0
449.6		0			0			0		−0.153546	−	4.99764i		0		−2.35627	+	1.36039i		0			0			0
449.7		0			0			0		1.60400	−	4.73573i		0		6.36292	−	3.67363i		0			0			0
449.8		0			0			0		2.98105	+	4.01414i		0		−0.578439	+	0.333962i		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	540.3.t.a		24
3.b	odd	2	1		180.3.t.a	✓	24
5.b	even	2	1	inner	540.3.t.a		24
5.c	odd	4	2		2700.3.p.f		24
9.c	even	3	1		180.3.t.a	✓	24
9.c	even	3	1		1620.3.b.b		24
9.d	odd	6	1	inner	540.3.t.a		24
9.d	odd	6	1		1620.3.b.b		24
15.d	odd	2	1		180.3.t.a	✓	24
15.e	even	4	2		900.3.p.f		24
45.h	odd	6	1	inner	540.3.t.a		24
45.h	odd	6	1		1620.3.b.b		24
45.j	even	6	1		180.3.t.a	✓	24
45.j	even	6	1		1620.3.b.b		24
45.k	odd	12	2		900.3.p.f		24
45.l	even	12	2		2700.3.p.f		24

    

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

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(540, [\chi])\).