Newform orbit 2700.3.u.d

• Label: 2700.3.u.d
• Level: $2700$
• Weight: $3$
• Character orbit: 2700.u
• Analytic conductor: $73.570$
• Analytic rank: $0$
• Dimension: $32$
• 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.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(73.5696713773\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 900)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
449.1		0			0			0			0			0		−9.36178	+	5.40503i		0			0			0
449.2		0			0			0			0			0		−8.59526	+	4.96248i		0			0			0
449.3		0			0			0			0			0		−8.13249	+	4.69530i		0			0			0
449.4		0			0			0			0			0		−7.15437	+	4.13058i		0			0			0
449.5		0			0			0			0			0		−4.69840	+	2.71262i		0			0			0
449.6		0			0			0			0			0		−4.03103	+	2.32731i		0			0			0
449.7		0			0			0			0			0		−3.00081	+	1.73252i		0			0			0
449.8		0			0			0			0			0		−1.25581	+	0.725042i		0			0			0
449.9		0			0			0			0			0		1.25581	−	0.725042i		0			0			0
449.10		0			0			0			0			0		3.00081	−	1.73252i		0			0			0
449.11		0			0			0			0			0		4.03103	−	2.32731i		0			0			0
449.12		0			0			0			0			0		4.69840	−	2.71262i		0			0			0
449.13		0			0			0			0			0		7.15437	−	4.13058i		0			0			0
449.14		0			0			0			0			0		8.13249	−	4.69530i		0			0			0
449.15		0			0			0			0			0		8.59526	−	4.96248i		0			0			0
449.16		0			0			0			0			0		9.36178	−	5.40503i		0			0			0
2249.1		0			0			0			0			0		−9.36178	−	5.40503i		0			0			0
2249.2		0			0			0			0			0		−8.59526	−	4.96248i		0			0			0
2249.3		0			0			0			0			0		−8.13249	−	4.69530i		0			0			0
2249.4		0			0			0			0			0		−7.15437	−	4.13058i		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.u.d		32
3.b	odd	2	1		900.3.u.d		32
5.b	even	2	1	inner	2700.3.u.d		32
5.c	odd	4	1		2700.3.p.d		16
5.c	odd	4	1		2700.3.p.e		16
9.c	even	3	1		900.3.u.d		32
9.d	odd	6	1	inner	2700.3.u.d		32
15.d	odd	2	1		900.3.u.d		32
15.e	even	4	1		900.3.p.d	✓	16
15.e	even	4	1		900.3.p.e	yes	16
45.h	odd	6	1	inner	2700.3.u.d		32
45.j	even	6	1		900.3.u.d		32
45.k	odd	12	1		900.3.p.d	✓	16
45.k	odd	12	1		900.3.p.e	yes	16
45.l	even	12	1		2700.3.p.d		16
45.l	even	12	1		2700.3.p.e		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.3.p.d	✓	16	15.e	even	4	1
900.3.p.d	✓	16	45.k	odd	12	1
900.3.p.e	yes	16	15.e	even	4	1
900.3.p.e	yes	16	45.k	odd	12	1
900.3.u.d		32	3.b	odd	2	1
900.3.u.d		32	9.c	even	3	1
900.3.u.d		32	15.d	odd	2	1
900.3.u.d		32	45.j	even	6	1
2700.3.p.d		16	5.c	odd	4	1
2700.3.p.d		16	45.l	even	12	1
2700.3.p.e		16	5.c	odd	4	1
2700.3.p.e		16	45.l	even	12	1
2700.3.u.d		32	1.a	even	1	1	trivial
2700.3.u.d		32	5.b	even	2	1	inner
2700.3.u.d		32	9.d	odd	6	1	inner
2700.3.u.d		32	45.h	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^32 - 437*T7^30 + 114123*T7^28 - 19658878*T7^26 + 2517239723*T7^24 - 241948830138*T7^22 + 18055201883038*T7^20 - 1030268011855988*T7^18 + 45464366553053913*T7^16 - 1498817739106580588*T7^14 + 37550355864057189508*T7^12 - 680348466299470190568*T7^10 + 9021186806266571621168*T7^8 - 77199096237971459245168*T7^6 + 438059165420792867917008*T7^4 - 850433328472662340357952*T7^2 + 1243886322563271483986176