Newform orbit 720.2.cu.d

• Label: 720.2.cu.d
• Level: $720$
• Weight: $2$
• Character orbit: 720.cu
• Analytic conductor: $5.749$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.74922894553\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{3}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
113.1		0		−1.67566	−	0.438358i		0		−1.22927	+	1.86786i		0		−1.08311	−	0.290218i		0		2.61569	+	1.46908i		0
113.2		0		−0.341771	+	1.69800i		0		1.98584	+	1.02783i		0		−0.616053	−	0.165071i		0		−2.76639	−	1.16065i		0
113.3		0		−0.318010	−	1.70261i		0		2.13582	−	0.662020i		0		−0.941955	−	0.252396i		0		−2.79774	+	1.08289i		0
113.4		0		0.655337	+	1.60329i		0		−2.00484	−	0.990270i		0		3.36603	+	0.901926i		0		−2.14107	+	2.10139i		0
113.5		0		1.38294	−	1.04282i		0		−0.579537	+	2.15966i		0		3.90075	+	1.04520i		0		0.825048	−	2.88432i		0
113.6		0		1.66319	−	0.483525i		0		−1.17404	−	1.90306i		0		−4.62566	−	1.23944i		0		2.53241	−	1.60839i		0
257.1		0		−1.70261	+	0.318010i		0		0.494584	+	2.18068i		0		0.252396	−	0.941955i		0		2.79774	−	1.08289i		0
257.2		0		−1.04282	−	1.38294i		0		1.58055	−	1.58172i		0		−1.04520	+	3.90075i		0		−0.825048	+	2.88432i		0
257.3		0		−0.483525	−	1.66319i		0		−2.23512	−	0.0652184i		0		1.23944	−	4.62566i		0		−2.53241	+	1.60839i		0
257.4		0		−0.438358	+	1.67566i		0		1.00297	−	1.99851i		0		0.290218	−	1.08311i		0		−2.61569	−	1.46908i		0
257.5		0		1.60329	−	0.655337i		0		−1.86002	−	1.24110i		0		−0.901926	+	3.36603i		0		2.14107	−	2.10139i		0
257.6		0		1.69800	+	0.341771i		0		1.88305	+	1.20587i		0		0.165071	−	0.616053i		0		2.76639	+	1.16065i		0
353.1		0		−1.70261	−	0.318010i		0		0.494584	−	2.18068i		0		0.252396	+	0.941955i		0		2.79774	+	1.08289i		0
353.2		0		−1.04282	+	1.38294i		0		1.58055	+	1.58172i		0		−1.04520	−	3.90075i		0		−0.825048	−	2.88432i		0
353.3		0		−0.483525	+	1.66319i		0		−2.23512	+	0.0652184i		0		1.23944	+	4.62566i		0		−2.53241	−	1.60839i		0
353.4		0		−0.438358	−	1.67566i		0		1.00297	+	1.99851i		0		0.290218	+	1.08311i		0		−2.61569	+	1.46908i		0
353.5		0		1.60329	+	0.655337i		0		−1.86002	+	1.24110i		0		−0.901926	−	3.36603i		0		2.14107	+	2.10139i		0
353.6		0		1.69800	−	0.341771i		0		1.88305	−	1.20587i		0		0.165071	+	0.616053i		0		2.76639	−	1.16065i		0
497.1		0		−1.67566	+	0.438358i		0		−1.22927	−	1.86786i		0		−1.08311	+	0.290218i		0		2.61569	−	1.46908i		0
497.2		0		−0.341771	−	1.69800i		0		1.98584	−	1.02783i		0		−0.616053	+	0.165071i		0		−2.76639	+	1.16065i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
9.d	odd	6	1	inner
45.l	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	720.2.cu.d		24
4.b	odd	2	1		180.2.w.a	✓	24
5.c	odd	4	1	inner	720.2.cu.d		24
9.d	odd	6	1	inner	720.2.cu.d		24
12.b	even	2	1		540.2.x.a		24
20.d	odd	2	1		900.2.be.e		24
20.e	even	4	1		180.2.w.a	✓	24
20.e	even	4	1		900.2.be.e		24
36.f	odd	6	1		540.2.x.a		24
36.f	odd	6	1		1620.2.j.b		24
36.h	even	6	1		180.2.w.a	✓	24
36.h	even	6	1		1620.2.j.b		24
45.l	even	12	1	inner	720.2.cu.d		24
60.h	even	2	1		2700.2.bf.e		24
60.l	odd	4	1		540.2.x.a		24
60.l	odd	4	1		2700.2.bf.e		24
180.n	even	6	1		900.2.be.e		24
180.p	odd	6	1		2700.2.bf.e		24
180.v	odd	12	1		180.2.w.a	✓	24
180.v	odd	12	1		900.2.be.e		24
180.v	odd	12	1		1620.2.j.b		24
180.x	even	12	1		540.2.x.a		24
180.x	even	12	1		1620.2.j.b		24
180.x	even	12	1		2700.2.bf.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
180.2.w.a	✓	24	4.b	odd	2	1
180.2.w.a	✓	24	20.e	even	4	1
180.2.w.a	✓	24	36.h	even	6	1
180.2.w.a	✓	24	180.v	odd	12	1
540.2.x.a		24	12.b	even	2	1
540.2.x.a		24	36.f	odd	6	1
540.2.x.a		24	60.l	odd	4	1
540.2.x.a		24	180.x	even	12	1
720.2.cu.d		24	1.a	even	1	1	trivial
720.2.cu.d		24	5.c	odd	4	1	inner
720.2.cu.d		24	9.d	odd	6	1	inner
720.2.cu.d		24	45.l	even	12	1	inner
900.2.be.e		24	20.d	odd	2	1
900.2.be.e		24	20.e	even	4	1
900.2.be.e		24	180.n	even	6	1
900.2.be.e		24	180.v	odd	12	1
1620.2.j.b		24	36.f	odd	6	1
1620.2.j.b		24	36.h	even	6	1
1620.2.j.b		24	180.v	odd	12	1
1620.2.j.b		24	180.x	even	12	1
2700.2.bf.e		24	60.h	even	2	1
2700.2.bf.e		24	60.l	odd	4	1
2700.2.bf.e		24	180.p	odd	6	1
2700.2.bf.e		24	180.x	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^24 + 4*T7^21 - 471*T7^20 - 264*T7^19 + 8*T7^18 + 4986*T7^17 + 202134*T7^16 - 178328*T7^15 + 58560*T7^14 - 5613192*T7^13 - 7571879*T7^12 + 22809384*T7^11 + 63020610*T7^10 + 112421534*T7^9 + 201505854*T7^8 + 255768048*T7^7 + 247386542*T7^6 + 229763292*T7^5 + 177385569*T7^4 + 98365172*T7^3 + 48708450*T7^2 + 21802830*T7 + 4879681