Newform orbit 580.2.j.a

• Label: 580.2.j.a
• Level: $580$
• Weight: $2$
• Character orbit: 580.j
• Analytic conductor: $4.631$
• Analytic rank: $0$
• Dimension: $30$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.63132331723\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(15\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0			−	3.02258i		0		2.22983	−	0.166966i		0		0.186244	+	0.186244i		0		−6.13596				0
17.2		0			−	2.99066i		0		−1.63787	−	1.52229i		0		−1.61250	−	1.61250i		0		−5.94404				0
17.3		0			−	2.68138i		0		−1.12534	+	1.93226i		0		3.30434	+	3.30434i		0		−4.18982				0
17.4		0			−	2.30110i		0		0.312235	+	2.21416i		0		−2.56511	−	2.56511i		0		−2.29505				0
17.5		0			−	0.993874i		0		0.775222	−	2.09739i		0		1.61651	+	1.61651i		0		2.01221				0
17.6		0			−	0.938623i		0		−2.12400	+	0.699017i		0		0.222978	+	0.222978i		0		2.11899				0
17.7		0			−	0.548138i		0		2.23196	+	0.135478i		0		1.10894	+	1.10894i		0		2.69955				0
17.8		0				0.121921i		0		−2.20227	+	0.387294i		0		−2.56056	−	2.56056i		0		2.98514				0
17.9		0				0.357354i		0		1.56439	+	1.59771i		0		−1.34106	−	1.34106i		0		2.87230				0
17.10		0				1.57681i		0		−1.09241	−	1.95106i		0		−1.37454	−	1.37454i		0		0.513683				0
17.11		0				1.59876i		0		0.354774	+	2.20774i		0		2.73334	+	2.73334i		0		0.443956				0
17.12		0				1.61432i		0		−1.66951	−	1.48752i		0		1.96009	+	1.96009i		0		0.393986				0
17.13		0				1.94358i		0		1.60038	−	1.56166i		0		−2.43648	−	2.43648i		0		−0.777490				0
17.14		0				2.93055i		0		−0.953330	+	2.02266i		0		−1.87865	−	1.87865i		0		−5.58815				0
17.15		0				3.33306i		0		1.73594	−	1.40943i		0		2.63647	+	2.63647i		0		−8.10929				0
273.1		0			−	3.33306i		0		1.73594	+	1.40943i		0		2.63647	−	2.63647i		0		−8.10929				0
273.2		0			−	2.93055i		0		−0.953330	−	2.02266i		0		−1.87865	+	1.87865i		0		−5.58815				0
273.3		0			−	1.94358i		0		1.60038	+	1.56166i		0		−2.43648	+	2.43648i		0		−0.777490				0
273.4		0			−	1.61432i		0		−1.66951	+	1.48752i		0		1.96009	−	1.96009i		0		0.393986				0
273.5		0			−	1.59876i		0		0.354774	−	2.20774i		0		2.73334	−	2.73334i		0		0.443956				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
145.j	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	580.2.j.a	✓	30
5.b	even	2	1		2900.2.j.d		30
5.c	odd	4	1		580.2.s.a	yes	30
5.c	odd	4	1		2900.2.s.d		30
29.c	odd	4	1		580.2.s.a	yes	30
145.e	even	4	1		2900.2.j.d		30
145.f	odd	4	1		2900.2.s.d		30
145.j	even	4	1	inner	580.2.j.a	✓	30

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
580.2.j.a	✓	30	1.a	even	1	1	trivial
580.2.j.a	✓	30	145.j	even	4	1	inner
580.2.s.a	yes	30	5.c	odd	4	1
580.2.s.a	yes	30	29.c	odd	4	1
2900.2.j.d		30	5.b	even	2	1
2900.2.j.d		30	145.e	even	4	1
2900.2.s.d		30	5.c	odd	4	1
2900.2.s.d		30	145.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(580, [\chi])\).