Newform orbit 520.2.g.a

• Label: 520.2.g.a
• Level: $520$
• Weight: $2$
• Character orbit: 520.g
• Analytic conductor: $4.152$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.15222090511\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{2} + 2 q^{6} - 16 q^{7} + 2 q^{8} - 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
261.1	−1.34108	−	0.448904i			0.601115i	1.59697	+	1.20403i			1.00000i	0.269843	−	0.806141i	−3.20726			−1.60117	−	2.33158i	2.63866			0.448904	−	1.34108i
261.2	−1.34108	+	0.448904i		−	0.601115i	1.59697	−	1.20403i		−	1.00000i	0.269843	+	0.806141i	−3.20726			−1.60117	+	2.33158i	2.63866			0.448904	+	1.34108i
261.3	−1.25169	−	0.658225i		−	2.91145i	1.13348	+	1.64779i		−	1.00000i	−1.91639	+	3.64425i	−1.95534			−0.334150	−	2.80862i	−5.47656			−0.658225	+	1.25169i
261.4	−1.25169	+	0.658225i			2.91145i	1.13348	−	1.64779i			1.00000i	−1.91639	−	3.64425i	−1.95534			−0.334150	+	2.80862i	−5.47656			−0.658225	−	1.25169i
261.5	−1.02892	−	0.970216i			1.68090i	0.117362	+	1.99655i			1.00000i	1.63084	−	1.72952i	3.58543			1.81633	−	2.16817i	0.174562			0.970216	−	1.02892i
261.6	−1.02892	+	0.970216i		−	1.68090i	0.117362	−	1.99655i		−	1.00000i	1.63084	+	1.72952i	3.58543			1.81633	+	2.16817i	0.174562			0.970216	+	1.02892i
261.7	−0.835094	−	1.14132i			0.601279i	−0.605237	+	1.90622i		−	1.00000i	0.686253	−	0.502124i	−4.98089			2.68105	−	0.901105i	2.63846			−1.14132	+	0.835094i
261.8	−0.835094	+	1.14132i		−	0.601279i	−0.605237	−	1.90622i			1.00000i	0.686253	+	0.502124i	−4.98089			2.68105	+	0.901105i	2.63846			−1.14132	−	0.835094i
261.9	−0.481628	−	1.32967i		−	1.22302i	−1.53607	+	1.28082i			1.00000i	−1.62622	+	0.589041i	0.685077			2.44288	+	1.42559i	1.50422			1.32967	−	0.481628i
261.10	−0.481628	+	1.32967i			1.22302i	−1.53607	−	1.28082i		−	1.00000i	−1.62622	−	0.589041i	0.685077			2.44288	−	1.42559i	1.50422			1.32967	+	0.481628i
261.11	−0.0701382	−	1.41247i			0.360301i	−1.99016	+	0.198137i		−	1.00000i	0.508916	−	0.0252709i	1.97386			0.419449	+	2.79715i	2.87018			−1.41247	+	0.0701382i
261.12	−0.0701382	+	1.41247i		−	0.360301i	−1.99016	−	0.198137i			1.00000i	0.508916	+	0.0252709i	1.97386			0.419449	−	2.79715i	2.87018			−1.41247	−	0.0701382i
261.13	0.579792	−	1.28990i			2.54544i	−1.32768	−	1.49575i		−	1.00000i	3.28336	+	1.47582i	−4.22375			−2.69914	+	0.845354i	−3.47926			−1.28990	−	0.579792i
261.14	0.579792	+	1.28990i		−	2.54544i	−1.32768	+	1.49575i			1.00000i	3.28336	−	1.47582i	−4.22375			−2.69914	−	0.845354i	−3.47926			−1.28990	+	0.579792i
261.15	0.670304	−	1.24527i		−	1.79082i	−1.10139	−	1.66942i		−	1.00000i	−2.23005	−	1.20039i	2.36726			−2.81713	+	0.252504i	−0.207044			−1.24527	−	0.670304i
261.16	0.670304	+	1.24527i			1.79082i	−1.10139	+	1.66942i			1.00000i	−2.23005	+	1.20039i	2.36726			−2.81713	−	0.252504i	−0.207044			−1.24527	+	0.670304i
261.17	0.855598	−	1.12603i		−	2.88793i	−0.535903	−	1.92686i			1.00000i	−3.25191	−	2.47091i	−0.427933			−2.62823	−	1.04518i	−5.34015			1.12603	+	0.855598i
261.18	0.855598	+	1.12603i			2.88793i	−0.535903	+	1.92686i		−	1.00000i	−3.25191	+	2.47091i	−0.427933			−2.62823	+	1.04518i	−5.34015			1.12603	−	0.855598i
261.19	1.12418	−	0.858032i			3.18499i	0.527561	−	1.92917i			1.00000i	2.73282	+	3.58050i	−3.77752			−1.06221	−	2.62139i	−7.14416			0.858032	+	1.12418i
261.20	1.12418	+	0.858032i		−	3.18499i	0.527561	+	1.92917i		−	1.00000i	2.73282	−	3.58050i	−3.77752			−1.06221	+	2.62139i	−7.14416			0.858032	−	1.12418i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	520.2.g.a	✓	24
4.b	odd	2	1		2080.2.g.b		24
8.b	even	2	1	inner	520.2.g.a	✓	24
8.d	odd	2	1		2080.2.g.b		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
520.2.g.a	✓	24	1.a	even	1	1	trivial
520.2.g.a	✓	24	8.b	even	2	1	inner
2080.2.g.b		24	4.b	odd	2	1
2080.2.g.b		24	8.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^24 + 48*T3^22 + 988*T3^20 + 11440*T3^18 + 82240*T3^16 + 382592*T3^14 + 1165504*T3^12 + 2300672*T3^10 + 2844992*T3^8 + 2067968*T3^6 + 798464*T3^4 + 145408*T3^2 + 9216