Newform orbit 520.2.e.a

• Label: 520.2.e.a
• Level: $520$
• Weight: $2$
• Character orbit: 520.e
• Analytic conductor: $4.152$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.15222090511\)
Analytic rank:	\(0\)
Dimension:	\(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
181.1	−1.36759	−	0.360123i			1.23850i	1.74062	+	0.985004i	−1.00000			0.446012	−	1.69376i		−	0.510733i	−2.02574	−	1.97392i	1.46612			1.36759	+	0.360123i
181.2	−1.36759	+	0.360123i		−	1.23850i	1.74062	−	0.985004i	−1.00000			0.446012	+	1.69376i			0.510733i	−2.02574	+	1.97392i	1.46612			1.36759	−	0.360123i
181.3	−1.33977	−	0.452797i		−	2.30485i	1.58995	+	1.21329i	−1.00000			−1.04363	+	3.08797i			2.10161i	−1.58079	−	2.34544i	−2.31235			1.33977	+	0.452797i
181.4	−1.33977	+	0.452797i			2.30485i	1.58995	−	1.21329i	−1.00000			−1.04363	−	3.08797i		−	2.10161i	−1.58079	+	2.34544i	−2.31235			1.33977	−	0.452797i
181.5	−1.19659	−	0.753776i			3.31803i	0.863644	+	1.80392i	−1.00000			2.50105	−	3.97031i			3.29791i	0.326323	−	2.80954i	−8.00931			1.19659	+	0.753776i
181.6	−1.19659	+	0.753776i		−	3.31803i	0.863644	−	1.80392i	−1.00000			2.50105	+	3.97031i		−	3.29791i	0.326323	+	2.80954i	−8.00931			1.19659	−	0.753776i
181.7	−1.06763	−	0.927448i		−	1.27290i	0.279682	+	1.98035i	−1.00000			−1.18055	+	1.35899i		−	4.18045i	1.53807	−	2.37368i	1.37972			1.06763	+	0.927448i
181.8	−1.06763	+	0.927448i			1.27290i	0.279682	−	1.98035i	−1.00000			−1.18055	−	1.35899i			4.18045i	1.53807	+	2.37368i	1.37972			1.06763	−	0.927448i
181.9	−0.773809	−	1.18373i			0.404212i	−0.802440	+	1.83196i	−1.00000			0.478479	−	0.312783i			0.0169500i	2.78949	−	0.467717i	2.83661			0.773809	+	1.18373i
181.10	−0.773809	+	1.18373i		−	0.404212i	−0.802440	−	1.83196i	−1.00000			0.478479	+	0.312783i		−	0.0169500i	2.78949	+	0.467717i	2.83661			0.773809	−	1.18373i
181.11	−0.449908	−	1.34074i			2.78604i	−1.59516	+	1.20642i	−1.00000			3.73536	−	1.25346i		−	4.49892i	2.33517	+	1.59592i	−4.76202			0.449908	+	1.34074i
181.12	−0.449908	+	1.34074i		−	2.78604i	−1.59516	−	1.20642i	−1.00000			3.73536	+	1.25346i			4.49892i	2.33517	−	1.59592i	−4.76202			0.449908	−	1.34074i
181.13	−0.0696055	−	1.41250i		−	0.202513i	−1.99031	+	0.196636i	−1.00000			−0.286050	+	0.0140960i			2.14591i	0.416284	+	2.79763i	2.95899			0.0696055	+	1.41250i
181.14	−0.0696055	+	1.41250i			0.202513i	−1.99031	−	0.196636i	−1.00000			−0.286050	−	0.0140960i		−	2.14591i	0.416284	−	2.79763i	2.95899			0.0696055	−	1.41250i
181.15	0.127008	−	1.40850i		−	3.03478i	−1.96774	−	0.357781i	−1.00000			−4.27448	−	0.385440i			2.54973i	−0.753852	+	2.72612i	−6.20986			−0.127008	+	1.40850i
181.16	0.127008	+	1.40850i			3.03478i	−1.96774	+	0.357781i	−1.00000			−4.27448	+	0.385440i		−	2.54973i	−0.753852	−	2.72612i	−6.20986			−0.127008	−	1.40850i
181.17	0.588919	−	1.28576i			2.17521i	−1.30635	−	1.51442i	−1.00000			2.79680	+	1.28103i		−	1.21172i	−2.71651	+	0.787780i	−1.73156			−0.588919	+	1.28576i
181.18	0.588919	+	1.28576i		−	2.17521i	−1.30635	+	1.51442i	−1.00000			2.79680	−	1.28103i			1.21172i	−2.71651	−	0.787780i	−1.73156			−0.588919	−	1.28576i
181.19	0.694848	−	1.23174i			2.28835i	−1.03437	−	1.71175i	−1.00000			2.81866	+	1.59006i			4.39720i	−2.82716	+	0.0846728i	−2.23656			−0.694848	+	1.23174i
181.20	0.694848	+	1.23174i		−	2.28835i	−1.03437	+	1.71175i	−1.00000			2.81866	−	1.59006i		−	4.39720i	−2.82716	−	0.0846728i	−2.23656			−0.694848	−	1.23174i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
104.e	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.e.a	✓	28
4.b	odd	2	1		2080.2.e.a		28
8.b	even	2	1		520.2.e.b	yes	28
8.d	odd	2	1		2080.2.e.b		28
13.b	even	2	1		520.2.e.b	yes	28
52.b	odd	2	1		2080.2.e.b		28
104.e	even	2	1	inner	520.2.e.a	✓	28
104.h	odd	2	1		2080.2.e.a		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
520.2.e.a	✓	28	1.a	even	1	1	trivial
520.2.e.a	✓	28	104.e	even	2	1	inner
520.2.e.b	yes	28	8.b	even	2	1
520.2.e.b	yes	28	13.b	even	2	1
2080.2.e.a		28	4.b	odd	2	1
2080.2.e.a		28	104.h	odd	2	1
2080.2.e.b		28	8.d	odd	2	1
2080.2.e.b		28	52.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^14 + 4*T11^13 - 76*T11^12 - 268*T11^11 + 2132*T11^10 + 6408*T11^9 - 27712*T11^8 - 69432*T11^7 + 175056*T11^6 + 346768*T11^5 - 525768*T11^4 - 689424*T11^3 + 741552*T11^2 + 393200*T11 - 360000