Newform orbit 520.2.e.b

• Label: 520.2.e.b
• 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	−1.41414	−	0.0146767i		−	2.34222i	1.99957	+	0.0415097i	1.00000			−0.0343760	+	3.31222i			1.38277i	−2.82706	−	0.0880475i	−2.48598			−1.41414	−	0.0146767i
181.2	−1.41414	+	0.0146767i			2.34222i	1.99957	−	0.0415097i	1.00000			−0.0343760	−	3.31222i		−	1.38277i	−2.82706	+	0.0880475i	−2.48598			−1.41414	+	0.0146767i
181.3	−1.38368	−	0.292262i			0.453916i	1.82917	+	0.808798i	1.00000			0.132663	−	0.628077i			4.95047i	−2.29461	−	1.65372i	2.79396			−1.38368	−	0.292262i
181.4	−1.38368	+	0.292262i		−	0.453916i	1.82917	−	0.808798i	1.00000			0.132663	+	0.628077i		−	4.95047i	−2.29461	+	1.65372i	2.79396			−1.38368	+	0.292262i
181.5	−1.23147	−	0.695334i		−	0.385182i	1.03302	+	1.71256i	1.00000			−0.267830	+	0.474339i		−	2.57920i	−0.0813289	−	2.82726i	2.85163			−1.23147	−	0.695334i
181.6	−1.23147	+	0.695334i			0.385182i	1.03302	−	1.71256i	1.00000			−0.267830	−	0.474339i			2.57920i	−0.0813289	+	2.82726i	2.85163			−1.23147	+	0.695334i
181.7	−0.824839	−	1.14876i			1.88133i	−0.639281	+	1.89508i	1.00000			2.16119	−	1.55179i		−	1.32225i	2.70429	−	0.828757i	−0.539393			−0.824839	−	1.14876i
181.8	−0.824839	+	1.14876i		−	1.88133i	−0.639281	−	1.89508i	1.00000			2.16119	+	1.55179i			1.32225i	2.70429	+	0.828757i	−0.539393			−0.824839	+	1.14876i
181.9	−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
181.10	−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
181.11	−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
181.12	−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
181.13	−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
181.14	−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
181.15	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
181.16	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
181.17	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
181.18	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
181.19	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
181.20	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

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.b	yes	28
4.b	odd	2	1		2080.2.e.b		28
8.b	even	2	1		520.2.e.a	✓	28
8.d	odd	2	1		2080.2.e.a		28
13.b	even	2	1		520.2.e.a	✓	28
52.b	odd	2	1		2080.2.e.a		28
104.e	even	2	1	inner	520.2.e.b	yes	28
104.h	odd	2	1		2080.2.e.b		28

    

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