Newform orbit 820.2.bg.a

• Label: 820.2.bg.a
• Level: $820$
• Weight: $2$
• Character orbit: 820.bg
• Analytic conductor: $6.548$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bg (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.54773296574\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 24 * q + 6 * q^5 + 5 * q^7 - 6 * q^9 + 5 * q^11 - 5 * q^13 - 5 * q^17 - 5 * q^19 - 6 * q^21 + 10 * q^23 - 6 * q^25 - 25 * q^29 + 7 * q^31 - 12 * q^33 + 5 * q^35 - 13 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^43 + q^45 - 35 * q^47 + 23 * q^49 - 27 * q^51 + 35 * q^53 + 9 * q^57 - 14 * q^59 + 22 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 - 55 * q^71 + 8 * q^73 - 5 * q^75 + 6 * q^77 - 28 * q^81 - 82 * q^83 - 27 * q^87 + 50 * q^89 + 70 * q^91 - 80 * q^93 - 5 * q^95 - 20 * q^97 - 60 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
441.1		0			−	2.67508i		0		−0.309017	−	0.951057i		0		−2.42716	−	3.34070i		0		−4.15606				0
441.2		0			−	1.67459i		0		−0.309017	−	0.951057i		0		1.17963	+	1.62362i		0		0.195761				0
441.3		0			−	0.0367361i		0		−0.309017	−	0.951057i		0		−0.212825	−	0.292928i		0		2.99865				0
441.4		0				1.54157i		0		−0.309017	−	0.951057i		0		0.545675	+	0.751057i		0		0.623556				0
441.5		0				1.69546i		0		−0.309017	−	0.951057i		0		2.14281	+	2.94933i		0		0.125430				0
441.6		0				2.32495i		0		−0.309017	−	0.951057i		0		−1.65518	−	2.27816i		0		−2.40537				0
681.1		0			−	2.07903i		0		0.809017	+	0.587785i		0		0.0731487	−	0.0237674i		0		−1.32238				0
681.2		0			−	1.12175i		0		0.809017	+	0.587785i		0		−3.16195	+	1.02738i		0		1.74169				0
681.3		0			−	0.163494i		0		0.809017	+	0.587785i		0		4.59987	−	1.49459i		0		2.97327				0
681.4		0				0.525875i		0		0.809017	+	0.587785i		0		−3.06532	+	0.995983i		0		2.72346				0
681.5		0				1.57598i		0		0.809017	+	0.587785i		0		1.65168	−	0.536663i		0		0.516299				0
681.6		0				3.16454i		0		0.809017	+	0.587785i		0		2.82962	−	0.919400i		0		−7.01429				0
701.1		0			−	2.32495i		0		−0.309017	+	0.951057i		0		−1.65518	+	2.27816i		0		−2.40537				0
701.2		0			−	1.69546i		0		−0.309017	+	0.951057i		0		2.14281	−	2.94933i		0		0.125430				0
701.3		0			−	1.54157i		0		−0.309017	+	0.951057i		0		0.545675	−	0.751057i		0		0.623556				0
701.4		0				0.0367361i		0		−0.309017	+	0.951057i		0		−0.212825	+	0.292928i		0		2.99865				0
701.5		0				1.67459i		0		−0.309017	+	0.951057i		0		1.17963	−	1.62362i		0		0.195761				0
701.6		0				2.67508i		0		−0.309017	+	0.951057i		0		−2.42716	+	3.34070i		0		−4.15606				0
761.1		0			−	3.16454i		0		0.809017	−	0.587785i		0		2.82962	+	0.919400i		0		−7.01429				0
761.2		0			−	1.57598i		0		0.809017	−	0.587785i		0		1.65168	+	0.536663i		0		0.516299				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.f	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	820.2.bg.a	✓	24
41.f	even	10	1	inner	820.2.bg.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
820.2.bg.a	✓	24	1.a	even	1	1	trivial
820.2.bg.a	✓	24	41.f	even	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^24 + 39*T3^22 + 646*T3^20 + 5983*T3^18 + 34268*T3^16 + 126467*T3^14 + 302875*T3^12 + 459977*T3^10 + 415716*T3^8 + 194144*T3^6 + 32869*T3^4 + 785*T3^2 + 1