Newform orbit 531.5.b.a

• Label: 531.5.b.a
• Level: $531$
• Weight: $5$
• Character orbit: 531.b
• Analytic conductor: $54.889$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	531.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(54.8894503975\)
Analytic rank:	\(0\)
Dimension:	\(76\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 632 q^{4} - 48 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
296.1		−	7.89147i		0		−46.2753				−	30.7341i		0		−38.0387					238.917i		0		−242.537
296.2		−	7.80173i		0		−44.8670					42.3216i		0		−83.7809					225.212i		0		330.181
296.3		−	7.65883i		0		−42.6577				−	8.87825i		0		63.4860					204.167i		0		−67.9970
296.4		−	7.46017i		0		−39.6541				−	35.9805i		0		−39.8913					176.464i		0		−268.421
296.5		−	7.18445i		0		−35.6164					15.5237i		0		−43.6466					140.933i		0		111.529
296.6		−	7.13258i		0		−34.8737				−	3.77857i		0		39.6400					134.618i		0		−26.9510
296.7		−	6.80829i		0		−30.3528					49.1212i		0		61.0526					97.7182i		0		334.431
296.8		−	6.57981i		0		−27.2939					2.90496i		0		−11.6090					74.3115i		0		19.1141
296.9		−	6.47072i		0		−25.8703					30.8868i		0		46.2877					63.8678i		0		199.860
296.10		−	6.40563i		0		−25.0320					18.5372i		0		29.7242					57.8559i		0		118.743
296.11		−	6.38419i		0		−24.7578				−	16.4296i		0		84.4308					55.9116i		0		−104.890
296.12		−	6.05329i		0		−20.6423				−	34.3242i		0		−5.09902					28.1013i		0		−207.774
296.13		−	5.87705i		0		−18.5397				−	43.2688i		0		−12.4994					14.9259i		0		−254.293
296.14		−	5.75134i		0		−17.0779				−	6.47491i		0		−90.4283					6.19937i		0		−37.2394
296.15		−	5.65016i		0		−15.9243					29.6313i		0		−73.1972				−	0.427826i		0		167.422
296.16		−	5.40748i		0		−13.2409					5.33509i		0		−40.2707				−	14.9200i		0		28.8494
296.17		−	5.38034i		0		−12.9480				−	37.0493i		0		−57.6896				−	16.4207i		0		−199.337
296.18		−	4.71716i		0		−6.25160					39.7285i		0		−15.3622				−	45.9848i		0		187.405
296.19		−	4.51417i		0		−4.37776				−	15.3988i		0		19.6389				−	52.4648i		0		−69.5129
296.20		−	4.32230i		0		−2.68230				−	35.4048i		0		80.8997				−	57.5631i		0		−153.030

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	531.5.b.a	✓	76
3.b	odd	2	1	inner	531.5.b.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
531.5.b.a	✓	76	1.a	even	1	1	trivial
531.5.b.a	✓	76	3.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(531, [\chi])\).