Newform orbit 5004.2.bc.a

• Label: 5004.2.bc.a
• Level: $5004$
• Weight: $2$
• Character orbit: 5004.bc
• Analytic conductor: $39.957$
• Analytic rank: $0$
• Dimension: $92$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5004 = 2^{2} \cdot 3^{2} \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5004.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(39.9571411714\)
Analytic rank:	\(0\)
Dimension:	\(92\)
Relative dimension:	\(46\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 92 q - 2 q^{7} - 4 q^{13} + 12 q^{19} + 34 q^{25} - 16 q^{31} + 6 q^{37} + 18 q^{43} - 28 q^{49} + 24 q^{61} - 2 q^{67} + 6 q^{73} - 40 q^{79} + 48 q^{85} + 72 q^{91} + 18 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2321.1		0			0			0		−3.83280	+	2.21287i		0		−1.22088	−	2.11463i		0			0			0
2321.2		0			0			0		−3.53871	+	2.04308i		0		0.667962	+	1.15694i		0			0			0
2321.3		0			0			0		−3.36610	+	1.94342i		0		−1.33777	−	2.31708i		0			0			0
2321.4		0			0			0		−3.03025	+	1.74952i		0		2.43994	+	4.22610i		0			0			0
2321.5		0			0			0		−2.76084	+	1.59397i		0		1.82687	+	3.16423i		0			0			0
2321.6		0			0			0		−2.53368	+	1.46282i		0		0.675151	+	1.16940i		0			0			0
2321.7		0			0			0		−2.31772	+	1.33813i		0		−0.371964	−	0.644260i		0			0			0
2321.8		0			0			0		−2.22699	+	1.28575i		0		0.676147	+	1.17112i		0			0			0
2321.9		0			0			0		−2.00137	+	1.15549i		0		−1.33158	−	2.30637i		0			0			0
2321.10		0			0			0		−1.98684	+	1.14710i		0		−2.43293	−	4.21396i		0			0			0
2321.11		0			0			0		−1.98416	+	1.14555i		0		0.292993	+	0.507479i		0			0			0
2321.12		0			0			0		−1.95263	+	1.12735i		0		1.19500	+	2.06981i		0			0			0
2321.13		0			0			0		−1.88950	+	1.09090i		0		−1.00907	−	1.74776i		0			0			0
2321.14		0			0			0		−1.56993	+	0.906401i		0		−2.10405	−	3.64432i		0			0			0
2321.15		0			0			0		−1.41337	+	0.816008i		0		−0.290584	−	0.503306i		0			0			0
2321.16		0			0			0		−0.952219	+	0.549764i		0		0.805547	+	1.39525i		0			0			0
2321.17		0			0			0		−0.851802	+	0.491788i		0		−1.55786	−	2.69830i		0			0			0
2321.18		0			0			0		−0.725465	+	0.418847i		0		−0.803130	−	1.39106i		0			0			0
2321.19		0			0			0		−0.687469	+	0.396910i		0		1.36468	+	2.36369i		0			0			0
2321.20		0			0			0		−0.681928	+	0.393712i		0		−1.72005	−	2.97922i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
139.d	odd	6	1	inner
417.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5004.2.bc.a	✓	92
3.b	odd	2	1	inner	5004.2.bc.a	✓	92
139.d	odd	6	1	inner	5004.2.bc.a	✓	92
417.f	even	6	1	inner	5004.2.bc.a	✓	92

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5004.2.bc.a	✓	92	1.a	even	1	1	trivial
5004.2.bc.a	✓	92	3.b	odd	2	1	inner
5004.2.bc.a	✓	92	139.d	odd	6	1	inner
5004.2.bc.a	✓	92	417.f	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(5004, [\chi])\).