Newform orbit 676.3.g.e

• Label: 676.3.g.e
• Level: $676$
• Weight: $3$
• Character orbit: 676.g
• Analytic conductor: $18.420$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	676.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.4196658708\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} + 116 q^{9} - 100 q^{27} + 244 q^{29} - 464 q^{35} - 236 q^{53} - 192 q^{55} - 136 q^{61} + 20 q^{79} + 1488 q^{81} - 1240 q^{87}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
437.1		0		−5.70706				0		−1.97948	−	1.97948i		0		−7.20460	+	7.20460i		0		23.5705				0
437.2		0		−5.70706				0		1.97948	+	1.97948i		0		7.20460	−	7.20460i		0		23.5705				0
437.3		0		−3.34471				0		−4.39937	−	4.39937i		0		9.83004	−	9.83004i		0		2.18709				0
437.4		0		−3.34471				0		4.39937	+	4.39937i		0		−9.83004	+	9.83004i		0		2.18709				0
437.5		0		−1.17343				0		1.94562	+	1.94562i		0		−1.43565	+	1.43565i		0		−7.62305				0
437.6		0		−1.17343				0		−1.94562	−	1.94562i		0		1.43565	−	1.43565i		0		−7.62305				0
437.7		0		1.20765				0		1.36878	+	1.36878i		0		−7.24814	+	7.24814i		0		−7.54159				0
437.8		0		1.20765				0		−1.36878	−	1.36878i		0		7.24814	−	7.24814i		0		−7.54159				0
437.9		0		2.54823				0		1.24009	+	1.24009i		0		1.62745	−	1.62745i		0		−2.50654				0
437.10		0		2.54823				0		−1.24009	−	1.24009i		0		−1.62745	+	1.62745i		0		−2.50654				0
437.11		0		5.46933				0		−5.87625	−	5.87625i		0		3.11750	−	3.11750i		0		20.9136				0
437.12		0		5.46933				0		5.87625	+	5.87625i		0		−3.11750	+	3.11750i		0		20.9136				0
577.1		0		−5.70706				0		−1.97948	+	1.97948i		0		−7.20460	−	7.20460i		0		23.5705				0
577.2		0		−5.70706				0		1.97948	−	1.97948i		0		7.20460	+	7.20460i		0		23.5705				0
577.3		0		−3.34471				0		−4.39937	+	4.39937i		0		9.83004	+	9.83004i		0		2.18709				0
577.4		0		−3.34471				0		4.39937	−	4.39937i		0		−9.83004	−	9.83004i		0		2.18709				0
577.5		0		−1.17343				0		1.94562	−	1.94562i		0		−1.43565	−	1.43565i		0		−7.62305				0
577.6		0		−1.17343				0		−1.94562	+	1.94562i		0		1.43565	+	1.43565i		0		−7.62305				0
577.7		0		1.20765				0		1.36878	−	1.36878i		0		−7.24814	−	7.24814i		0		−7.54159				0
577.8		0		1.20765				0		−1.36878	+	1.36878i		0		7.24814	+	7.24814i		0		−7.54159				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.b	even	2	1	inner
13.d	odd	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	676.3.g.e	✓	24
13.b	even	2	1	inner	676.3.g.e	✓	24
13.d	odd	4	2	inner	676.3.g.e	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
676.3.g.e	✓	24	1.a	even	1	1	trivial
676.3.g.e	✓	24	13.b	even	2	1	inner
676.3.g.e	✓	24	13.d	odd	4	2	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(676, [\chi])\):

\( T_{3}^{6} + T_{3}^{5} - 41T_{3}^{4} - 27T_{3}^{3} + 323T_{3}^{2} + 29T_{3} - 377 \)

T5^24 + 6410*T5^20 + 8044285*T5^16 + 1056926737*T5^12 + 46663196960*T5^8 + 706806607104*T5^4 + 3341233033216