Newform orbit 100.6.i.a

• Label: 100.6.i.a
• Level: $100$
• Weight: $6$
• Character orbit: 100.i
• Analytic conductor: $16.038$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.0383819813\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 135 q^{5} + 872 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−26.9495	+	8.75642i		0		47.9824	+	28.6826i		0			−	106.620i		0		453.009	−	329.131i		0
9.2		0		−21.4268	+	6.96199i		0		−31.4059	−	46.2458i		0			−	33.2168i		0		214.048	−	155.515i		0
9.3		0		−17.5832	+	5.71314i		0		−41.8714	+	37.0376i		0				198.538i		0		79.9395	−	58.0794i		0
9.4		0		−12.8412	+	4.17234i		0		37.4841	−	41.4722i		0				70.7922i		0		−49.1043	+	35.6764i		0
9.5		0		−7.61590	+	2.47456i		0		−21.0394	+	51.7913i		0			−	160.433i		0		−144.713	+	105.140i		0
9.6		0		−2.92767	+	0.951259i		0		−45.1471	−	32.9657i		0			−	161.169i		0		−188.925	+	137.262i		0
9.7		0		3.42908	−	1.11418i		0		45.2903	+	32.7688i		0				91.2427i		0		−186.074	+	135.191i		0
9.8		0		8.84041	−	2.87242i		0		44.5318	−	33.7923i		0			−	213.784i		0		−126.689	+	92.0451i		0
9.9		0		11.3128	−	3.67576i		0		−27.4359	−	48.7060i		0				218.557i		0		−82.1221	+	59.6652i		0
9.10		0		15.7378	−	5.11351i		0		−54.8356	+	10.8656i		0			−	1.49639i		0		24.9379	−	18.1185i		0
9.11		0		24.3305	−	7.90547i		0		28.0589	−	48.3498i		0			−	16.3790i		0		332.887	−	241.857i		0
9.12		0		24.5756	−	7.98511i		0		7.55764	+	55.3885i		0			−	27.6709i		0		343.609	−	249.646i		0
29.1		0		−15.4110	+	21.2114i		0		−50.3650	−	24.2564i		0			−	44.9792i		0		−137.333	−	422.668i		0
29.2		0		−11.7585	+	16.1842i		0		53.3838	+	16.5884i		0			−	180.218i		0		−48.5740	−	149.495i		0
29.3		0		−10.9800	+	15.1127i		0		−8.49336	+	55.2527i		0				89.0154i		0		−32.7410	−	100.767i		0
29.4		0		−10.3590	+	14.2579i		0		28.5667	−	48.0515i		0				156.576i		0		−20.8885	−	64.2882i		0
29.5		0		−2.14021	+	2.94575i		0		−17.7969	+	52.9931i		0				29.5497i		0		70.9942	+	218.498i		0
29.6		0		−0.977286	+	1.34512i		0		12.2429	−	54.5446i		0			−	227.555i		0		74.2369	+	228.478i		0
29.7		0		0.953996	−	1.31306i		0		−45.6533	−	32.2611i		0				104.872i		0		74.2771	+	228.601i		0
29.8		0		3.51700	−	4.84073i		0		−54.2639	+	13.4325i		0			−	140.976i		0		64.0277	+	197.057i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	100.6.i.a	✓	48
25.e	even	10	1	inner	100.6.i.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
100.6.i.a	✓	48	1.a	even	1	1	trivial
100.6.i.a	✓	48	25.e	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(100, [\chi])\).