Newform orbit 100.3.k.a

• Label: 100.3.k.a
• Level: $100$
• Weight: $3$
• Character orbit: 100.k
• Analytic conductor: $2.725$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.k (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.72480264360\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(5\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 2 q^{3} + 6 q^{5} + 14 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−2.33954	+	4.59160i		0		−4.05683	−	2.92270i		0		−1.26237	+	1.26237i		0		−10.3193	−	14.2032i		0
13.2		0		−0.471197	+	0.924777i		0		3.48598	−	3.58440i		0		3.49975	−	3.49975i		0		4.65688	+	6.40965i		0
13.3		0		−0.348616	+	0.684197i		0		−0.109312	+	4.99880i		0		−3.17236	+	3.17236i		0		4.94348	+	6.80411i		0
13.4		0		1.65159	−	3.24143i		0		−4.96781	+	0.566445i		0		8.98966	−	8.98966i		0		−2.48907	−	3.42590i		0
13.5		0		2.40456	−	4.71921i		0		4.88790	−	1.05284i		0		−4.82283	+	4.82283i		0		−11.1990	−	15.4141i		0
17.1		0		−0.745176	+	4.70485i		0		0.433462	+	4.98118i		0		−7.12199	−	7.12199i		0		−13.0209	−	4.23073i		0
17.2		0		−0.254106	+	1.60437i		0		3.96096	−	3.05136i		0		2.11792	+	2.11792i		0		6.05009	+	1.96579i		0
17.3		0		0.0224162	−	0.141530i		0		−3.16779	+	3.86847i		0		8.18870	+	8.18870i		0		8.53998	+	2.77481i		0
17.4		0		0.361805	−	2.28435i		0		−4.15949	−	2.77465i		0		−7.10013	−	7.10013i		0		3.47217	+	1.12818i		0
17.5		0		0.757100	−	4.78014i		0		4.82966	+	1.29397i		0		1.02021	+	1.02021i		0		−13.7171	−	4.45695i		0
33.1		0		−5.60956	−	0.888467i		0		2.47405	+	4.34501i		0		7.36921	−	7.36921i		0		22.1182	+	7.18665i		0
33.2		0		−1.89422	−	0.300014i		0		1.55555	−	4.75187i		0		1.02461	−	1.02461i		0		−5.06147	−	1.64457i		0
33.3		0		−1.52697	−	0.241849i		0		−4.86035	+	1.17346i		0		−4.50851	+	4.50851i		0		−6.28636	−	2.04256i		0
33.4		0		3.16228	+	0.500856i		0		3.09921	+	3.92363i		0		−1.65162	+	1.65162i		0		1.18965	+	0.386542i		0
33.5		0		4.10839	+	0.650705i		0		−1.54723	−	4.75459i		0		5.27964	−	5.27964i		0		7.89594	+	2.56555i		0
37.1		0		−2.89514	−	1.47515i		0		4.93551	+	0.800472i		0		−9.17345	−	9.17345i		0		0.915703	+	1.26036i		0
37.2		0		−2.50258	−	1.27513i		0		−1.06126	+	4.88607i		0		7.79083	+	7.79083i		0		−0.653110	−	0.898929i		0
37.3		0		−1.44337	−	0.735433i		0		−4.57845	−	2.00943i		0		−1.10144	−	1.10144i		0		−3.74761	−	5.15815i		0
37.4		0		2.32641	+	1.18536i		0		3.15402	−	3.87971i		0		2.33746	+	2.33746i		0		−1.28299	−	1.76588i		0
37.5		0		4.23591	+	2.15831i		0		−1.30779	+	4.82594i		0		−0.703294	−	0.703294i		0		7.99462	+	11.0036i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.f	odd	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	100.3.k.a	✓	40
4.b	odd	2	1		400.3.bg.d		40
25.f	odd	20	1	inner	100.3.k.a	✓	40
100.l	even	20	1		400.3.bg.d		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
100.3.k.a	✓	40	1.a	even	1	1	trivial
100.3.k.a	✓	40	25.f	odd	20	1	inner
400.3.bg.d		40	4.b	odd	2	1
400.3.bg.d		40	100.l	even	20	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(100, [\chi])\).