Newform orbit 55.3.h.a

• Label: 55.3.h.a
• Level: $55$
• Weight: $3$
• Character orbit: 55.h
• Analytic conductor: $1.499$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.h (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.49864145398\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(10\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 22 q^{4} + 2 q^{5} - 10 q^{6} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−3.14234	+	2.28305i	2.18043	−	0.708465i	3.42596	−	10.5440i	4.81985	−	1.33006i	−5.23420	+	7.20426i	1.07415	−	3.30590i	8.50585	+	26.1783i	−3.02880	+	2.20055i	−12.1090	+	15.1834i
19.2	−1.93953	+	1.40915i	0.655881	−	0.213109i	0.539997	−	1.66194i	−2.58117	+	4.28224i	−0.971797	+	1.33756i	−1.39706	+	4.29970i	−1.66875	−	5.13589i	−6.89639	+	5.01052i	−1.02806	−	11.9428i
19.3	−1.93573	+	1.40639i	−2.48291	+	0.806746i	0.533048	−	1.64055i	−1.82346	−	4.65564i	3.67164	−	5.05358i	1.11629	−	3.43559i	−1.68211	−	5.17701i	−1.76716	+	1.28392i	10.0774	+	6.44756i
19.4	−0.733351	+	0.532811i	4.79404	−	1.55768i	−0.982152	+	3.02275i	0.633370	−	4.95972i	−2.68577	+	3.69664i	−1.55900	+	4.79812i	−2.01075	−	6.18846i	13.2753	−	9.64509i	2.17811	+	3.97468i
19.5	−0.0280831	+	0.0204036i	−2.65739	+	0.863439i	−1.23570	+	3.80308i	4.99984	+	0.0395361i	0.0570106	−	0.0784683i	−3.62139	+	11.1455i	−0.0858014	−	0.264070i	−0.964951	+	0.701078i	−0.141218	+	0.100904i
19.6	0.0280831	−	0.0204036i	2.65739	−	0.863439i	−1.23570	+	3.80308i	1.58264	+	4.74292i	0.0570106	−	0.0784683i	3.62139	−	11.1455i	0.0858014	+	0.264070i	−0.964951	+	0.701078i	0.141218	+	0.100904i
19.7	0.733351	−	0.532811i	−4.79404	+	1.55768i	−0.982152	+	3.02275i	−4.52125	+	2.13501i	−2.68577	+	3.69664i	1.55900	−	4.79812i	2.01075	+	6.18846i	13.2753	−	9.64509i	−2.17811	+	3.97468i
19.8	1.93573	−	1.40639i	2.48291	−	0.806746i	0.533048	−	1.64055i	−4.99126	−	0.295545i	3.67164	−	5.05358i	−1.11629	+	3.43559i	1.68211	+	5.17701i	−1.76716	+	1.28392i	−10.0774	+	6.44756i
19.9	1.93953	−	1.40915i	−0.655881	+	0.213109i	0.539997	−	1.66194i	3.27503	−	3.77812i	−0.971797	+	1.33756i	1.39706	−	4.29970i	1.66875	+	5.13589i	−6.89639	+	5.01052i	1.02806	−	11.9428i
19.10	3.14234	−	2.28305i	−2.18043	+	0.708465i	3.42596	−	10.5440i	0.224452	+	4.99496i	−5.23420	+	7.20426i	−1.07415	+	3.30590i	−8.50585	−	26.1783i	−3.02880	+	2.20055i	12.1090	+	15.1834i
24.1	−1.09764	+	3.37818i	0.896484	+	1.23390i	−6.97124	−	5.06490i	−0.630874	+	4.96004i	−5.15237	+	1.67411i	−0.882039	−	0.640839i	13.2675	−	9.63938i	2.06232	−	6.34716i	−16.0635	−	7.57554i
24.2	−0.971512	+	2.99001i	−2.68096	−	3.69002i	−4.76024	−	3.45851i	−1.02557	−	4.89369i	13.6378	−	4.43118i	−2.39174	−	1.73770i	4.79180	−	3.48144i	−3.64756	+	11.2260i	15.6285	+	1.68781i
24.3	−0.670028	+	2.06213i	2.29134	+	3.15376i	−0.567391	−	0.412234i	3.30368	−	3.75309i	−8.03874	+	2.61194i	−4.84595	−	3.52079i	−5.78637	+	4.20405i	−1.91480	+	5.89316i	5.52581	+	9.32731i
24.4	−0.427998	+	1.31724i	−1.61445	−	2.22210i	1.68412	+	1.22359i	3.35777	+	3.70478i	3.61803	−	1.17557i	7.52022	+	5.46376i	−6.81461	+	4.95111i	0.449863	−	1.38454i	−6.31721	+	2.83735i
24.5	−0.217958	+	0.670807i	1.22810	+	1.69033i	2.83359	+	2.05873i	−4.87482	−	1.11180i	−1.40156	+	0.455395i	4.53519	+	3.29501i	−4.28110	+	3.11040i	1.43215	−	4.40771i	1.80831	−	3.02774i
24.6	0.217958	−	0.670807i	−1.22810	−	1.69033i	2.83359	+	2.05873i	3.29031	−	3.76482i	−1.40156	+	0.455395i	−4.53519	−	3.29501i	4.28110	−	3.11040i	1.43215	−	4.40771i	−1.80831	−	3.02774i
24.7	0.427998	−	1.31724i	1.61445	+	2.22210i	1.68412	+	1.22359i	−0.538873	+	4.97088i	3.61803	−	1.17557i	−7.52022	−	5.46376i	6.81461	−	4.95111i	0.449863	−	1.38454i	6.31721	+	2.83735i
24.8	0.670028	−	2.06213i	−2.29134	−	3.15376i	−0.567391	−	0.412234i	−4.87875	−	1.09446i	−8.03874	+	2.61194i	4.84595	+	3.52079i	5.78637	−	4.20405i	−1.91480	+	5.89316i	−5.52581	+	9.32731i
24.9	0.971512	−	2.99001i	2.68096	+	3.69002i	−4.76024	−	3.45851i	−2.04673	−	4.56189i	13.6378	−	4.43118i	2.39174	+	1.73770i	−4.79180	+	3.48144i	−3.64756	+	11.2260i	−15.6285	+	1.68781i
24.10	1.09764	−	3.37818i	−0.896484	−	1.23390i	−6.97124	−	5.06490i	3.42583	+	3.64194i	−5.15237	+	1.67411i	0.882039	+	0.640839i	−13.2675	+	9.63938i	2.06232	−	6.34716i	16.0635	−	7.57554i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
11.d	odd	10	1	inner
55.h	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	55.3.h.a	✓	40
5.b	even	2	1	inner	55.3.h.a	✓	40
5.c	odd	4	2		275.3.x.j		40
11.c	even	5	1		605.3.d.b		40
11.d	odd	10	1	inner	55.3.h.a	✓	40
11.d	odd	10	1		605.3.d.b		40
55.h	odd	10	1	inner	55.3.h.a	✓	40
55.h	odd	10	1		605.3.d.b		40
55.j	even	10	1		605.3.d.b		40
55.l	even	20	2		275.3.x.j		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.3.h.a	✓	40	1.a	even	1	1	trivial
55.3.h.a	✓	40	5.b	even	2	1	inner
55.3.h.a	✓	40	11.d	odd	10	1	inner
55.3.h.a	✓	40	55.h	odd	10	1	inner
275.3.x.j		40	5.c	odd	4	2
275.3.x.j		40	55.l	even	20	2
605.3.d.b		40	11.c	even	5	1
605.3.d.b		40	11.d	odd	10	1
605.3.d.b		40	55.h	odd	10	1
605.3.d.b		40	55.j	even	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(55, [\chi])\).