Newform orbit 153.2.s.a

• Label: 153.2.s.a
• Level: $153$
• Weight: $2$
• Character orbit: 153.s
• Analytic conductor: $1.222$
• Analytic rank: $0$
• Dimension: $256$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$153 = 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
5.1	−2.18373	−	1.67563i	1.29886	−	1.14584i	1.44329	+	5.38642i	−0.164844	+	0.187968i	−4.75638	+	0.325791i	2.51761	−	2.20789i	3.76722	−	9.09488i	0.374089	−	2.97658i	0.674941	−	0.134254i
5.2	−1.93474	−	1.48458i	−1.55420	−	0.764493i	1.02161	+	3.81269i	0.541710	−	0.617701i	1.87203	+	3.78643i	−3.71094	+	3.25440i	1.81720	−	4.38711i	1.83110	+	2.37636i	−1.96509	+	0.390881i
5.3	−1.55959	−	1.19672i	1.16178	+	1.28463i	0.482560	+	1.80094i	−1.78450	+	2.03483i	−0.274574	−	3.39382i	−1.16370	+	1.02054i	−0.101958	+	0.246149i	−0.300523	+	2.98491i	5.21821	−	1.03797i
5.4	−1.50245	−	1.15287i	−1.48352	+	0.893963i	0.410611	+	1.53242i	−1.19430	+	1.36184i	3.25954	+	0.367171i	2.49823	−	2.19089i	−0.299691	+	0.723517i	1.40166	−	2.65242i	3.36440	−	0.669221i
5.5	−1.12404	−	0.862508i	1.69438	−	0.359292i	0.00191254	+	0.00713769i	2.50849	−	2.86038i	−2.21444	−	1.05755i	−2.28298	+	2.00212i	−1.08038	+	2.60828i	2.74182	−	1.21755i	−5.28675	+	1.05160i
5.6	−1.06065	−	0.813864i	−0.369214	−	1.69224i	−0.0550376	−	0.205403i	0.984560	−	1.12268i	−0.985649	+	2.09536i	2.03121	−	1.78132i	−1.13203	+	2.73296i	−2.72736	+	1.24960i	−1.95798	+	0.389466i
5.7	−0.490187	−	0.376133i	0.343811	+	1.69758i	−0.418832	−	1.56310i	1.49606	−	1.70593i	0.469987	−	0.961452i	1.62514	−	1.42521i	−0.855523	+	2.06542i	−2.76359	+	1.16730i	−1.37500	+	0.273505i
5.8	−0.183891	−	0.141104i	−1.43824	−	0.965129i	−0.503733	−	1.87996i	−2.35903	+	2.68996i	0.128295	+	0.380420i	−0.826331	+	0.724673i	−0.350042	+	0.845077i	1.13705	+	2.77617i	0.813369	−	0.161789i
5.9	−0.0707646	−	0.0542996i	1.70868	+	0.283550i	−0.515579	−	1.92417i	−1.47631	+	1.68341i	−0.105518	−	0.112846i	3.03807	−	2.66432i	−0.136265	+	0.328973i	2.83920	+	0.968993i	0.195879	−	0.0389627i
5.10	0.501640	+	0.384922i	0.437145	−	1.67598i	−0.414160	−	1.54567i	0.147778	−	0.168508i	0.864411	−	0.672472i	−1.44130	+	1.26399i	0.871146	−	2.10313i	−2.61781	−	1.46529i	0.138994	−	0.0276476i
5.11	0.564127	+	0.432870i	−1.71373	+	0.251259i	−0.386775	−	1.44347i	1.71199	−	1.95215i	−1.07552	−	0.600080i	0.0419494	−	0.0367886i	0.950868	−	2.29560i	2.87374	−	0.861179i	1.81081	−	0.360192i
5.12	1.00677	+	0.772524i	1.70648	+	0.296551i	−0.100840	−	0.376340i	0.0953134	−	0.108684i	1.48894	+	1.61685i	−2.38350	+	2.09027i	1.16047	−	2.80161i	2.82411	+	1.01211i	0.179920	−	0.0357883i
5.13	1.40306	+	1.07661i	0.184815	+	1.72216i	0.291859	+	1.08923i	0.349197	−	0.398183i	−1.59478	+	2.61527i	0.487217	−	0.427278i	0.590386	−	1.42532i	−2.93169	+	0.636563i	0.918630	−	0.182727i
5.14	1.78424	+	1.36910i	0.827829	−	1.52141i	0.791458	+	2.95376i	−2.27494	+	2.59407i	3.56001	−	1.58119i	2.00390	−	1.75737i	−0.910532	+	2.19822i	−1.62940	−	2.51894i	−7.61057	+	1.51384i
5.15	1.78977	+	1.37334i	−1.65992	+	0.494620i	0.799582	+	2.98408i	−1.53223	+	1.74718i	−3.65017	−	1.39438i	−0.511998	+	0.449011i	−0.940452	+	2.27045i	2.51070	−	1.64206i	−5.14182	+	1.02277i
5.16	2.00872	+	1.54135i	−0.894687	−	1.48308i	1.14157	+	4.26041i	2.50546	−	2.85693i	0.488768	−	4.35812i	−1.62924	+	1.42880i	−2.33580	+	5.63913i	−1.39907	+	2.65379i	9.43628	−	1.87699i
11.1	−1.63540	−	2.13130i	1.11938	+	1.32173i	−1.35025	+	5.03920i	−2.13674	−	0.140050i	0.986361	−	4.54731i	0.0884715	+	1.34981i	7.98434	−	3.30722i	−0.493955	+	2.95906i	3.19595	+	4.78307i
11.2	−1.53625	−	2.00208i	−1.72157	+	0.190287i	−1.13062	+	4.21953i	3.62526	+	0.237612i	3.02572	+	3.15438i	0.115282	+	1.75887i	5.52180	−	2.28721i	2.92758	−	0.655185i	−5.09359	−	7.62309i
11.3	−1.34967	−	1.75893i	−0.353226	−	1.69565i	−0.754572	+	2.81610i	−1.95144	−	0.127904i	−2.50579	+	2.90987i	−0.0117682	−	0.179547i	1.87511	−	0.776696i	−2.75046	+	1.19790i	2.40883	+	3.60506i
11.4	−1.03701	−	1.35146i	−0.776090	+	1.54845i	−0.233410	+	0.871097i	−0.974191	−	0.0638519i	2.89747	−	0.556901i	−0.213223	−	3.25316i	−1.72831	+	0.715890i	−1.79537	−	2.40347i	0.923953	+	1.38279i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
17.e	odd	16	1	inner
153.s	even	48	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	153.2.s.a	✓	256
3.b	odd	2	1		459.2.y.a		256
9.c	even	3	1		459.2.y.a		256
9.d	odd	6	1	inner	153.2.s.a	✓	256
17.e	odd	16	1	inner	153.2.s.a	✓	256
51.i	even	16	1		459.2.y.a		256
153.s	even	48	1	inner	153.2.s.a	✓	256
153.t	odd	48	1		459.2.y.a		256

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
153.2.s.a	✓	256	1.a	even	1	1	trivial
153.2.s.a	✓	256	9.d	odd	6	1	inner
153.2.s.a	✓	256	17.e	odd	16	1	inner
153.2.s.a	✓	256	153.s	even	48	1	inner
459.2.y.a		256	3.b	odd	2	1
459.2.y.a		256	9.c	even	3	1
459.2.y.a		256	51.i	even	16	1
459.2.y.a		256	153.t	odd	48	1

Hecke kernels

This newform subspace is the entire newspace $S_{2}^{\mathrm{new}}(153, [\chi])$.