Newform orbit 124.2.p.a

• Label: 124.2.p.a
• Level: $124$
• Weight: $2$
• Character orbit: 124.p
• Analytic conductor: $0.990$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.p (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.990144985064\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(14\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 33 q^{6} - 9 q^{8} - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.40876	+	0.124087i	−0.130272	+	1.23946i	1.96920	−	0.349618i	1.03203	−	1.78753i	0.0297212	−	1.76226i	0.311298	+	1.46454i	−2.73075	+	0.736882i	1.41516	+	0.300802i	−1.23207	+	2.64625i
3.2	−1.37846	+	0.315988i	0.298401	−	2.83910i	1.80030	−	0.871153i	−0.269294	+	0.466430i	0.485787	+	4.00788i	−0.376548	−	1.77152i	−2.20637	+	1.76972i	−5.03700	−	1.07065i	0.223824	−	0.728049i
3.3	−1.20776	−	0.735750i	0.0575319	−	0.547380i	0.917345	+	1.77721i	−1.88683	+	3.26808i	−0.472219	+	0.618772i	0.727319	+	3.42177i	0.199654	−	2.82137i	2.63813	+	0.560751i	4.68331	−	2.55881i
3.4	−0.952505	−	1.04534i	−0.0194475	+	0.185031i	−0.185469	+	1.99138i	0.691301	−	1.19737i	0.211944	−	0.155913i	−0.900538	−	4.23670i	2.25833	−	1.70292i	2.90058	+	0.616538i	−1.91012	+	0.417855i
3.5	−0.726490	+	1.21335i	−0.298401	+	2.83910i	−0.944425	−	1.76297i	−0.269294	+	0.466430i	−3.22803	−	2.42464i	0.376548	+	1.77152i	2.82521	+	0.134864i	−5.03700	−	1.07065i	−0.370303	−	0.665604i
3.6	−0.553345	+	1.30146i	0.130272	−	1.23946i	−1.38762	−	1.44032i	1.03203	−	1.78753i	1.54102	+	0.855391i	−0.311298	−	1.46454i	2.64235	−	1.00895i	1.41516	+	0.300802i	1.75533	+	2.33227i
3.7	−0.506641	−	1.32035i	0.308762	−	2.93767i	−1.48663	+	1.33788i	1.56132	−	2.70429i	−4.03518	+	1.08067i	0.883280	+	4.15550i	2.51966	+	1.28504i	−5.60015	−	1.19035i	−4.36163	−	0.691384i
3.8	−0.182213	−	1.40243i	−0.257581	+	2.45072i	−1.93360	+	0.511081i	−0.786115	+	1.36159i	3.48389	−	0.0853156i	0.234244	+	1.10203i	1.06908	+	2.61860i	−3.00525	−	0.638785i	2.05277	+	0.854368i
3.9	0.326523	+	1.37600i	−0.0575319	+	0.547380i	−1.78677	+	0.898592i	−1.88683	+	3.26808i	−0.771981	+	0.0995678i	−0.727319	−	3.42177i	−1.81988	−	2.16518i	2.63813	+	0.560751i	−5.11298	−	1.52918i
3.10	0.699837	+	1.22891i	0.0194475	−	0.185031i	−1.02046	+	1.72008i	0.691301	−	1.19737i	0.240997	−	0.105592i	0.900538	+	4.23670i	−2.82798	−	0.0502801i	2.90058	+	0.616538i	1.95526	+	0.0115868i
3.11	0.878788	−	1.10803i	0.184585	−	1.75621i	−0.455463	−	1.94745i	−0.842418	+	1.45911i	−1.78372	−	1.74786i	0.0707307	+	0.332762i	−2.55809	−	1.20673i	−0.115759	−	0.0246052i	0.876432	+	2.21567i
3.12	1.09916	+	0.889853i	−0.308762	+	2.93767i	0.416322	+	1.95619i	1.56132	−	2.70429i	−2.95348	+	2.95423i	−0.883280	−	4.15550i	−1.28312	+	2.52064i	−5.60015	−	1.19035i	4.12257	−	1.58311i
3.13	1.27748	+	0.606669i	0.257581	−	2.45072i	1.26391	+	1.55001i	−0.786115	+	1.36159i	1.81583	−	2.97448i	−0.234244	−	1.10203i	0.674270	+	2.74688i	−3.00525	−	0.638785i	−1.83028	+	1.26249i
3.14	1.32536	−	0.493377i	−0.184585	+	1.75621i	1.51316	−	1.30780i	−0.842418	+	1.45911i	0.621832	+	2.41868i	−0.0707307	−	0.332762i	1.36024	−	2.47987i	−0.115759	−	0.0246052i	−0.396616	+	2.34948i
11.1	−1.39926	+	0.205086i	1.36017	+	1.51062i	1.91588	−	0.573940i	0.360804	+	0.624930i	−2.21305	−	1.83481i	0.886730	−	0.0931991i	−2.56311	+	1.19601i	−0.118331	+	1.12584i	−0.633024	−	0.800447i
11.2	−1.28829	−	0.583353i	−0.963066	−	1.06959i	1.31940	+	1.50306i	1.81486	+	3.14343i	0.616761	+	1.93976i	0.437436	−	0.0459763i	−0.822957	−	2.70606i	0.0970520	−	0.923388i	−0.504342	−	5.10836i
11.3	−1.12427	−	0.857914i	−0.304683	−	0.338385i	0.527967	+	1.92905i	−1.49536	−	2.59004i	0.0522411	+	0.641828i	−1.34213	+	0.141064i	1.06138	−	2.62173i	0.291913	−	2.77737i	−0.540843	+	4.19480i
11.4	−0.875050	+	1.11099i	−0.584722	−	0.649399i	−0.468577	−	1.94433i	−0.567618	−	0.983143i	1.23313	−	0.0813606i	3.71586	−	0.390553i	2.57015	+	1.18081i	0.233766	−	2.22413i	1.58895	+	0.229684i
11.5	−0.683091	−	1.23830i	2.11915	+	2.35355i	−1.06677	+	1.69174i	−0.103778	−	0.179749i	1.46683	−	4.23183i	−1.63343	+	0.171681i	2.82359	+	0.165369i	−0.734833	+	6.99146i	−0.151693	+	0.251293i
11.6	−0.266023	+	1.38897i	0.974705	+	1.08252i	−1.85846	−	0.738995i	1.14850	+	1.98927i	−1.76288	+	1.06586i	−2.24092	+	0.235530i	1.52083	−	2.38476i	0.0917868	−	0.873293i	−3.06856	+	1.06604i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.h	odd	30	1	inner
124.p	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.2.p.a	✓	112
4.b	odd	2	1	inner	124.2.p.a	✓	112
31.h	odd	30	1	inner	124.2.p.a	✓	112
124.p	even	30	1	inner	124.2.p.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.2.p.a	✓	112	1.a	even	1	1	trivial
124.2.p.a	✓	112	4.b	odd	2	1	inner
124.2.p.a	✓	112	31.h	odd	30	1	inner
124.2.p.a	✓	112	124.p	even	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(124, [\chi])\).