Newform orbit 124.3.n.a

• Label: 124.3.n.a
• Level: $124$
• Weight: $3$
• Character orbit: 124.n
• Analytic conductor: $3.379$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.n (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.37875527807\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(30\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 240 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 5 q^{6} - 27 q^{8} - 96 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−1.99926	+	0.0544568i	−0.0879632	−	0.413834i	3.99407	−	0.217747i	−0.624847	+	1.08227i	0.198397	+	0.822572i	−2.70372	+	6.07265i	−7.97332	+	0.652836i	8.05839	−	3.58783i	1.19029	−	2.19776i
7.2	−1.99505	+	0.140610i	0.741912	+	3.49042i	3.96046	−	0.561050i	2.31670	−	4.01264i	−1.97094	−	6.85925i	5.02348	−	11.2829i	−7.82243	+	1.67620i	−3.41071	+	1.51855i	−4.05771	+	8.33116i
7.3	−1.86891	+	0.712155i	−1.15158	−	5.41775i	2.98567	−	2.66191i	4.16039	−	7.20601i	6.01048	+	9.30520i	0.685204	−	1.53899i	−3.68426	+	7.10114i	−19.8040	+	8.81730i	−2.64361	+	16.4302i
7.4	−1.82229	+	0.824162i	−0.469244	−	2.20762i	2.64151	−	3.00373i	−2.85641	+	4.94745i	2.67454	+	3.63620i	3.33744	−	7.49600i	−2.33806	+	7.65072i	3.56852	−	1.58881i	1.12772	−	11.3698i
7.5	−1.76073	−	0.948596i	−1.13434	−	5.33667i	2.20033	+	3.34044i	−3.56746	+	6.17902i	−3.06507	+	10.4725i	−0.864598	+	1.94192i	−0.705452	−	7.96884i	−18.9714	+	8.44661i	12.1427	−	7.49550i
7.6	−1.73916	−	0.987589i	−0.272138	−	1.28031i	2.04934	+	3.43515i	2.35737	−	4.08308i	−0.791127	+	2.49542i	−1.03353	+	2.32136i	−0.171606	−	7.99816i	6.65678	−	2.96379i	−8.13224	+	4.77301i
7.7	−1.60673	−	1.19097i	0.931035	+	4.38017i	1.16319	+	3.82714i	−0.973390	+	1.68596i	3.72072	−	8.14661i	−1.13057	+	2.53929i	2.68905	−	7.53452i	−10.0972	+	4.49556i	3.57190	−	1.54962i
7.8	−1.59315	+	1.20909i	0.932435	+	4.38676i	1.07622	−	3.85250i	−1.13754	+	1.97029i	−6.78947	−	5.86135i	−2.59346	+	5.82500i	2.94342	+	7.43884i	−10.1523	+	4.52010i	−0.569970	−	4.51434i
7.9	−1.15685	+	1.63147i	−0.354741	−	1.66892i	−1.32341	−	3.77473i	−1.19665	+	2.07266i	3.13318	+	1.35194i	−1.19159	+	2.67635i	7.68935	+	2.20769i	5.56244	−	2.47656i	−1.99714	−	4.35005i
7.10	−1.07956	−	1.68361i	0.0275934	+	0.129817i	−1.66909	+	3.63512i	−2.86810	+	4.96769i	0.188772	−	0.186602i	4.37751	−	9.83205i	7.92202	−	1.11424i	8.20582	−	3.65347i	11.4599	−	0.534167i
7.11	−0.864102	+	1.80370i	0.286400	+	1.34741i	−2.50666	−	3.11716i	3.60353	−	6.24150i	−2.67780	−	0.647717i	1.82861	−	4.10713i	7.78842	−	1.82771i	6.48843	−	2.88883i	8.14397	+	11.8930i
7.12	−0.673616	−	1.88315i	−0.736057	−	3.46287i	−3.09248	+	2.53704i	3.42633	−	5.93457i	−6.02528	+	3.71875i	2.34572	−	5.26857i	6.86076	+	4.11461i	−3.22781	+	1.43711i	−13.4837	−	2.45465i
7.13	−0.561919	−	1.91944i	0.736057	+	3.46287i	−3.36849	+	2.15714i	3.42633	−	5.93457i	6.23317	−	3.35867i	−2.34572	+	5.26857i	6.03332	+	5.25348i	−3.22781	+	1.43711i	−13.3164	−	3.24188i
7.14	−0.329666	+	1.97264i	−0.974786	−	4.58601i	−3.78264	−	1.30063i	−0.229111	+	0.396833i	9.36791	−	0.411054i	−4.30093	+	9.66006i	3.81268	−	7.03303i	−11.8594	+	5.28013i	−0.707279	−	0.582777i
7.15	−0.199060	+	1.99007i	0.547049	+	2.57366i	−3.92075	−	0.792285i	−4.34583	+	7.52719i	−5.23066	+	0.576352i	2.27507	−	5.10989i	2.35717	−	7.64485i	1.89744	−	0.844793i	−14.1146	−	10.1469i
7.16	−0.116218	−	1.99662i	−0.0275934	−	0.129817i	−3.97299	+	0.464087i	−2.86810	+	4.96769i	−0.255988	+	0.0701807i	−4.37751	+	9.83205i	1.38834	+	7.87861i	8.20582	−	3.65347i	10.2519	+	5.14916i
7.17	0.595729	+	1.90922i	−0.631742	−	2.97211i	−3.29021	+	2.27475i	1.43502	−	2.48553i	5.29806	−	2.97670i	3.93413	−	8.83620i	−6.30307	−	4.92660i	−0.212439	+	0.0945840i	5.60029	+	1.25906i
7.18	0.599843	−	1.90793i	−0.931035	−	4.38017i	−3.28038	−	2.28891i	−0.973390	+	1.68596i	−8.91553	−	0.851069i	1.13057	−	2.53929i	−6.33479	+	4.88573i	−10.0972	+	4.49556i	2.63281	+	2.86847i
7.19	0.640254	+	1.89475i	0.631742	+	2.97211i	−3.18015	+	2.42624i	1.43502	−	2.48553i	−5.22693	+	3.09990i	−3.93413	+	8.83620i	−6.63323	−	4.47217i	−0.212439	+	0.0945840i	5.62823	+	1.12763i
7.20	0.826518	−	1.82123i	0.272138	+	1.28031i	−2.63374	−	3.01055i	2.35737	−	4.08308i	2.55666	+	0.562572i	1.03353	−	2.32136i	−7.65973	+	2.30836i	6.65678	−	2.96379i	−5.48781	−	7.66804i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.g	even	15	1	inner
124.n	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.3.n.a	✓	240
4.b	odd	2	1	inner	124.3.n.a	✓	240
31.g	even	15	1	inner	124.3.n.a	✓	240
124.n	odd	30	1	inner	124.3.n.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.3.n.a	✓	240	1.a	even	1	1	trivial
124.3.n.a	✓	240	4.b	odd	2	1	inner
124.3.n.a	✓	240	31.g	even	15	1	inner
124.3.n.a	✓	240	124.n	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(124, [\chi])\).