Newform orbit 124.5.l.a

• Label: 124.5.l.a
• Level: $124$
• Weight: $5$
• Character orbit: 124.l
• Analytic conductor: $12.818$
• Analytic rank: $0$
• Dimension: $248$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.8178754224\)
Analytic rank:	\(0\)
Dimension:	\(248\)
Relative dimension:	\(62\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
35.1	−3.99936	+	0.0713539i	−12.2995	−	3.99635i	15.9898	−	0.570740i	−9.81905			49.4753	+	15.1052i	−39.5116	−	54.3830i	−63.9084	+	3.42353i	69.7765	+	50.6956i	39.2699	−	0.700627i
35.2	−3.99862	−	0.105051i	7.35414	+	2.38950i	15.9779	+	0.840119i	−14.1850			−29.1554	−	10.3273i	12.6030	+	17.3466i	−63.8014	−	5.03782i	−17.1567	−	12.4651i	56.7206	+	1.49015i
35.3	−3.93789	−	0.702183i	−10.2382	−	3.32660i	15.0139	+	5.53023i	46.1374			37.9811	+	20.2889i	4.75019	+	6.53807i	−55.2397	−	32.3199i	28.2248	+	20.5065i	−181.684	−	32.3969i
35.4	−3.91239	−	0.832603i	1.75381	+	0.569849i	14.6135	+	6.51493i	6.69903			−6.38714	−	3.68970i	−11.9816	−	16.4913i	−51.7495	−	37.6562i	−62.7792	−	45.6118i	−26.2092	−	5.57763i
35.5	−3.87510	+	0.991761i	−1.78210	−	0.579038i	14.0328	−	7.68635i	5.30562			7.48007	+	0.476417i	40.2102	+	55.3445i	−46.7556	+	43.7026i	−62.6898	−	45.5468i	−20.5598	+	5.26191i
35.6	−3.85822	−	1.05551i	−12.5298	−	4.07117i	13.7718	+	8.14480i	−42.3430			44.0455	+	28.9328i	48.2598	+	66.4239i	−44.5377	−	45.9608i	74.8906	+	54.4112i	163.369	+	44.6935i
35.7	−3.83059	−	1.15178i	14.8017	+	4.80936i	13.3468	+	8.82396i	−27.7531			−51.1599	−	35.4709i	−6.94187	−	9.55467i	−40.9630	−	49.1735i	130.430	+	94.7627i	106.311	+	31.9653i
35.8	−3.74593	+	1.40285i	14.0191	+	4.55508i	12.0640	−	10.5100i	29.1074			−58.9047	+	2.60365i	16.1694	+	22.2552i	−30.4472	+	56.2936i	110.256	+	80.1058i	−109.034	+	40.8333i
35.9	−3.68342	+	1.55963i	−0.0674233	−	0.0219071i	11.1351	−	11.4895i	−46.6687			0.282515	−	0.0244621i	−17.3603	−	23.8944i	−23.0959	+	59.6874i	−65.5263	−	47.6077i	171.900	−	72.7859i
35.10	−3.63647	+	1.66615i	2.24232	+	0.728573i	10.4479	−	12.1179i	22.7008			−9.36804	+	1.08661i	−53.6590	−	73.8553i	−17.8031	+	61.4740i	−61.0332	−	44.3432i	−82.5508	+	37.8230i
35.11	−3.39722	−	2.11161i	11.5855	+	3.76434i	7.08217	+	14.3472i	37.5609			−31.4095	−	37.2523i	−50.0886	−	68.9410i	6.23614	−	63.6955i	54.5221	+	39.6126i	−127.603	−	79.3142i
35.12	−3.34806	+	2.18871i	−13.0122	−	4.22791i	6.41907	−	14.6559i	2.44474			52.8193	−	14.3246i	8.79561	+	12.1061i	10.5861	+	63.1184i	85.9112	+	62.4182i	−8.18516	+	5.35084i
35.13	−3.12327	−	2.49904i	9.51100	+	3.09031i	3.50959	+	15.6103i	25.8175			−21.9826	−	33.4202i	52.0808	+	71.6831i	28.0495	−	57.5259i	15.3787	+	11.1732i	−80.6349	−	64.5190i
35.14	−3.11474	−	2.50965i	−5.26084	−	1.70935i	3.40327	+	15.6339i	8.56811			12.0963	+	18.5271i	14.7234	+	20.2651i	28.6353	−	57.2365i	−40.7758	−	29.6254i	−26.6875	−	21.5030i
35.15	−3.10903	−	2.51673i	−3.93487	−	1.27852i	3.33209	+	15.6492i	−23.8871			9.01594	+	13.8780i	−31.1843	−	42.9214i	29.0253	−	57.0397i	−51.6817	−	37.5490i	74.2656	+	60.1175i
35.16	−3.10796	+	2.51805i	12.5846	+	4.08897i	3.31889	−	15.6520i	−25.4386			−49.4086	+	18.9801i	−16.7342	−	23.0326i	29.0974	+	57.0030i	76.1209	+	55.3051i	79.0623	−	64.0556i
35.17	−2.55746	+	3.07561i	−1.74347	−	0.566487i	−2.91878	−	15.7315i	42.7016			6.20114	−	3.91346i	8.91114	+	12.2651i	55.8487	+	31.2557i	−62.8116	−	45.6353i	−109.208	+	131.334i
35.18	−2.39076	−	3.20691i	−16.8121	−	5.46259i	−4.56851	+	15.3339i	9.80967			22.6758	+	66.9747i	−16.8606	−	23.2066i	60.0966	−	22.0089i	187.278	+	136.065i	−23.4526	−	31.4587i
35.19	−2.29841	−	3.27373i	7.29605	+	2.37063i	−5.43464	+	15.0487i	−40.8790			−9.00849	−	29.3340i	39.2063	+	53.9628i	61.7566	−	16.7966i	−17.9179	−	13.0181i	93.9566	+	133.827i
35.20	−2.22430	+	3.32453i	3.03403	+	0.985817i	−6.10499	−	14.7895i	−15.2943			−10.0260	+	7.89398i	44.5004	+	61.2496i	62.7474	+	12.6000i	−57.2969	−	41.6286i	34.0190	−	50.8462i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.d	even	5	1	inner
124.l	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.5.l.a	✓	248
4.b	odd	2	1	inner	124.5.l.a	✓	248
31.d	even	5	1	inner	124.5.l.a	✓	248
124.l	odd	10	1	inner	124.5.l.a	✓	248

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.5.l.a	✓	248	1.a	even	1	1	trivial
124.5.l.a	✓	248	4.b	odd	2	1	inner
124.5.l.a	✓	248	31.d	even	5	1	inner
124.5.l.a	✓	248	124.l	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).