Newform orbit 123.5.f.a

• Label: 123.5.f.a
• Level: $123$
• Weight: $5$
• Character orbit: 123.f
• Analytic conductor: $12.715$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	123.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.7145054593\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(54\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 10 q^{3} + 824 q^{4} + 128 q^{6} - 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−7.97039			5.72451	−	6.94478i	47.5271			14.9850			−45.6266	+	55.3526i	−29.6569	+	29.6569i	−251.284			−15.4599	−	79.5109i	−119.437
32.2	−7.71663			−8.57600	+	2.72986i	43.5464			−31.2572			66.1779	−	21.0653i	−22.3016	+	22.3016i	−212.566			66.0957	−	46.8226i	241.201
32.3	−7.28010			0.735778	+	8.96987i	36.9998			1.61694			−5.35653	−	65.3015i	39.5357	−	39.5357i	−152.881			−79.9173	+	13.1997i	−11.7715
32.4	−6.77618			−7.21099	−	5.38531i	29.9166			10.6057			48.8630	+	36.4919i	−18.0325	+	18.0325i	−94.3016			22.9968	+	77.6669i	−71.8659
32.5	−6.75865			−4.66792	−	7.69484i	29.6794			7.95462			31.5488	+	52.0068i	62.9328	−	62.9328i	−92.4544			−37.4211	+	71.8377i	−53.7625
32.6	−6.65735			8.85159	+	1.62771i	28.3203			−33.6181			−58.9281	−	10.8362i	8.96521	−	8.96521i	−82.0203			75.7011	+	28.8156i	223.808
32.7	−6.34976			5.99835	+	6.70968i	24.3195			23.5220			−38.0881	−	42.6049i	−57.4389	+	57.4389i	−52.8268			−9.03953	+	80.4940i	−149.359
32.8	−6.34368			−7.79996	+	4.49005i	24.2422			47.9084			49.4804	−	28.4834i	9.03077	−	9.03077i	−52.2860			40.6789	−	70.0445i	−303.916
32.9	−5.63041			4.26896	−	7.92313i	15.7015			−9.13063			−24.0360	+	44.6105i	13.9441	−	13.9441i	1.68061			−44.5519	−	67.6471i	51.4092
32.10	−5.58694			−2.10265	−	8.75093i	15.2139			−41.6855			11.7474	+	48.8909i	−31.3745	+	31.3745i	4.39192			−72.1577	+	36.8004i	232.894
32.11	−5.51848			−3.73901	+	8.18656i	14.4536			−16.0304			20.6337	−	45.1774i	−40.7340	+	40.7340i	8.53366			−53.0396	−	61.2193i	88.4636
32.12	−5.34501			8.79433	−	1.91304i	12.5691			34.7199			−47.0058	+	10.2252i	31.6611	−	31.6611i	18.3381			73.6805	−	33.6479i	−185.578
32.13	−4.58268			−8.93824	+	1.05252i	5.00097			−42.7713			40.9611	−	4.82336i	67.1249	−	67.1249i	50.4050			78.7844	−	18.8154i	196.007
32.14	−4.22569			−8.82930	−	1.74458i	1.85641			0.983872			37.3098	+	7.37203i	−36.9837	+	36.9837i	59.7663			74.9129	+	30.8068i	−4.15753
32.15	−4.08526			−5.02593	+	7.46592i	0.689357			−3.13578			20.5323	−	30.5002i	9.53314	−	9.53314i	62.5480			−30.4800	−	75.0465i	12.8105
32.16	−3.81302			0.198618	−	8.99781i	−1.46087			41.0848			−0.757335	+	34.3088i	−42.9942	+	42.9942i	66.5787			−80.9211	−	3.57426i	−156.657
32.17	−3.78771			5.33134	+	7.25099i	−1.65327			−12.8497			−20.1936	−	27.4646i	32.3243	−	32.3243i	66.8654			−24.1536	+	77.3150i	48.6709
32.18	−2.83792			8.98645	+	0.493624i	−7.94619			−0.00401250			−25.5029	−	1.40087i	−24.9794	+	24.9794i	67.9575			80.5127	+	8.87186i	0.0113872
32.19	−2.76441			3.68133	+	8.21266i	−8.35801			31.6710			−10.1767	−	22.7032i	39.9891	−	39.9891i	67.3356			−53.8956	+	60.4671i	−87.5517
32.20	−2.65979			−7.99430	−	4.13415i	−8.92553			13.2321			21.2631	+	10.9960i	15.6137	−	15.6137i	66.2966			46.8176	+	66.0993i	−35.1946

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
41.c	even	4	1	inner
123.f	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	123.5.f.a	✓	108
3.b	odd	2	1	inner	123.5.f.a	✓	108
41.c	even	4	1	inner	123.5.f.a	✓	108
123.f	odd	4	1	inner	123.5.f.a	✓	108

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
123.5.f.a	✓	108	1.a	even	1	1	trivial
123.5.f.a	✓	108	3.b	odd	2	1	inner
123.5.f.a	✓	108	41.c	even	4	1	inner
123.5.f.a	✓	108	123.f	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(123, [\chi])\).