Newform orbit 79.5.d.a

• Label: 79.5.d.a
• Level: $79$
• Weight: $5$
• Character orbit: 79.d
• Analytic conductor: $8.166$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	79.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.16622708362\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Relative dimension:	\(26\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q + 2 q^{2} + 6 q^{3} - 234 q^{4} - q^{5} - 3 q^{6} + 120 q^{7} + 112 q^{8} + 640 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
24.1	−3.80092	+	6.58339i	11.8323	+	6.83138i	−20.8940	−	36.1894i	−18.8097	−	32.5793i	−89.9472	+	51.9310i	68.8798	−	39.7678i	196.036			52.8355	+	91.5137i	285.976
24.2	−3.77623	+	6.54062i	−9.28711	−	5.36192i	−20.5198	−	35.5414i	23.3794	+	40.4943i	70.1406	−	40.4957i	61.8061	−	35.6838i	189.111			17.0003	+	29.4454i	−353.144
24.3	−3.69654	+	6.40260i	−5.65613	−	3.26557i	−19.3289	−	33.4786i	−13.3616	−	23.1429i	41.8163	−	24.1426i	−61.0048	+	35.2211i	167.511			−19.1721	−	33.2071i	197.566
24.4	−3.04993	+	5.28263i	1.82944	+	1.05623i	−10.6041	−	18.3668i	2.83213	+	4.90539i	−11.1593	+	6.44283i	−19.7597	+	11.4083i	31.7693			−38.2688	−	66.2834i	−34.5511
24.5	−2.92725	+	5.07014i	9.11011	+	5.25972i	−9.13755	−	15.8267i	12.1322	+	21.0136i	−53.3351	+	30.7930i	2.38917	−	1.37939i	13.3196			14.8294	+	25.6852i	−142.056
24.6	−2.61590	+	4.53086i	−12.7137	−	7.34025i	−5.68582	−	9.84814i	−13.4455	−	23.2883i	66.5154	−	38.4027i	25.6627	−	14.8164i	−24.2146			67.2586	+	116.495i	140.688
24.7	−2.00291	+	3.46914i	−0.261440	−	0.150943i	−0.0233097	−	0.0403736i	−8.26508	−	14.3155i	1.04728	−	0.604649i	75.0244	−	43.3154i	−63.9064			−40.4544	−	70.0691i	66.2169
24.8	−1.85143	+	3.20678i	−10.5594	−	6.09650i	1.14439	+	1.98215i	11.5613	+	20.0247i	39.1002	−	22.5745i	−37.6867	+	21.7585i	−67.7209			33.8345	+	58.6031i	−85.6196
24.9	−1.80630	+	3.12861i	14.3398	+	8.27908i	1.47453	+	2.55397i	−7.01771	−	12.1550i	−51.8040	+	29.9091i	−49.6554	+	28.6685i	−68.4555			96.5862	+	167.292i	50.7045
24.10	−1.15283	+	1.99675i	2.43731	+	1.40718i	5.34199	+	9.25260i	−18.8657	−	32.6763i	−5.61959	+	3.24447i	−21.6881	+	12.5216i	−61.5239			−36.5397	−	63.2886i	86.9952
24.11	−0.849163	+	1.47079i	8.98392	+	5.18687i	6.55784	+	11.3585i	22.2316	+	38.5063i	−15.2576	+	8.80900i	36.3969	−	21.0138i	−49.4479			13.3072	+	23.0488i	−75.5131
24.12	−0.728886	+	1.26247i	−4.27989	−	2.47100i	6.93745	+	12.0160i	10.9460	+	18.9590i	6.23910	−	3.60215i	29.0237	−	16.7568i	−43.5508			−28.2884	−	48.9969i	−31.9135
24.13	0.148173	−	0.256643i	2.17495	+	1.25571i	7.95609	+	13.7804i	10.6629	+	18.4688i	0.644538	−	0.372124i	−78.3749	+	45.2497i	9.45705			−37.3464	−	64.6859i	6.31985
24.14	0.446812	−	0.773901i	11.4752	+	6.62520i	7.60072	+	13.1648i	−7.31431	−	12.6688i	10.2545	−	5.92043i	48.9149	−	28.2410i	27.8823			47.2865	+	81.9025i	−13.0725
24.15	0.508419	−	0.880607i	−11.6483	−	6.72515i	7.48302	+	12.9610i	−14.3771	−	24.9019i	−11.8444	+	6.83839i	−28.5918	+	16.5075i	31.4874			49.9553	+	86.5252i	−29.2384
24.16	0.697858	−	1.20873i	−8.47508	−	4.89309i	7.02599	+	12.1694i	−0.519176	−	0.899239i	−11.8288	+	6.82937i	36.3927	−	21.0114i	41.9440			7.38469	+	12.7907i	−1.44924
24.17	1.43591	−	2.48707i	9.16687	+	5.29250i	3.87631	+	6.71397i	1.55861	+	2.69960i	26.3257	−	15.1991i	−14.4458	+	8.34027i	68.2134			15.5210	+	26.8832i	8.95213
24.18	1.82909	−	3.16808i	2.34646	+	1.35473i	1.30885	+	2.26700i	−16.1149	−	27.9118i	8.58379	−	4.95585i	10.2231	−	5.90231i	68.1070			−36.8294	−	63.7904i	−117.903
24.19	2.17886	−	3.77390i	−2.97833	−	1.71954i	−1.49487	−	2.58919i	16.1442	+	27.9625i	−12.9787	+	7.49326i	33.6397	−	19.4219i	56.6951			−34.5864	−	59.9054i	140.703
24.20	2.29268	−	3.97105i	−14.1802	−	8.18693i	−2.51280	−	4.35230i	20.8386	+	36.0935i	−65.0214	+	37.5401i	−44.4394	+	25.6571i	50.3216			93.5517	+	162.036i	191.105

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.5.d.a	✓	52
79.d	odd	6	1	inner	79.5.d.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.5.d.a	✓	52	1.a	even	1	1	trivial
79.5.d.a	✓	52	79.d	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(79, [\chi])\).