Newform orbit 84.4.o.a

• Label: 84.4.o.a
• Level: $84$
• Weight: $4$
• Character orbit: 84.o
• Analytic conductor: $4.956$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.95616044048\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - q^{2} - 36 q^{3} - 5 q^{4} + 6 q^{6} + 10 q^{7} - 76 q^{8} - 108 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−2.75199	+	0.653091i	−1.50000	−	2.59808i	7.14694	−	3.59460i	9.22104	+	5.32377i	5.82477	+	6.17025i	−18.0489	−	4.15182i	−17.3207	+	14.5599i	−4.50000	+	7.79423i	−28.8532	−	8.62881i
19.2	−2.65324	−	0.979961i	−1.50000	−	2.59808i	6.07935	+	5.20014i	−3.65498	−	2.11020i	1.43384	+	8.36326i	4.33605	−	18.0055i	−11.0340	−	19.7547i	−4.50000	+	7.79423i	7.62961	+	9.18060i
19.3	−2.51510	+	1.29394i	−1.50000	−	2.59808i	4.65146	−	6.50876i	−13.3774	−	7.72344i	7.13439	+	4.59352i	10.8861	+	14.9831i	−3.27697	+	22.3889i	−4.50000	+	7.79423i	43.6391	+	2.11574i
19.4	−1.80305	−	2.17922i	−1.50000	−	2.59808i	−1.49801	+	7.85850i	8.01713	+	4.62869i	−2.95720	+	7.95330i	11.9290	+	14.1668i	19.8264	−	10.9048i	−4.50000	+	7.79423i	−4.36836	−	25.8169i
19.5	−0.746666	+	2.72809i	−1.50000	−	2.59808i	−6.88498	−	4.07395i	13.2084	+	7.62590i	8.20779	−	2.15224i	−10.0891	+	15.5309i	16.2549	−	15.7410i	−4.50000	+	7.79423i	−30.6665	+	30.3399i
19.6	−0.199616	−	2.82137i	−1.50000	−	2.59808i	−7.92031	+	1.12638i	−0.0819989	−	0.0473421i	−7.03072	+	4.75068i	−18.4054	−	2.05975i	4.75896	+	22.1213i	−4.50000	+	7.79423i	−0.117202	+	0.240800i
19.7	−0.0644263	+	2.82769i	−1.50000	−	2.59808i	−7.99170	−	0.364356i	−4.32707	−	2.49824i	7.44320	−	4.07416i	15.5037	−	10.1309i	1.54516	−	22.5746i	−4.50000	+	7.79423i	7.34303	−	12.0747i
19.8	1.49919	+	2.39842i	−1.50000	−	2.59808i	−3.50484	+	7.19139i	−11.8351	−	6.83298i	3.98249	−	7.49265i	−16.3232	+	8.74950i	−22.5024	+	2.37520i	−4.50000	+	7.79423i	−1.35469	−	38.6294i
19.9	1.63466	−	2.30822i	−1.50000	−	2.59808i	−2.65580	−	7.54631i	−12.0209	−	6.94026i	−8.44893	−	0.784626i	13.4721	+	12.7083i	−21.7599	−	6.20544i	−4.50000	+	7.79423i	−35.6697	+	16.4020i
19.10	2.12158	−	1.87053i	−1.50000	−	2.59808i	1.00225	−	7.93697i	18.9410	+	10.9356i	−8.04215	−	2.70625i	2.66595	−	18.3274i	−12.7200	−	18.7137i	−4.50000	+	7.79423i	60.6402	−	12.2289i
19.11	2.22073	+	1.75167i	−1.50000	−	2.59808i	1.86331	+	7.77998i	7.82897	+	4.52006i	1.21987	−	8.39714i	17.6230	−	5.69464i	−9.49004	+	20.5412i	−4.50000	+	7.79423i	9.46840	+	23.7516i
19.12	2.75793	−	0.627568i	−1.50000	−	2.59808i	7.21232	−	3.46157i	−11.9192	−	6.88154i	−5.76736	−	6.22395i	−8.54943	−	16.4289i	17.7187	−	14.0730i	−4.50000	+	7.79423i	−37.1908	−	11.4987i
31.1	−2.75199	−	0.653091i	−1.50000	+	2.59808i	7.14694	+	3.59460i	9.22104	−	5.32377i	5.82477	−	6.17025i	−18.0489	+	4.15182i	−17.3207	−	14.5599i	−4.50000	−	7.79423i	−28.8532	+	8.62881i
31.2	−2.65324	+	0.979961i	−1.50000	+	2.59808i	6.07935	−	5.20014i	−3.65498	+	2.11020i	1.43384	−	8.36326i	4.33605	+	18.0055i	−11.0340	+	19.7547i	−4.50000	−	7.79423i	7.62961	−	9.18060i
31.3	−2.51510	−	1.29394i	−1.50000	+	2.59808i	4.65146	+	6.50876i	−13.3774	+	7.72344i	7.13439	−	4.59352i	10.8861	−	14.9831i	−3.27697	−	22.3889i	−4.50000	−	7.79423i	43.6391	−	2.11574i
31.4	−1.80305	+	2.17922i	−1.50000	+	2.59808i	−1.49801	−	7.85850i	8.01713	−	4.62869i	−2.95720	−	7.95330i	11.9290	−	14.1668i	19.8264	+	10.9048i	−4.50000	−	7.79423i	−4.36836	+	25.8169i
31.5	−0.746666	−	2.72809i	−1.50000	+	2.59808i	−6.88498	+	4.07395i	13.2084	−	7.62590i	8.20779	+	2.15224i	−10.0891	−	15.5309i	16.2549	+	15.7410i	−4.50000	−	7.79423i	−30.6665	−	30.3399i
31.6	−0.199616	+	2.82137i	−1.50000	+	2.59808i	−7.92031	−	1.12638i	−0.0819989	+	0.0473421i	−7.03072	−	4.75068i	−18.4054	+	2.05975i	4.75896	−	22.1213i	−4.50000	−	7.79423i	−0.117202	−	0.240800i
31.7	−0.0644263	−	2.82769i	−1.50000	+	2.59808i	−7.99170	+	0.364356i	−4.32707	+	2.49824i	7.44320	+	4.07416i	15.5037	+	10.1309i	1.54516	+	22.5746i	−4.50000	−	7.79423i	7.34303	+	12.0747i
31.8	1.49919	−	2.39842i	−1.50000	+	2.59808i	−3.50484	−	7.19139i	−11.8351	+	6.83298i	3.98249	+	7.49265i	−16.3232	−	8.74950i	−22.5024	−	2.37520i	−4.50000	−	7.79423i	−1.35469	+	38.6294i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
28.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	84.4.o.a	✓	24
4.b	odd	2	1		84.4.o.b	yes	24
7.d	odd	6	1		84.4.o.b	yes	24
28.f	even	6	1	inner	84.4.o.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
84.4.o.a	✓	24	1.a	even	1	1	trivial
84.4.o.a	✓	24	28.f	even	6	1	inner
84.4.o.b	yes	24	4.b	odd	2	1
84.4.o.b	yes	24	7.d	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^24 - 6*T11^23 - 8863*T11^22 + 53250*T11^21 + 51135286*T11^20 + 142105854*T11^19 - 170527079539*T11^18 - 1485933449130*T11^17 + 411534757315526*T11^16 + 7410402989622066*T11^15 - 604957076717101195*T11^14 - 15983488365272236698*T11^13 + 607258959107296526269*T11^12 + 24449160511976034474708*T11^11 - 173344260018810071722268*T11^10 - 15889241807866742263508688*T11^9 + 775178701358328287363168*T11^8 + 7450949872315422219311774016*T11^7 + 58086811657369394316413038144*T11^6 - 1374734460840923323189735895808*T11^5 - 11315568371390250967525500844544*T11^4 + 200680462451674062676540720684032*T11^3 + 1456053841650355810182341352297472*T11^2 - 13645519652268251311812202801827840*T11 + 32172246338231211707459234616217600