Newform orbit 102.3.g.a

• Label: 102.3.g.a
• Level: $102$
• Weight: $3$
• Character orbit: 102.g
• Analytic conductor: $2.779$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	102.g (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.77929869648\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} - 4 q^{3} + 8 q^{5} - 4 q^{6} + 48 q^{8} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−1.00000	+	1.00000i	−2.99213	+	0.217178i		−	2.00000i	6.80153	−	2.81729i	2.77495	−	3.20931i	−4.23680	+	10.2285i	2.00000	+	2.00000i	8.90567	−	1.29965i	−3.98424	+	9.61881i
53.2	−1.00000	+	1.00000i	−2.75240	+	1.19345i		−	2.00000i	−4.11443	+	1.70425i	1.55895	−	3.94584i	3.38980	−	8.18369i	2.00000	+	2.00000i	6.15136	−	6.56968i	2.41018	−	5.81868i
53.3	−1.00000	+	1.00000i	−0.652740	−	2.92813i		−	2.00000i	−4.65399	+	1.92774i	3.58087	+	2.27539i	−2.09074	+	5.04748i	2.00000	+	2.00000i	−8.14786	+	3.82261i	2.72624	−	6.58173i
53.4	−1.00000	+	1.00000i	1.44150	+	2.63099i		−	2.00000i	8.38391	−	3.47273i	−4.07248	−	1.18949i	4.03095	−	9.73156i	2.00000	+	2.00000i	−4.84418	+	7.58511i	−4.91118	+	11.8566i
53.5	−1.00000	+	1.00000i	2.25893	+	1.97414i		−	2.00000i	−5.37152	+	2.22495i	−4.23307	+	0.284793i	−2.50368	+	6.04441i	2.00000	+	2.00000i	1.20555	+	8.91889i	3.14656	−	7.59647i
53.6	−1.00000	+	1.00000i	2.40394	−	1.79473i		−	2.00000i	0.954492	−	0.395364i	−0.609212	+	4.19867i	1.41047	−	3.40519i	2.00000	+	2.00000i	2.55788	−	8.62886i	−0.559128	+	1.34986i
59.1	−1.00000	−	1.00000i	−2.93919	+	0.600948i			2.00000i	−0.428717	+	1.03501i	3.54014	+	2.33825i	6.44216	−	2.66843i	2.00000	−	2.00000i	8.27772	−	3.53260i	1.46373	−	0.606297i
59.2	−1.00000	−	1.00000i	−1.74901	−	2.43741i			2.00000i	2.86999	−	6.92878i	−0.688400	+	4.18642i	−3.89899	+	1.61501i	2.00000	−	2.00000i	−2.88193	+	8.52611i	−9.79877	+	4.05878i
59.3	−1.00000	−	1.00000i	−1.09720	+	2.79216i			2.00000i	0.662668	−	1.59982i	3.88936	−	1.69497i	−6.62040	+	2.74226i	2.00000	−	2.00000i	−6.59233	−	6.12709i	−2.26249	+	0.937154i
59.4	−1.00000	−	1.00000i	−1.02341	−	2.82004i			2.00000i	−3.17305	+	7.66043i	−1.79663	+	3.84345i	−4.03128	+	1.66981i	2.00000	−	2.00000i	−6.90527	+	5.77210i	10.8335	−	4.48738i
59.5	−1.00000	−	1.00000i	2.30284	−	1.92275i			2.00000i	−0.384648	+	0.928622i	−4.22558	−	0.380090i	10.5359	−	4.36410i	2.00000	−	2.00000i	1.60610	−	8.85553i	1.31327	−	0.543974i
59.6	−1.00000	−	1.00000i	2.79886	+	1.07998i			2.00000i	2.45376	−	5.92389i	−1.71888	−	3.87885i	−2.42737	+	1.00545i	2.00000	−	2.00000i	6.66728	+	6.04544i	−8.37765	+	3.47014i
77.1	−1.00000	−	1.00000i	−2.99213	−	0.217178i			2.00000i	6.80153	+	2.81729i	2.77495	+	3.20931i	−4.23680	−	10.2285i	2.00000	−	2.00000i	8.90567	+	1.29965i	−3.98424	−	9.61881i
77.2	−1.00000	−	1.00000i	−2.75240	−	1.19345i			2.00000i	−4.11443	−	1.70425i	1.55895	+	3.94584i	3.38980	+	8.18369i	2.00000	−	2.00000i	6.15136	+	6.56968i	2.41018	+	5.81868i
77.3	−1.00000	−	1.00000i	−0.652740	+	2.92813i			2.00000i	−4.65399	−	1.92774i	3.58087	−	2.27539i	−2.09074	−	5.04748i	2.00000	−	2.00000i	−8.14786	−	3.82261i	2.72624	+	6.58173i
77.4	−1.00000	−	1.00000i	1.44150	−	2.63099i			2.00000i	8.38391	+	3.47273i	−4.07248	+	1.18949i	4.03095	+	9.73156i	2.00000	−	2.00000i	−4.84418	−	7.58511i	−4.91118	−	11.8566i
77.5	−1.00000	−	1.00000i	2.25893	−	1.97414i			2.00000i	−5.37152	−	2.22495i	−4.23307	−	0.284793i	−2.50368	−	6.04441i	2.00000	−	2.00000i	1.20555	−	8.91889i	3.14656	+	7.59647i
77.6	−1.00000	−	1.00000i	2.40394	+	1.79473i			2.00000i	0.954492	+	0.395364i	−0.609212	−	4.19867i	1.41047	+	3.40519i	2.00000	−	2.00000i	2.55788	+	8.62886i	−0.559128	−	1.34986i
83.1	−1.00000	+	1.00000i	−2.93919	−	0.600948i		−	2.00000i	−0.428717	−	1.03501i	3.54014	−	2.33825i	6.44216	+	2.66843i	2.00000	+	2.00000i	8.27772	+	3.53260i	1.46373	+	0.606297i
83.2	−1.00000	+	1.00000i	−1.74901	+	2.43741i		−	2.00000i	2.86999	+	6.92878i	−0.688400	−	4.18642i	−3.89899	−	1.61501i	2.00000	+	2.00000i	−2.88193	−	8.52611i	−9.79877	−	4.05878i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
51.g	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	102.3.g.a	✓	24
3.b	odd	2	1		102.3.g.b	yes	24
17.d	even	8	1		102.3.g.b	yes	24
51.g	odd	8	1	inner	102.3.g.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
102.3.g.a	✓	24	1.a	even	1	1	trivial
102.3.g.a	✓	24	51.g	odd	8	1	inner
102.3.g.b	yes	24	3.b	odd	2	1
102.3.g.b	yes	24	17.d	even	8	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 8*T5^23 + 56*T5^21 + 576*T5^20 + 11016*T5^19 - 59376*T5^18 + 1059576*T5^17 + 12110505*T5^16 - 84387920*T5^15 - 245460016*T5^14 + 3467459808*T5^13 - 1245606016*T5^12 - 33192071648*T5^11 + 879685071264*T5^10 + 4759729775552*T5^9 + 5672953107224*T5^8 + 3580808570688*T5^7 + 31630015937344*T5^6 - 16393917851136*T5^5 + 31139403330048*T5^4 - 66663062668288*T5^3 + 39538358744448*T5^2 - 13228995013760*T5 + 48988408685584