Newform orbit 105.3.t.b

• Label: 105.3.t.b
• Level: $105$
• Weight: $3$
• Character orbit: 105.t
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−3.31814	+	1.91573i	1.84164	+	2.36819i	5.34002	−	9.24919i	−1.93649	+	1.11803i	−10.6476	−	4.32991i	−5.86414	+	3.82255i			25.5943i	−2.21669	+	8.72274i	4.28370	−	7.41958i
11.2	−2.61597	+	1.51033i	−0.469377	−	2.96305i	2.56220	−	4.43785i	1.93649	−	1.11803i	5.70307	+	7.04234i	−4.99419	+	4.90490i			3.39641i	−8.55937	+	2.78158i	−3.37720	+	5.84948i
11.3	−2.60397	+	1.50340i	2.88780	−	0.812762i	2.52044	−	4.36553i	1.93649	−	1.11803i	−6.29785	+	6.45794i	−0.494553	−	6.98251i			3.12973i	7.67884	−	4.69420i	−3.36171	+	5.82265i
11.4	−2.46897	+	1.42546i	−2.92531	−	0.665249i	2.06389	−	3.57476i	−1.93649	+	1.11803i	8.17081	−	2.52744i	−5.93505	−	3.71149i			0.364297i	8.11489	+	3.89212i	3.18743	−	5.52080i
11.5	−2.31825	+	1.33844i	2.46021	−	1.71679i	1.58287	−	2.74161i	−1.93649	+	1.11803i	−3.40557	+	7.27281i	4.89419	+	5.00469i		−	2.23323i	3.10528	−	8.44732i	2.99285	−	5.18377i
11.6	−1.50527	+	0.869067i	−1.65926	+	2.49937i	−0.489445	+	0.847743i	−1.93649	+	1.11803i	0.325501	−	5.20423i	2.93407	+	6.35541i		−	8.65398i	−3.49374	−	8.29420i	1.94329	−	3.36588i
11.7	−0.987174	+	0.569945i	−0.202464	−	2.99316i	−1.35032	+	2.33883i	−1.93649	+	1.11803i	1.90581	+	2.83938i	2.61061	−	6.49498i		−	7.63801i	−8.91802	+	1.21201i	1.27444	−	2.20739i
11.8	−0.860118	+	0.496589i	2.51213	+	1.63987i	−1.50680	+	2.60985i	1.93649	−	1.11803i	−2.97507	−	0.162987i	−1.66850	+	6.79824i		−	6.96575i	3.62163	+	8.23916i	−1.11041	+	1.92328i
11.9	−0.644768	+	0.372257i	−2.67627	+	1.35556i	−1.72285	+	2.98406i	1.93649	−	1.11803i	1.22096	−	1.87029i	−5.98242	−	3.63464i		−	5.54343i	5.32489	−	7.25573i	−0.832392	+	1.44175i
11.10	0.644768	−	0.372257i	0.164184	+	2.99550i	−1.72285	+	2.98406i	−1.93649	+	1.11803i	1.22096	+	1.87029i	−5.98242	−	3.63464i			5.54343i	−8.94609	+	0.983626i	−0.832392	+	1.44175i
11.11	0.860118	−	0.496589i	−2.67624	−	1.35563i	−1.50680	+	2.60985i	−1.93649	+	1.11803i	−2.97507	+	0.162987i	−1.66850	+	6.79824i			6.96575i	5.32451	+	7.25600i	−1.11041	+	1.92328i
11.12	0.987174	−	0.569945i	2.69338	−	1.32124i	−1.35032	+	2.33883i	1.93649	−	1.11803i	1.90581	−	2.83938i	2.61061	−	6.49498i			7.63801i	5.50864	−	7.11722i	1.27444	−	2.20739i
11.13	1.50527	−	0.869067i	−1.33489	+	2.68664i	−0.489445	+	0.847743i	1.93649	−	1.11803i	0.325501	+	5.20423i	2.93407	+	6.35541i			8.65398i	−5.43612	−	7.17277i	1.94329	−	3.36588i
11.14	2.31825	−	1.33844i	0.256676	−	2.98900i	1.58287	−	2.74161i	1.93649	−	1.11803i	−3.40557	−	7.27281i	4.89419	+	5.00469i			2.23323i	−8.86824	−	1.53441i	2.99285	−	5.18377i
11.15	2.46897	−	1.42546i	2.03878	+	2.20077i	2.06389	−	3.57476i	1.93649	−	1.11803i	8.17081	+	2.52744i	−5.93505	−	3.71149i		−	0.364297i	−0.686770	+	8.97376i	3.18743	−	5.52080i
11.16	2.60397	−	1.50340i	−0.740030	−	2.90729i	2.52044	−	4.36553i	−1.93649	+	1.11803i	−6.29785	−	6.45794i	−0.494553	−	6.98251i		−	3.12973i	−7.90471	+	4.30297i	−3.36171	+	5.82265i
11.17	2.61597	−	1.51033i	2.80077	−	1.07503i	2.56220	−	4.43785i	−1.93649	+	1.11803i	5.70307	−	7.04234i	−4.99419	+	4.90490i		−	3.39641i	6.68860	−	6.02184i	−3.37720	+	5.84948i
11.18	3.31814	−	1.91573i	−2.97174	−	0.410813i	5.34002	−	9.24919i	1.93649	−	1.11803i	−10.6476	+	4.32991i	−5.86414	+	3.82255i		−	25.5943i	8.66247	+	2.44166i	4.28370	−	7.41958i
86.1	−3.31814	−	1.91573i	1.84164	−	2.36819i	5.34002	+	9.24919i	−1.93649	−	1.11803i	−10.6476	+	4.32991i	−5.86414	−	3.82255i		−	25.5943i	−2.21669	−	8.72274i	4.28370	+	7.41958i
86.2	−2.61597	−	1.51033i	−0.469377	+	2.96305i	2.56220	+	4.43785i	1.93649	+	1.11803i	5.70307	−	7.04234i	−4.99419	−	4.90490i		−	3.39641i	−8.55937	−	2.78158i	−3.37720	−	5.84948i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
21.h	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.3.t.b	✓	36
3.b	odd	2	1	inner	105.3.t.b	✓	36
7.c	even	3	1	inner	105.3.t.b	✓	36
21.h	odd	6	1	inner	105.3.t.b	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.3.t.b	✓	36	1.a	even	1	1	trivial
105.3.t.b	✓	36	3.b	odd	2	1	inner
105.3.t.b	✓	36	7.c	even	3	1	inner
105.3.t.b	✓	36	21.h	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^36 - 54*T2^34 + 1713*T2^32 - 36282*T2^30 + 573854*T2^28 - 6959778*T2^26 + 66770733*T2^24 - 507416694*T2^22 + 3076742670*T2^20 - 14659706670*T2^18 + 54620790105*T2^16 - 153959182710*T2^14 + 329628738209*T2^12 - 511720301004*T2^10 + 594289603224*T2^8 - 486224490072*T2^6 + 286715060416*T2^4 - 102420074880*T2^2 + 22915904400