Newform orbit 105.4.q.b

• Label: 105.4.q.b
• Level: $105$
• Weight: $4$
• Character orbit: 105.q
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−4.85916	+	2.80544i	−2.59808	−	1.50000i	11.7410	−	20.3360i	2.40235	−	10.9192i	16.8326			−9.44251	−	15.9323i			86.8672i	4.50000	+	7.79423i	18.9597	+	59.7978i
4.2	−4.10597	+	2.37058i	−2.59808	−	1.50000i	7.23930	−	12.5388i	−2.66182	+	10.8589i	14.2235			15.6813	+	9.85381i			30.7161i	4.50000	+	7.79423i	−14.8124	−	50.8961i
4.3	−3.89316	+	2.24772i	2.59808	+	1.50000i	6.10447	−	10.5732i	−0.533135	−	11.1676i	−13.4863			−3.71892	+	18.1430i			18.9210i	4.50000	+	7.79423i	27.1772	+	42.2790i
4.4	−3.00489	+	1.73487i	−2.59808	−	1.50000i	2.01958	−	3.49802i	−10.2956	−	4.35891i	10.4092			−12.4845	+	13.6798i		−	13.7431i	4.50000	+	7.79423i	38.4994	−	4.76357i
4.5	−2.89323	+	1.67041i	−2.59808	−	1.50000i	1.58052	−	2.73755i	9.21296	+	6.33414i	10.0224			−6.15758	−	17.4667i		−	16.1660i	4.50000	+	7.79423i	−37.2358	−	2.93674i
4.6	−2.21373	+	1.27810i	2.59808	+	1.50000i	−0.732945	+	1.26950i	5.74885	−	9.58910i	−7.66857			−2.98784	−	18.2777i		−	24.1966i	4.50000	+	7.79423i	−0.470588	+	28.5752i
4.7	−2.01833	+	1.16528i	2.59808	+	1.50000i	−1.28423	+	2.22435i	7.90497	+	7.90642i	−6.99170			18.1257	+	3.80267i		−	24.6305i	4.50000	+	7.79423i	−25.1681	−	6.74622i
4.8	−1.96118	+	1.13229i	2.59808	+	1.50000i	−1.43586	+	2.48698i	−5.60388	+	9.67453i	−6.79371			−18.1088	−	3.88231i		−	24.6198i	4.50000	+	7.79423i	0.0358556	−	25.3186i
4.9	−1.50072	+	0.866440i	−2.59808	−	1.50000i	−2.49856	+	4.32764i	10.6609	−	3.36827i	5.19864			−14.9159	+	10.9780i		−	22.5225i	4.50000	+	7.79423i	−13.0806	+	14.2919i
4.10	−0.761268	+	0.439518i	−2.59808	−	1.50000i	−3.61365	+	6.25902i	0.571597	−	11.1657i	2.63711			18.5184	−	0.260966i		−	13.3854i	4.50000	+	7.79423i	4.47240	+	8.75133i
4.11	−0.755385	+	0.436122i	−2.59808	−	1.50000i	−3.61960	+	6.26932i	−7.84576	+	7.96518i	2.61673			10.7711	−	15.0659i		−	13.2923i	4.50000	+	7.79423i	2.45278	−	9.43848i
4.12	0.755385	−	0.436122i	2.59808	+	1.50000i	−3.61960	+	6.26932i	10.8209	−	2.81204i	2.61673			−10.7711	+	15.0659i			13.2923i	4.50000	+	7.79423i	6.94757	−	6.84341i
4.13	0.761268	−	0.439518i	2.59808	+	1.50000i	−3.61365	+	6.25902i	−9.95559	−	5.08784i	2.63711			−18.5184	+	0.260966i			13.3854i	4.50000	+	7.79423i	−9.81508	+	0.502454i
4.14	1.50072	−	0.866440i	2.59808	+	1.50000i	−2.49856	+	4.32764i	−8.24745	+	7.54848i	5.19864			14.9159	−	10.9780i			22.5225i	4.50000	+	7.79423i	−5.83680	+	18.4741i
4.15	1.96118	−	1.13229i	−2.59808	−	1.50000i	−1.43586	+	2.48698i	11.1803	−	0.0158333i	−6.79371			18.1088	+	3.88231i			24.6198i	4.50000	+	7.79423i	21.9087	−	12.6904i
4.16	2.01833	−	1.16528i	−2.59808	−	1.50000i	−1.28423	+	2.22435i	2.89467	+	10.7991i	−6.99170			−18.1257	−	3.80267i			24.6305i	4.50000	+	7.79423i	18.4264	+	18.4231i
4.17	2.21373	−	1.27810i	−2.59808	−	1.50000i	−0.732945	+	1.26950i	−11.1788	+	0.184097i	−7.66857			2.98784	+	18.2777i			24.1966i	4.50000	+	7.79423i	−24.5116	+	14.6951i
4.18	2.89323	−	1.67041i	2.59808	+	1.50000i	1.58052	−	2.73755i	0.879049	+	11.1457i	10.0224			6.15758	+	17.4667i			16.1660i	4.50000	+	7.79423i	21.1612	+	30.7788i
4.19	3.00489	−	1.73487i	2.59808	+	1.50000i	2.01958	−	3.49802i	1.37289	−	11.0957i	10.4092			12.4845	−	13.6798i			13.7431i	4.50000	+	7.79423i	−15.1243	−	35.7232i
4.20	3.89316	−	2.24772i	−2.59808	−	1.50000i	6.10447	−	10.5732i	−9.40488	−	6.04552i	−13.4863			3.71892	−	18.1430i		−	18.9210i	4.50000	+	7.79423i	−50.2033	−	2.39667i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.c	even	3	1	inner
35.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.4.q.b	✓	44
5.b	even	2	1	inner	105.4.q.b	✓	44
7.c	even	3	1	inner	105.4.q.b	✓	44
35.j	even	6	1	inner	105.4.q.b	✓	44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.4.q.b	✓	44	1.a	even	1	1	trivial
105.4.q.b	✓	44	5.b	even	2	1	inner
105.4.q.b	✓	44	7.c	even	3	1	inner
105.4.q.b	✓	44	35.j	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^44 - 119*T2^42 + 8222*T2^40 - 380331*T2^38 + 13122870*T2^36 - 349049139*T2^34 + 7390505005*T2^32 - 125992945308*T2^30 + 1752715229332*T2^28 - 19967363779452*T2^26 + 187293711900220*T2^24 - 1444058189798352*T2^22 + 9153959489267248*T2^20 - 47358491196280128*T2^18 + 198741153119470096*T2^16 - 664619000079658560*T2^14 + 1743111469820213248*T2^12 - 3446517512462797824*T2^10 + 5009670010940267520*T2^8 - 4877223084564029440*T2^6 + 3403802875256029184*T2^4 - 1437968411901100032*T2^2 + 381211289352994816