Newform orbit 105.3.w.a

• Label: 105.3.w.a
• Level: $105$
• Weight: $3$
• Character orbit: 105.w
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 6 q^{3} - 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−3.72728	−	0.998723i	2.12159	+	2.12105i	9.43110	+	5.44505i	4.76718	+	1.50798i	−5.78944	−	10.0246i	−6.13877	+	3.36385i	−18.8000	−	18.8000i	0.00230342	+	9.00000i	−16.2626	−	10.3818i
17.2	−3.32412	−	0.890695i	−2.80275	−	1.06987i	6.79233	+	3.92155i	3.30138	−	3.75512i	8.36374	+	6.05276i	3.32240	−	6.16130i	−9.35192	−	9.35192i	6.71077	+	5.99713i	−14.3188	+	9.54193i
17.3	−3.26791	−	0.875634i	−2.44299	+	1.74120i	6.44841	+	3.72299i	−4.71757	+	1.65668i	9.50814	−	3.55093i	1.33404	+	6.87171i	−8.24376	−	8.24376i	2.93642	−	8.50749i	16.8672	−	1.28301i
17.4	−3.02468	−	0.810462i	−0.664693	−	2.92544i	5.02776	+	2.90278i	−2.83293	+	4.12001i	−0.360468	+	9.38723i	−5.96475	−	3.66357i	−3.99791	−	3.99791i	−8.11637	+	3.88904i	11.9078	−	10.1658i
17.5	−2.63032	−	0.704792i	1.27430	+	2.71591i	2.95775	+	1.70766i	−2.97248	−	4.02050i	−1.43765	−	8.04182i	6.12741	−	3.38450i	1.12583	+	1.12583i	−5.75234	+	6.92175i	4.98495	+	12.6702i
17.6	−2.58075	−	0.691511i	1.70571	−	2.46791i	2.71800	+	1.56924i	4.71996	+	1.64985i	−6.10859	+	5.18955i	6.61831	+	2.27990i	1.62763	+	1.62763i	−3.18114	−	8.41905i	−11.0402	−	7.52176i
17.7	−2.40293	−	0.643864i	2.79517	−	1.08950i	1.89543	+	1.09433i	−1.28155	−	4.83297i	−7.41810	+	0.818277i	−6.92060	−	1.05130i	3.18629	+	3.18629i	6.62599	−	6.09067i	−0.0322977	+	12.4385i
17.8	−1.98706	−	0.532431i	−0.853896	+	2.87591i	0.200820	+	0.115943i	1.13457	+	4.86958i	3.22797	−	5.25996i	−2.37777	−	6.58378i	5.48120	+	5.48120i	−7.54172	−	4.91146i	0.338264	−	10.2802i
17.9	−1.55206	−	0.415874i	−2.55828	+	1.56691i	−1.22815	−	0.709073i	3.76090	−	3.29479i	4.62225	−	1.36802i	−5.75785	+	3.98085i	6.15604	+	6.15604i	4.08961	−	8.01718i	−7.20738	+	3.54966i
17.10	−1.40147	−	0.375522i	−1.48402	−	2.60724i	−1.64101	−	0.947435i	−3.73472	−	3.32444i	1.10073	+	4.21124i	2.97299	+	6.33730i	6.04782	+	6.04782i	−4.59537	+	7.73838i	3.98568	+	6.06157i
17.11	−1.31040	−	0.351121i	2.87804	+	0.846693i	−1.87023	−	1.07978i	−2.09369	+	4.54054i	−3.47410	−	2.12005i	1.11647	+	6.91039i	5.90875	+	5.90875i	7.56622	+	4.87363i	4.33785	−	5.21479i
17.12	−0.667244	−	0.178787i	−2.94454	−	0.574167i	−3.05085	−	1.76141i	1.04868	+	4.88879i	1.86207	+	0.909557i	6.73061	−	1.92324i	3.67457	+	3.67457i	8.34066	+	3.38132i	0.174326	−	3.44951i
17.13	−0.161935	−	0.0433902i	−1.19649	−	2.75108i	−3.43976	−	1.98595i	4.97108	+	0.537016i	0.0743827	+	0.497410i	−6.97488	−	0.592480i	0.945023	+	0.945023i	−6.13684	+	6.58325i	−0.781688	−	0.302658i
17.14	−0.0875643	−	0.0234628i	2.77616	+	1.13706i	−3.45698	−	1.99589i	4.80744	−	1.37424i	−0.216414	−	0.164703i	2.18034	−	6.65178i	0.512285	+	0.512285i	6.41417	+	6.31335i	−0.453203	+	0.00753886i
17.15	0.0875643	+	0.0234628i	1.83570	−	2.37281i	−3.45698	−	1.99589i	−4.80744	+	1.37424i	0.216414	−	0.164703i	2.18034	−	6.65178i	−0.512285	−	0.512285i	−2.26044	−	8.71151i	−0.453203	+	0.00753886i
17.16	0.161935	+	0.0433902i	0.339350	+	2.98075i	−3.43976	−	1.98595i	−4.97108	−	0.537016i	−0.0743827	+	0.497410i	−6.97488	−	0.592480i	−0.945023	−	0.945023i	−8.76968	+	2.02303i	−0.781688	−	0.302658i
17.17	0.667244	+	0.178787i	−2.26297	+	1.96951i	−3.05085	−	1.76141i	−1.04868	−	4.88879i	−1.86207	+	0.909557i	6.73061	−	1.92324i	−3.67457	−	3.67457i	1.24202	−	8.91389i	0.174326	−	3.44951i
17.18	1.31040	+	0.351121i	2.06911	−	2.17228i	−1.87023	−	1.07978i	2.09369	−	4.54054i	3.47410	−	2.12005i	1.11647	+	6.91039i	−5.90875	−	5.90875i	−0.437576	−	8.98936i	4.33785	−	5.21479i
17.19	1.40147	+	0.375522i	0.0184202	+	2.99994i	−1.64101	−	0.947435i	3.73472	+	3.32444i	−1.10073	+	4.21124i	2.97299	+	6.33730i	−6.04782	−	6.04782i	−8.99932	+	0.110519i	3.98568	+	6.06157i
17.20	1.55206	+	0.415874i	−2.99899	−	0.0778404i	−1.22815	−	0.709073i	−3.76090	+	3.29479i	−4.62225	−	1.36802i	−5.75785	+	3.98085i	−6.15604	−	6.15604i	8.98788	+	0.466885i	−7.20738	+	3.54966i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.d	odd	6	1	inner
15.e	even	4	1	inner
21.g	even	6	1	inner
35.k	even	12	1	inner
105.w	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.3.w.a	✓	112
3.b	odd	2	1	inner	105.3.w.a	✓	112
5.c	odd	4	1	inner	105.3.w.a	✓	112
7.d	odd	6	1	inner	105.3.w.a	✓	112
15.e	even	4	1	inner	105.3.w.a	✓	112
21.g	even	6	1	inner	105.3.w.a	✓	112
35.k	even	12	1	inner	105.3.w.a	✓	112
105.w	odd	12	1	inner	105.3.w.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.3.w.a	✓	112	1.a	even	1	1	trivial
105.3.w.a	✓	112	3.b	odd	2	1	inner
105.3.w.a	✓	112	5.c	odd	4	1	inner
105.3.w.a	✓	112	7.d	odd	6	1	inner
105.3.w.a	✓	112	15.e	even	4	1	inner
105.3.w.a	✓	112	21.g	even	6	1	inner
105.3.w.a	✓	112	35.k	even	12	1	inner
105.3.w.a	✓	112	105.w	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(105, [\chi])\).