Newform orbit 126.3.i.a

• Label: 126.3.i.a
• Level: $126$
• Weight: $3$
• Character orbit: 126.i
• Analytic conductor: $3.433$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.43325133094\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
65.1	−1.22474	+	0.707107i	−2.78154	+	1.12385i	1.00000	−	1.73205i		−	1.41430i	2.61199	−	3.34328i	3.88340	−	5.82402i			2.82843i	6.47391	−	6.25207i	1.00006	+	1.73216i
65.2	−1.22474	+	0.707107i	−2.66837	−	1.37106i	1.00000	−	1.73205i		−	2.72742i	4.23756	−	0.207617i	−4.37650	+	5.46317i			2.82843i	5.24037	+	7.31701i	1.92857	+	3.34039i
65.3	−1.22474	+	0.707107i	−2.19206	−	2.04814i	1.00000	−	1.73205i			6.40162i	4.13297	+	0.958429i	2.49631	−	6.53976i			2.82843i	0.610246	+	8.97929i	−4.52663	−	7.84035i
65.4	−1.22474	+	0.707107i	−0.515888	+	2.95531i	1.00000	−	1.73205i		−	7.66608i	−1.45789	−	3.98429i	−6.97124	+	0.633929i			2.82843i	−8.46772	−	3.04922i	5.42073	+	9.38899i
65.5	−1.22474	+	0.707107i	0.810726	+	2.88838i	1.00000	−	1.73205i			2.39465i	−3.03532	−	2.96426i	6.52929	+	2.52357i			2.82843i	−7.68545	+	4.68336i	−1.69327	−	2.93283i
65.6	−1.22474	+	0.707107i	0.894073	−	2.86367i	1.00000	−	1.73205i		−	3.35218i	0.929913	+	4.13948i	−6.40395	−	2.82655i			2.82843i	−7.40127	−	5.12067i	2.37035	+	4.10556i
65.7	−1.22474	+	0.707107i	2.28054	−	1.94914i	1.00000	−	1.73205i		−	0.989713i	−1.41483	+	3.99978i	4.95314	+	4.94635i			2.82843i	1.40174	−	8.89017i	0.699833	+	1.21215i
65.8	−1.22474	+	0.707107i	2.94777	+	0.557369i	1.00000	−	1.73205i			7.35342i	−4.00438	+	1.40175i	−6.95892	+	0.757275i			2.82843i	8.37868	+	3.28599i	−5.19965	−	9.00606i
65.9	1.22474	−	0.707107i	−2.97687	−	0.371810i	1.00000	−	1.73205i			8.56422i	−3.90882	+	1.64959i	4.01479	+	5.73423i		−	2.82843i	8.72351	+	2.21366i	6.05582	+	10.4890i
65.10	1.22474	−	0.707107i	−2.84195	+	0.960892i	1.00000	−	1.73205i		−	2.96160i	−2.80121	+	3.18641i	−2.14099	−	6.66455i		−	2.82843i	7.15337	−	5.46162i	−2.09417	−	3.62721i
65.11	1.22474	−	0.707107i	−1.40668	−	2.64976i	1.00000	−	1.73205i		−	6.30630i	−3.59649	−	2.25061i	−3.75927	+	5.90490i		−	2.82843i	−5.04249	+	7.45475i	−4.45923	−	7.72361i
65.12	1.22474	−	0.707107i	0.878690	−	2.86843i	1.00000	−	1.73205i			1.75162i	−0.952117	−	4.13443i	6.58841	−	2.36493i		−	2.82843i	−7.45581	−	5.04093i	1.23858	+	2.14528i
65.13	1.22474	−	0.707107i	0.907763	+	2.85936i	1.00000	−	1.73205i			8.31909i	3.13365	+	2.86011i	0.934868	−	6.93729i		−	2.82843i	−7.35193	+	5.19125i	5.88249	+	10.1888i
65.14	1.22474	−	0.707107i	0.953952	+	2.84429i	1.00000	−	1.73205i		−	9.69788i	3.17956	+	2.80898i	6.99572	+	0.244854i		−	2.82843i	−7.17995	+	5.42663i	−6.85744	−	11.8774i
65.15	1.22474	−	0.707107i	2.84405	−	0.954676i	1.00000	−	1.73205i		−	2.12829i	2.80817	−	3.18028i	−5.95128	−	3.68541i		−	2.82843i	7.17719	−	5.43028i	−1.50493	−	2.60662i
65.16	1.22474	−	0.707107i	2.86580	+	0.887244i	1.00000	−	1.73205i			2.45915i	4.13725	−	0.939777i	1.16622	+	6.90217i		−	2.82843i	7.42560	+	5.08533i	1.73888	+	3.01183i
95.1	−1.22474	−	0.707107i	−2.78154	−	1.12385i	1.00000	+	1.73205i			1.41430i	2.61199	+	3.34328i	3.88340	+	5.82402i		−	2.82843i	6.47391	+	6.25207i	1.00006	−	1.73216i
95.2	−1.22474	−	0.707107i	−2.66837	+	1.37106i	1.00000	+	1.73205i			2.72742i	4.23756	+	0.207617i	−4.37650	−	5.46317i		−	2.82843i	5.24037	−	7.31701i	1.92857	−	3.34039i
95.3	−1.22474	−	0.707107i	−2.19206	+	2.04814i	1.00000	+	1.73205i		−	6.40162i	4.13297	−	0.958429i	2.49631	+	6.53976i		−	2.82843i	0.610246	−	8.97929i	−4.52663	+	7.84035i
95.4	−1.22474	−	0.707107i	−0.515888	−	2.95531i	1.00000	+	1.73205i			7.66608i	−1.45789	+	3.98429i	−6.97124	−	0.633929i		−	2.82843i	−8.46772	+	3.04922i	5.42073	−	9.38899i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.n	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	126.3.i.a	✓	32
3.b	odd	2	1		378.3.i.a		32
7.c	even	3	1		126.3.r.a	yes	32
9.c	even	3	1		378.3.r.a		32
9.d	odd	6	1		126.3.r.a	yes	32
21.h	odd	6	1		378.3.r.a		32
63.g	even	3	1		378.3.i.a		32
63.n	odd	6	1	inner	126.3.i.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.3.i.a	✓	32	1.a	even	1	1	trivial
126.3.i.a	✓	32	63.n	odd	6	1	inner
126.3.r.a	yes	32	7.c	even	3	1
126.3.r.a	yes	32	9.d	odd	6	1
378.3.i.a		32	3.b	odd	2	1
378.3.i.a		32	63.g	even	3	1
378.3.r.a		32	9.c	even	3	1
378.3.r.a		32	21.h	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(126, [\chi])\).