Newform orbit 126.4.h.b

• Label: 126.4.h.b
• Level: $126$
• Weight: $4$
• Character orbit: 126.h
• Analytic conductor: $7.434$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.43424066072\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{2} + q^{3} - 48 q^{4} - 20 q^{5} + 4 q^{6} + 28 q^{7} - 192 q^{8} + 35 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	1.00000	−	1.73205i	−5.19502	+	0.108352i	−2.00000	−	3.46410i	−14.9231			−5.00735	+	9.10640i	14.0821	+	12.0289i	−8.00000			26.9765	−	1.12579i	−14.9231	+	25.8476i
67.2	1.00000	−	1.73205i	−5.07224	+	1.12799i	−2.00000	−	3.46410i	18.7213			−3.11852	+	9.91337i	−15.3695	+	10.3334i	−8.00000			24.4553	−	11.4428i	18.7213	−	32.4263i
67.3	1.00000	−	1.73205i	−4.90963	−	1.70164i	−2.00000	−	3.46410i	1.46289			−7.85695	+	6.80208i	−3.71747	−	18.1433i	−8.00000			21.2088	+	16.7088i	1.46289	−	2.53380i
67.4	1.00000	−	1.73205i	−2.54512	+	4.53016i	−2.00000	−	3.46410i	−3.11229			5.30134	+	8.93844i	8.38218	−	16.5148i	−8.00000			−14.0447	−	23.0596i	−3.11229	+	5.39064i
67.5	1.00000	−	1.73205i	−1.50507	−	4.97341i	−2.00000	−	3.46410i	−4.38272			−10.1193	−	2.36654i	−16.3832	+	8.63665i	−8.00000			−22.4695	+	14.9707i	−4.38272	+	7.59110i
67.6	1.00000	−	1.73205i	−1.14222	+	5.06906i	−2.00000	−	3.46410i	−0.521453			7.63764	+	7.04744i	−3.56519	+	18.1739i	−8.00000			−24.3907	−	11.5799i	−0.521453	+	0.903183i
67.7	1.00000	−	1.73205i	0.828671	−	5.12965i	−2.00000	−	3.46410i	15.6350			−8.05614	−	6.56495i	17.1578	−	6.97217i	−8.00000			−25.6266	−	8.50159i	15.6350	−	27.0807i
67.8	1.00000	−	1.73205i	2.97238	−	4.26204i	−2.00000	−	3.46410i	−20.5539			−4.40968	−	9.41035i	18.4043	+	2.06929i	−8.00000			−9.32991	−	25.3368i	−20.5539	+	35.6003i
67.9	1.00000	−	1.73205i	3.56146	+	3.78365i	−2.00000	−	3.46410i	−1.52253			10.1149	−	2.38499i	18.1220	−	3.82009i	−8.00000			−1.63195	+	26.9506i	−1.52253	+	2.63709i
67.10	1.00000	−	1.73205i	3.78642	+	3.55851i	−2.00000	−	3.46410i	−19.8520			9.94995	−	2.99976i	−18.1695	−	3.58722i	−8.00000			1.67397	+	26.9481i	−19.8520	+	34.3846i
67.11	1.00000	−	1.73205i	4.64047	−	2.33795i	−2.00000	−	3.46410i	3.49343			0.591024	−	10.3755i	−11.9430	−	14.1550i	−8.00000			16.0680	−	21.6984i	3.49343	−	6.05080i
67.12	1.00000	−	1.73205i	5.07990	+	1.09299i	−2.00000	−	3.46410i	15.5553			6.97302	−	7.70565i	6.99950	+	17.1466i	−8.00000			24.6107	+	11.1046i	15.5553	−	26.9425i
79.1	1.00000	+	1.73205i	−5.19502	−	0.108352i	−2.00000	+	3.46410i	−14.9231			−5.00735	−	9.10640i	14.0821	−	12.0289i	−8.00000			26.9765	+	1.12579i	−14.9231	−	25.8476i
79.2	1.00000	+	1.73205i	−5.07224	−	1.12799i	−2.00000	+	3.46410i	18.7213			−3.11852	−	9.91337i	−15.3695	−	10.3334i	−8.00000			24.4553	+	11.4428i	18.7213	+	32.4263i
79.3	1.00000	+	1.73205i	−4.90963	+	1.70164i	−2.00000	+	3.46410i	1.46289			−7.85695	−	6.80208i	−3.71747	+	18.1433i	−8.00000			21.2088	−	16.7088i	1.46289	+	2.53380i
79.4	1.00000	+	1.73205i	−2.54512	−	4.53016i	−2.00000	+	3.46410i	−3.11229			5.30134	−	8.93844i	8.38218	+	16.5148i	−8.00000			−14.0447	+	23.0596i	−3.11229	−	5.39064i
79.5	1.00000	+	1.73205i	−1.50507	+	4.97341i	−2.00000	+	3.46410i	−4.38272			−10.1193	+	2.36654i	−16.3832	−	8.63665i	−8.00000			−22.4695	−	14.9707i	−4.38272	−	7.59110i
79.6	1.00000	+	1.73205i	−1.14222	−	5.06906i	−2.00000	+	3.46410i	−0.521453			7.63764	−	7.04744i	−3.56519	−	18.1739i	−8.00000			−24.3907	+	11.5799i	−0.521453	−	0.903183i
79.7	1.00000	+	1.73205i	0.828671	+	5.12965i	−2.00000	+	3.46410i	15.6350			−8.05614	+	6.56495i	17.1578	+	6.97217i	−8.00000			−25.6266	+	8.50159i	15.6350	+	27.0807i
79.8	1.00000	+	1.73205i	2.97238	+	4.26204i	−2.00000	+	3.46410i	−20.5539			−4.40968	+	9.41035i	18.4043	−	2.06929i	−8.00000			−9.32991	+	25.3368i	−20.5539	−	35.6003i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.g	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	126.4.h.b	yes	24
3.b	odd	2	1		378.4.h.a		24
7.c	even	3	1		126.4.e.a	✓	24
9.c	even	3	1		126.4.e.a	✓	24
9.d	odd	6	1		378.4.e.b		24
21.h	odd	6	1		378.4.e.b		24
63.g	even	3	1	inner	126.4.h.b	yes	24
63.n	odd	6	1		378.4.h.a		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.4.e.a	✓	24	7.c	even	3	1
126.4.e.a	✓	24	9.c	even	3	1
126.4.h.b	yes	24	1.a	even	1	1	trivial
126.4.h.b	yes	24	63.g	even	3	1	inner
378.4.e.b		24	9.d	odd	6	1
378.4.e.b		24	21.h	odd	6	1
378.4.h.a		24	3.b	odd	2	1
378.4.h.a		24	63.n	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^12 + 10*T5^11 - 911*T5^10 - 7525*T5^9 + 277022*T5^8 + 1817453*T5^7 - 29010303*T5^6 - 150721743*T5^5 + 314293320*T5^4 + 1830241872*T5^3 + 199981629*T5^2 - 3281373099*T5 - 1534397742