Newform orbit 144.5.q.d

• Label: 144.5.q.d
• Level: $144$
• Weight: $5$
• Character orbit: 144.q
• Analytic conductor: $14.885$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.8852746841\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 72)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 100 q^{9}+O(q^{10}) \)

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		0		−8.92978	+	1.12208i		0		12.3374	−	7.12298i		0		−11.5784	+	20.0543i		0		78.4819	−	20.0399i		0
65.2		0		−8.44225	−	3.11903i		0		−14.6470	+	8.45647i		0		42.9574	−	74.4045i		0		61.5433	+	52.6632i		0
65.3		0		−5.77378	+	6.90387i		0		−33.3715	+	19.2670i		0		−45.3759	+	78.5934i		0		−14.3269	−	79.7229i		0
65.4		0		−4.50339	−	7.79227i		0		20.8375	−	12.0305i		0		−37.9185	+	65.6768i		0		−40.4389	+	70.1833i		0
65.5		0		−3.21271	+	8.40705i		0		36.5152	−	21.0820i		0		13.5757	−	23.5138i		0		−60.3569	−	54.0189i		0
65.6		0		−2.41484	+	8.66998i		0		−25.9859	+	15.0030i		0		37.7553	−	65.3941i		0		−69.3371	−	41.8733i		0
65.7		0		−2.36760	−	8.68300i		0		−20.4039	+	11.7802i		0		−0.0859679	+	0.148901i		0		−69.7889	+	41.1158i		0
65.8		0		5.34380	+	7.24181i		0		18.9074	−	10.9162i		0		−7.93787	+	13.7488i		0		−23.8877	+	77.3975i		0
65.9		0		5.78971	−	6.89052i		0		38.2277	−	22.0708i		0		25.3787	−	43.9571i		0		−13.9586	−	79.7882i		0
65.10		0		6.25234	−	6.47366i		0		−1.90728	+	1.10117i		0		9.68825	−	16.7805i		0		−2.81653	−	80.9510i		0
65.11		0		7.33134	+	5.22030i		0		−7.42683	+	4.28788i		0		2.37612	−	4.11556i		0		26.4970	+	76.5435i		0
65.12		0		8.92719	−	1.14252i		0		−23.0826	+	13.3268i		0		−28.8348	+	49.9434i		0		78.3893	−	20.3989i		0
113.1		0		−8.92978	−	1.12208i		0		12.3374	+	7.12298i		0		−11.5784	−	20.0543i		0		78.4819	+	20.0399i		0
113.2		0		−8.44225	+	3.11903i		0		−14.6470	−	8.45647i		0		42.9574	+	74.4045i		0		61.5433	−	52.6632i		0
113.3		0		−5.77378	−	6.90387i		0		−33.3715	−	19.2670i		0		−45.3759	−	78.5934i		0		−14.3269	+	79.7229i		0
113.4		0		−4.50339	+	7.79227i		0		20.8375	+	12.0305i		0		−37.9185	−	65.6768i		0		−40.4389	−	70.1833i		0
113.5		0		−3.21271	−	8.40705i		0		36.5152	+	21.0820i		0		13.5757	+	23.5138i		0		−60.3569	+	54.0189i		0
113.6		0		−2.41484	−	8.66998i		0		−25.9859	−	15.0030i		0		37.7553	+	65.3941i		0		−69.3371	+	41.8733i		0
113.7		0		−2.36760	+	8.68300i		0		−20.4039	−	11.7802i		0		−0.0859679	−	0.148901i		0		−69.7889	−	41.1158i		0
113.8		0		5.34380	−	7.24181i		0		18.9074	+	10.9162i		0		−7.93787	−	13.7488i		0		−23.8877	−	77.3975i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.5.q.d		24
3.b	odd	2	1		432.5.q.d		24
4.b	odd	2	1		72.5.m.a	✓	24
9.c	even	3	1		432.5.q.d		24
9.c	even	3	1		1296.5.e.j		24
9.d	odd	6	1	inner	144.5.q.d		24
9.d	odd	6	1		1296.5.e.j		24
12.b	even	2	1		216.5.m.a		24
36.f	odd	6	1		216.5.m.a		24
36.f	odd	6	1		648.5.e.c		24
36.h	even	6	1		72.5.m.a	✓	24
36.h	even	6	1		648.5.e.c		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.5.m.a	✓	24	4.b	odd	2	1
72.5.m.a	✓	24	36.h	even	6	1
144.5.q.d		24	1.a	even	1	1	trivial
144.5.q.d		24	9.d	odd	6	1	inner
216.5.m.a		24	12.b	even	2	1
216.5.m.a		24	36.f	odd	6	1
432.5.q.d		24	3.b	odd	2	1
432.5.q.d		24	9.c	even	3	1
648.5.e.c		24	36.f	odd	6	1
648.5.e.c		24	36.h	even	6	1
1296.5.e.j		24	9.c	even	3	1
1296.5.e.j		24	9.d	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 4500*T5^22 + 12994074*T5^20 + 63405000*T5^19 - 22136873440*T5^18 - 184228649208*T5^17 + 27230032673523*T5^16 + 368966933406000*T5^15 - 20521505188760760*T5^14 - 355858111510556472*T5^13 + 11236738801053051546*T5^12 + 243474015172406123376*T5^11 - 3636051076432086737004*T5^10 - 100911330839884179859704*T5^9 + 778680124668262737264321*T5^8 + 29731148427617019154635048*T5^7 - 7253930489155913418189592*T5^6 - 4351459363289796290005859904*T5^5 - 10535632580811997965453705936*T5^4 + 414998404094257061680663776000*T5^3 + 3756607593054610496249631749760*T5^2 + 10214474089355909732968110374400*T5 + 10435789190112251610840955404544