Newform orbit 1152.2.p.g

• Label: 1152.2.p.g
• Level: $1152$
• Weight: $2$
• Character orbit: 1152.p
• Analytic conductor: $9.199$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.19876631285\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1		0		−1.68783	+	0.388876i		0		−0.538609	−	0.932899i		0		−4.07105	−	2.35042i		0		2.69755	−	1.31271i		0
191.2		0		−1.54472	−	0.783472i		0		−1.07112	−	1.85524i		0		1.13037	+	0.652621i		0		1.77234	+	2.42050i		0
191.3		0		−1.33523	+	1.10325i		0		1.43889	+	2.49224i		0		1.90348	+	1.09898i		0		0.565669	−	2.94619i		0
191.4		0		−0.944152	−	1.45209i		0		−0.637560	−	1.10429i		0		1.73560	+	1.00205i		0		−1.21715	+	2.74200i		0
191.5		0		−0.765007	+	1.55395i		0		−0.781546	−	1.35368i		0		−0.954503	−	0.551083i		0		−1.82953	−	2.37757i		0
191.6		0		−0.0745691	+	1.73044i		0		−2.11539	−	3.66397i		0		3.25610	+	1.87991i		0		−2.98888	−	0.258075i		0
191.7		0		0.0745691	−	1.73044i		0		2.11539	+	3.66397i		0		3.25610	+	1.87991i		0		−2.98888	−	0.258075i		0
191.8		0		0.765007	−	1.55395i		0		0.781546	+	1.35368i		0		−0.954503	−	0.551083i		0		−1.82953	−	2.37757i		0
191.9		0		0.944152	+	1.45209i		0		0.637560	+	1.10429i		0		1.73560	+	1.00205i		0		−1.21715	+	2.74200i		0
191.10		0		1.33523	−	1.10325i		0		−1.43889	−	2.49224i		0		1.90348	+	1.09898i		0		0.565669	−	2.94619i		0
191.11		0		1.54472	+	0.783472i		0		1.07112	+	1.85524i		0		1.13037	+	0.652621i		0		1.77234	+	2.42050i		0
191.12		0		1.68783	−	0.388876i		0		0.538609	+	0.932899i		0		−4.07105	−	2.35042i		0		2.69755	−	1.31271i		0
959.1		0		−1.68783	−	0.388876i		0		−0.538609	+	0.932899i		0		−4.07105	+	2.35042i		0		2.69755	+	1.31271i		0
959.2		0		−1.54472	+	0.783472i		0		−1.07112	+	1.85524i		0		1.13037	−	0.652621i		0		1.77234	−	2.42050i		0
959.3		0		−1.33523	−	1.10325i		0		1.43889	−	2.49224i		0		1.90348	−	1.09898i		0		0.565669	+	2.94619i		0
959.4		0		−0.944152	+	1.45209i		0		−0.637560	+	1.10429i		0		1.73560	−	1.00205i		0		−1.21715	−	2.74200i		0
959.5		0		−0.765007	−	1.55395i		0		−0.781546	+	1.35368i		0		−0.954503	+	0.551083i		0		−1.82953	+	2.37757i		0
959.6		0		−0.0745691	−	1.73044i		0		−2.11539	+	3.66397i		0		3.25610	−	1.87991i		0		−2.98888	+	0.258075i		0
959.7		0		0.0745691	+	1.73044i		0		2.11539	−	3.66397i		0		3.25610	−	1.87991i		0		−2.98888	+	0.258075i		0
959.8		0		0.765007	+	1.55395i		0		0.781546	−	1.35368i		0		−0.954503	+	0.551083i		0		−1.82953	+	2.37757i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
36.h	even	6	1	inner
72.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1152.2.p.g	yes	24
3.b	odd	2	1		3456.2.p.g		24
4.b	odd	2	1		1152.2.p.f	✓	24
8.b	even	2	1	inner	1152.2.p.g	yes	24
8.d	odd	2	1		1152.2.p.f	✓	24
9.c	even	3	1		3456.2.p.f		24
9.d	odd	6	1		1152.2.p.f	✓	24
12.b	even	2	1		3456.2.p.f		24
24.f	even	2	1		3456.2.p.f		24
24.h	odd	2	1		3456.2.p.g		24
36.f	odd	6	1		3456.2.p.g		24
36.h	even	6	1	inner	1152.2.p.g	yes	24
72.j	odd	6	1		1152.2.p.f	✓	24
72.l	even	6	1	inner	1152.2.p.g	yes	24
72.n	even	6	1		3456.2.p.f		24
72.p	odd	6	1		3456.2.p.g		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1152.2.p.f	✓	24	4.b	odd	2	1
1152.2.p.f	✓	24	8.d	odd	2	1
1152.2.p.f	✓	24	9.d	odd	6	1
1152.2.p.f	✓	24	72.j	odd	6	1
1152.2.p.g	yes	24	1.a	even	1	1	trivial
1152.2.p.g	yes	24	8.b	even	2	1	inner
1152.2.p.g	yes	24	36.h	even	6	1	inner
1152.2.p.g	yes	24	72.l	even	6	1	inner
3456.2.p.f		24	9.c	even	3	1
3456.2.p.f		24	12.b	even	2	1
3456.2.p.f		24	24.f	even	2	1
3456.2.p.f		24	72.n	even	6	1
3456.2.p.g		24	3.b	odd	2	1
3456.2.p.g		24	24.h	odd	2	1
3456.2.p.g		24	36.f	odd	6	1
3456.2.p.g		24	72.p	odd	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1152, [\chi])\):

T5^24 + 36*T5^22 + 858*T5^20 + 11056*T5^18 + 100995*T5^16 + 604704*T5^14 + 2657082*T5^12 + 8061492*T5^10 + 18173409*T5^8 + 28371184*T5^6 + 32231616*T5^4 + 22428672*T5^2 + 9834496

T7^12 - 6*T7^11 - 6*T7^10 + 108*T7^9 + 93*T7^8 - 2532*T7^7 + 8182*T7^6 - 9678*T7^5 - 1623*T7^4 + 11592*T7^3 + 1680*T7^2 - 18816*T7 + 12544

T11^24 - 78*T11^22 + 4161*T11^20 - 115682*T11^18 + 2305878*T11^16 - 24612702*T11^14 + 188576733*T11^12 - 819088134*T11^10 + 2425084134*T11^8 - 1352059994*T11^6 + 553662801*T11^4 - 102186102*T11^2 + 13845841