Newform orbit 576.4.k.c

• Label: 576.4.k.c
• Level: $576$
• Weight: $4$
• Character orbit: 576.k
• Analytic conductor: $33.985$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	576.k (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(33.9851001633\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{19} - 744 q^{31} - 16 q^{37} + 376 q^{43} - 1176 q^{49} - 912 q^{61} - 1440 q^{67} + 328 q^{79} - 240 q^{85} + 104 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
145.1		0			0			0		−14.8202	+	14.8202i		0			−	10.4191i		0			0			0
145.2		0			0			0		−9.19636	+	9.19636i		0				31.8982i		0			0			0
145.3		0			0			0		−8.32567	+	8.32567i		0				22.1273i		0			0			0
145.4		0			0			0		−5.80444	+	5.80444i		0				3.41531i		0			0			0
145.5		0			0			0		−5.16526	+	5.16526i		0			−	7.03833i		0			0			0
145.6		0			0			0		−4.01270	+	4.01270i		0			−	25.9833i		0			0			0
145.7		0			0			0		4.01270	−	4.01270i		0			−	25.9833i		0			0			0
145.8		0			0			0		5.16526	−	5.16526i		0			−	7.03833i		0			0			0
145.9		0			0			0		5.80444	−	5.80444i		0				3.41531i		0			0			0
145.10		0			0			0		8.32567	−	8.32567i		0				22.1273i		0			0			0
145.11		0			0			0		9.19636	−	9.19636i		0				31.8982i		0			0			0
145.12		0			0			0		14.8202	−	14.8202i		0			−	10.4191i		0			0			0
433.1		0			0			0		−14.8202	−	14.8202i		0				10.4191i		0			0			0
433.2		0			0			0		−9.19636	−	9.19636i		0			−	31.8982i		0			0			0
433.3		0			0			0		−8.32567	−	8.32567i		0			−	22.1273i		0			0			0
433.4		0			0			0		−5.80444	−	5.80444i		0			−	3.41531i		0			0			0
433.5		0			0			0		−5.16526	−	5.16526i		0				7.03833i		0			0			0
433.6		0			0			0		−4.01270	−	4.01270i		0				25.9833i		0			0			0
433.7		0			0			0		4.01270	+	4.01270i		0				25.9833i		0			0			0
433.8		0			0			0		5.16526	+	5.16526i		0				7.03833i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
16.e	even	4	1	inner
48.i	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	576.4.k.c		24
3.b	odd	2	1	inner	576.4.k.c		24
4.b	odd	2	1		144.4.k.c	✓	24
12.b	even	2	1		144.4.k.c	✓	24
16.e	even	4	1	inner	576.4.k.c		24
16.f	odd	4	1		144.4.k.c	✓	24
48.i	odd	4	1	inner	576.4.k.c		24
48.k	even	4	1		144.4.k.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.4.k.c	✓	24	4.b	odd	2	1
144.4.k.c	✓	24	12.b	even	2	1
144.4.k.c	✓	24	16.f	odd	4	1
144.4.k.c	✓	24	48.k	even	4	1
576.4.k.c		24	1.a	even	1	1	trivial
576.4.k.c		24	3.b	odd	2	1	inner
576.4.k.c		24	16.e	even	4	1	inner
576.4.k.c		24	48.i	odd	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 249216*T5^20 + 11828373696*T5^16 + 193462878781440*T5^12 + 1098483748776980480*T5^8 + 2315746557663487983616*T5^4 + 1422555319731368919040000