Newform orbit 576.2.y.a

• Label: 576.2.y.a
• Level: $576$
• Weight: $2$
• Character orbit: 576.y
• Analytic conductor: $4.599$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.59938315643\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(22\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1		0		−1.72804	+	0.117756i		0		−0.961558	+	3.58858i		0		1.29216	−	2.23809i		0		2.97227	−	0.406975i		0
47.2		0		−1.68223	−	0.412428i		0		0.0776974	−	0.289971i		0		0.374023	−	0.647827i		0		2.65981	+	1.38760i		0
47.3		0		−1.53620	−	0.800065i		0		1.00059	−	3.73424i		0		1.68236	−	2.91393i		0		1.71979	+	2.45811i		0
47.4		0		−1.38573	+	1.03912i		0		0.310357	−	1.15827i		0		−0.356047	+	0.616691i		0		0.840471	−	2.87986i		0
47.5		0		−1.33407	+	1.10465i		0		0.178044	−	0.664471i		0		−0.645693	+	1.11837i		0		0.559489	−	2.94737i		0
47.6		0		−1.06447	−	1.36635i		0		0.619079	−	2.31044i		0		−2.51270	+	4.35213i		0		−0.733803	+	2.90887i		0
47.7		0		−1.05993	−	1.36987i		0		−0.746784	+	2.78704i		0		−1.16672	+	2.02082i		0		−0.753089	+	2.90394i		0
47.8		0		−0.819834	+	1.52574i		0		−0.206232	+	0.769670i		0		2.17574	−	3.76849i		0		−1.65574	−	2.50170i		0
47.9		0		−0.632098	+	1.61259i		0		−1.02195	+	3.81396i		0		−1.46715	+	2.54117i		0		−2.20090	−	2.03863i		0
47.10		0		−0.517369	−	1.65298i		0		−0.521033	+	1.94452i		0		0.322227	−	0.558114i		0		−2.46466	+	1.71040i		0
47.11		0		0.256373	−	1.71297i		0		0.546024	−	2.03779i		0		0.0638076	−	0.110518i		0		−2.86855	−	0.878321i		0
47.12		0		0.313101	+	1.70352i		0		0.752772	−	2.80938i		0		1.02581	−	1.77675i		0		−2.80394	+	1.06674i		0
47.13		0		0.377192	−	1.69048i		0		0.282421	−	1.05401i		0		1.93586	−	3.35301i		0		−2.71545	−	1.27527i		0
47.14		0		0.427367	+	1.67850i		0		−0.0458174	+	0.170993i		0		−1.17432	+	2.03397i		0		−2.63471	+	1.43467i		0
47.15		0		0.692394	−	1.58764i		0		−0.759273	+	2.83365i		0		−1.41719	+	2.45465i		0		−2.04118	−	2.19854i		0
47.16		0		1.21512	+	1.23430i		0		−0.726024	+	2.70956i		0		0.00424642	−	0.00735502i		0		−0.0469689	+	2.99963i		0
47.17		0		1.32549	+	1.11494i		0		0.323102	−	1.20583i		0		−0.140266	+	0.242948i		0		0.513832	+	2.95567i		0
47.18		0		1.49488	−	0.874828i		0		0.473330	−	1.76649i		0		−1.40613	+	2.43549i		0		1.46935	−	2.61553i		0
47.19		0		1.59321	−	0.679468i		0		−0.642590	+	2.39818i		0		1.93190	−	3.34616i		0		2.07665	−	2.16507i		0
47.20		0		1.65787	−	0.501476i		0		0.997280	−	3.72190i		0		0.481387	−	0.833787i		0		2.49704	−	1.66276i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
16.f	odd	4	1	inner
144.u	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	576.2.y.a		88
3.b	odd	2	1		1728.2.z.a		88
4.b	odd	2	1		144.2.u.a	✓	88
9.c	even	3	1		1728.2.z.a		88
9.d	odd	6	1	inner	576.2.y.a		88
12.b	even	2	1		432.2.v.a		88
16.e	even	4	1		144.2.u.a	✓	88
16.f	odd	4	1	inner	576.2.y.a		88
36.f	odd	6	1		432.2.v.a		88
36.h	even	6	1		144.2.u.a	✓	88
48.i	odd	4	1		432.2.v.a		88
48.k	even	4	1		1728.2.z.a		88
144.u	even	12	1	inner	576.2.y.a		88
144.v	odd	12	1		1728.2.z.a		88
144.w	odd	12	1		144.2.u.a	✓	88
144.x	even	12	1		432.2.v.a		88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.2.u.a	✓	88	4.b	odd	2	1
144.2.u.a	✓	88	16.e	even	4	1
144.2.u.a	✓	88	36.h	even	6	1
144.2.u.a	✓	88	144.w	odd	12	1
432.2.v.a		88	12.b	even	2	1
432.2.v.a		88	36.f	odd	6	1
432.2.v.a		88	48.i	odd	4	1
432.2.v.a		88	144.x	even	12	1
576.2.y.a		88	1.a	even	1	1	trivial
576.2.y.a		88	9.d	odd	6	1	inner
576.2.y.a		88	16.f	odd	4	1	inner
576.2.y.a		88	144.u	even	12	1	inner
1728.2.z.a		88	3.b	odd	2	1
1728.2.z.a		88	9.c	even	3	1
1728.2.z.a		88	48.k	even	4	1
1728.2.z.a		88	144.v	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(576, [\chi])\).