Space of modular forms of level 4752, weight 2, and Character 4752.o

• Label: 4752.2.o
• Level: $4752$
• Weight: $2$
• Character orbit: 4752.o
• Rep. character: $\chi_{4752}(703,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $1728$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 4752 = 2^{4} \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4752.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1728\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4752, [\chi])\).

	Total	New	Old
Modular forms	900	96	804
Cusp forms	828	96	732
Eisenstein series	72	0	72

Trace form

\( 96 q + 120 q^{25} + 72 q^{49} - 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4752, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4752.2.o.a	$4752$	$2$	4752.o	44.c	$2$	$4$	$4$	$37.945$	\(\Q(i, \sqrt{10})\)	None		✓			4752.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-q^{7}+(-\beta _{1}+\beta _{3})q^{11}-\beta _{2}q^{13}+\cdots\)
4752.2.o.b	$4752$	$2$	4752.o	44.c	$2$	$4$	$4$	$37.945$	\(\Q(i, \sqrt{10})\)	None		✓			4752.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+q^{7}+(\beta _{1}-\beta _{3})q^{11}-\beta _{2}q^{13}+\cdots\)
4752.2.o.c	$4752$	$2$	4752.o	44.c	$2$	$8$	$8$	$37.945$	\(\Q(i, \sqrt{6}, \sqrt{11})\)	\(\Q(\sqrt{-33}) \)		✓			4752.2.o.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{7}+\beta _{4}q^{11}+\beta _{3}q^{17}-\beta _{5}q^{19}+\cdots\)
4752.2.o.d	$4752$	$2$	4752.o	44.c	$2$	$16$	$16$	$37.945$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			4752.2.o.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{1}q^{7}+(-\beta _{7}-\beta _{9})q^{11}+\cdots\)
4752.2.o.e	$4752$	$2$	4752.o	44.c	$2$	$32$	$32$	$37.945$		None		✓			4752.2.o.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
4752.2.o.f	$4752$	$2$	4752.o	44.c	$2$	$32$	$32$	$37.945$		None		✓			4752.2.o.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4752, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4752, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1188, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1584, [\chi])\)\(^{\oplus 2}\)