Space of modular forms of level 4320, weight 2, and Character 4320.b

• Label: 4320.2.b
• Level: $4320$
• Weight: $2$
• Character orbit: 4320.b
• Rep. character: $\chi_{4320}(431,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $1728$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4320 = 2^{5} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4320.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1728\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4320, [\chi])\).

	Total	New	Old
Modular forms	912	64	848
Cusp forms	816	64	752
Eisenstein series	96	0	96

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4320, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4320.2.b.a	$4320$	$2$	4320.b	24.f	$2$	$16$	$16$	$34.495$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+\beta _{1}q^{7}+\beta _{8}q^{11}-\beta _{13}q^{13}+\cdots\)
4320.2.b.b	$4320$	$2$	4320.b	24.f	$2$	$16$	$16$	$34.495$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}-\beta _{2}q^{7}+\beta _{11}q^{11}-\beta _{9}q^{13}+\cdots\)
4320.2.b.c	$4320$	$2$	4320.b	24.f	$2$	$16$	$16$	$34.495$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+\beta _{1}q^{7}-\beta _{8}q^{11}-\beta _{13}q^{13}+\cdots\)
4320.2.b.d	$4320$	$2$	4320.b	24.f	$2$	$16$	$16$	$34.495$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}-\beta _{2}q^{7}-\beta _{11}q^{11}-\beta _{9}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 9}\)