Space of modular forms of level 4508, weight 2, and Character 4508.d

• Label: 4508.2.d
• Level: $4508$
• Weight: $2$
• Character orbit: 4508.d
• Rep. character: $\chi_{4508}(2253,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $1344$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4508 = 2^{2} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4508.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1344\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4508, [\chi])\).

	Total	New	Old
Modular forms	696	80	616
Cusp forms	648	80	568
Eisenstein series	48	0	48

Trace form

\( 80 q - 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4508, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4508.2.d.a	$4508$	$2$	4508.d	161.c	$2$	$32$	$32$	$35.997$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
4508.2.d.b	$4508$	$2$	4508.d	161.c	$2$	$48$	$48$	$35.997$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4508, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4508, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(644, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2254, [\chi])\)\(^{\oplus 2}\)