Space of modular forms of level 495, weight 4, and Character 495.f

• Label: 495.4.f
• Level: $495$
• Weight: $4$
• Character orbit: 495.f
• Rep. character: $\chi_{495}(296,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	495.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(495, [\chi])\).

	Total	New	Old
Modular forms	224	48	176
Cusp forms	208	48	160
Eisenstein series	16	0	16

Trace form

\( 48 q + 192 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.4.f.a	$495$	$4$	495.f	33.d	$2$	$48$	$48$	$29.206$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \)