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

• Label: 495.4.d
• Level: $495$
• Weight: $4$
• Character orbit: 495.d
• Rep. character: $\chi_{495}(494,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	495.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	224	72	152
Cusp forms	208	72	136
Eisenstein series	16	0	16

Trace form

\( 72 q - 288 q^{4} + O(q^{10}) \)

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.d.a	$495$	$4$	495.d	165.d	$2$	$16$	$16$	$29.206$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	\(\Q(\sqrt{-55}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{13}q^{2}+(-8-\beta _{2}-\beta _{3})q^{4}+5\beta _{5}q^{5}+\cdots\)
495.4.d.b	$495$	$4$	495.d	165.d	$2$	$56$	$56$	$29.206$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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