Space of modular forms of level 495, weight 2, and Character 495.u

• Label: 495.2.u
• Level: $495$
• Weight: $2$
• Character orbit: 495.u
• Rep. character: $\chi_{495}(34,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

	Total	New	Old
Modular forms	152	120	32
Cusp forms	136	120	16
Eisenstein series	16	0	16

Trace form

\( 120 q + 60 q^{4} - q^{5} + 8 q^{6} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.2.u.a	$495$	$2$	495.u	45.j	$6$	$52$	$26$	$3.953$		None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
495.2.u.b	$495$	$2$	495.u	45.j	$6$	$68$	$34$	$3.953$		None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)