Space of modular forms of level 405, weight 3, and Character 405.v

• Label: 405.3.v
• Level: $405$
• Weight: $3$
• Character orbit: 405.v
• Rep. character: $\chi_{405}(14,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $1908$
• Newform subspaces: $1$
• Sturm bound: $162$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.v (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 405 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(162\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(405, [\chi])\).

	Total	New	Old
Modular forms	1980	1980	0
Cusp forms	1908	1908	0
Eisenstein series	72	72	0

Trace form

\( 1908 q - 36 q^{4} - 18 q^{5} - 36 q^{6} - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(405, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
405.3.v.a	$405$	$3$	405.v	405.v	$54$	$1908$	$106$	$11.035$		None		$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{54}]$