Space of modular forms of level 465, weight 2, and Character 465.bk

• Label: 465.2.bk
• Level: $465$
• Weight: $2$
• Character orbit: 465.bk
• Rep. character: $\chi_{465}(58,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $256$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.bk (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).

	Total	New	Old
Modular forms	544	256	288
Cusp forms	480	256	224
Eisenstein series	64	0	64

Trace form

\( 256 q + 12 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
465.2.bk.a	$465$	$2$	465.bk	155.r	$20$	$256$	$32$	$3.713$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(465, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)