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

• Label: 465.2.k
• Level: $465$
• Weight: $2$
• Character orbit: 465.k
• Rep. character: $\chi_{465}(32,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

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

Trace form

\( 120 q - 8 q^{6} + O(q^{10}) \)

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.k.a	$465$	$2$	465.k	15.e	$4$	$60$	$30$	$3.713$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
465.2.k.b	$465$	$2$	465.k	15.e	$4$	$60$	$30$	$3.713$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$