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

• Label: 465.2.g
• Level: $465$
• Weight: $2$
• Character orbit: 465.g
• Rep. character: $\chi_{465}(464,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $6$
• Sturm bound: $128$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 465 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(128\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	68	68	0
Cusp forms	60	60	0
Eisenstein series	8	8	0

Trace form

\( 60 q + 44 q^{4} - 8 q^{9} + O(q^{10}) \)

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.g.a	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-2-\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\)
465.2.g.b	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+3q^{4}-\beta _{1}q^{5}+\beta _{3}q^{6}+\cdots\)
465.2.g.c	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(2+\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\)
465.2.g.d	$465$	$2$	465.g	465.g	$2$	$8$	$8$	$3.713$	8.0.\(\cdots\).6	\(\Q(\sqrt{-155}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-2q^{4}+\beta _{4}q^{5}+\beta _{2}q^{9}-2\beta _{1}q^{12}+\cdots\)
465.2.g.e	$465$	$2$	465.g	465.g	$2$	$8$	$8$	$3.713$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{2}q^{2}-\zeta_{24}^{5}q^{3}+q^{4}+(-\zeta_{24}+\cdots)q^{5}+\cdots\)
465.2.g.f	$465$	$2$	465.g	465.g	$2$	$32$	$32$	$3.713$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$