Space of modular forms of level 462, weight 2, and Character 462.g

• Label: 462.2.g
• Level: $462$
• Weight: $2$
• Character orbit: 462.g
• Rep. character: $\chi_{462}(419,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(462, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

\( 24 q - 24 q^{4} + 12 q^{7} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(462, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
462.2.g.a	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
462.2.g.b	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
462.2.g.c	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
462.2.g.d	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.g.e	$462$	$2$	462.g	21.c	$2$	$8$	$8$	$3.689$	8.0.342102016.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)