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

• Label: 462.2.j
• Level: $462$
• Weight: $2$
• Character orbit: 462.j
• Rep. character: $\chi_{462}(169,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	416	48	368
Cusp forms	352	48	304
Eisenstein series	64	0	64

Trace form

\( 48 q - 12 q^{4} - 12 q^{9} + O(q^{10}) \)

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.j.a	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(-1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.b	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.c	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(1\)	\(-1\)	\(5\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.d	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(1\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.e	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.484000000.9	None		$2$	$0$	\(-2\)	\(-2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)
462.2.j.f	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.64000000.1	None		$2$	$0$	\(-2\)	\(2\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.j.g	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.324000000.3	None		$2$	$0$	\(2\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
462.2.j.h	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.\(\cdots\).8	None		$2$	$0$	\(2\)	\(2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)