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

• Label: 462.2.n
• Level: $462$
• Weight: $2$
• Character orbit: 462.n
• Rep. character: $\chi_{462}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $6$
• 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.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 231 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	208	64	144
Cusp forms	176	64	112
Eisenstein series	32	0	32

Trace form

64 * q - 32 * q^4 + 8 * q^9 - 16 * q^15 - 32 * q^16 - 4 * q^22 + 44 * q^25 - 24 * q^27 - 4 * q^31 + 26 * q^33 - 8 * q^34 - 16 * q^36 - 4 * q^37 - 24 * q^42 - 56 * q^45 + 4 * q^49 + 84 * q^55 - 32 * q^58 + 8 * q^60 + 64 * q^64 + 8 * q^66 + 8 * q^67 - 64 * q^69 + 52 * q^70 - 52 * q^75 - 48 * q^78 - 24 * q^81 + 16 * q^82 + 2 * q^88 - 24 * q^91 - 44 * q^93 + 32 * q^97 - 24 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
462.2.n.a	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			462.2.n.a	$2$	$0$	\(-2\)	\(-6\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
462.2.n.b	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			462.2.n.a	$2$	$0$	\(-2\)	\(6\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.c	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			462.2.n.a	$2$	$0$	\(2\)	\(-6\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.n.d	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			462.2.n.a	$2$	$0$	\(2\)	\(6\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.e	$462$	$2$	462.n	231.l	$6$	$24$	$12$	$3.689$		None		✓			462.2.n.e	$4$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
462.2.n.f	$462$	$2$	462.n	231.l	$6$	$24$	$12$	$3.689$		None		✓			462.2.n.e	$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)