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

• Label: 462.2.p
• Level: $462$
• Weight: $2$
• Character orbit: 462.p
• Rep. character: $\chi_{462}(241,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(13\)

Dimensions

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

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

Trace form

32 * q + 16 * q^4 + 24 * q^5 + 16 * q^9 - 8 * q^11 + 16 * q^14 - 8 * q^15 - 16 * q^16 + 4 * q^22 - 8 * q^23 + 20 * q^25 + 24 * q^26 + 12 * q^31 + 6 * q^33 + 32 * q^36 + 28 * q^37 - 24 * q^38 + 12 * q^42 + 8 * q^44 + 24 * q^45 - 48 * q^47 - 12 * q^49 + 8 * q^56 - 4 * q^60 - 32 * q^64 - 32 * q^67 - 60 * q^70 - 112 * q^71 - 24 * q^75 - 20 * q^77 - 24 * q^80 - 16 * q^81 - 24 * q^82 - 24 * q^86 + 2 * q^88 - 72 * q^89 - 16 * q^91 - 16 * q^92 + 8 * q^93 - 16 * 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.p.a	$462$	$2$	462.p	77.i	$6$	$16$	$8$	$3.689$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			462.2.p.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{13}q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots\)
462.2.p.b	$462$	$2$	462.p	77.i	$6$	$16$	$8$	$3.689$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			462.2.p.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{12}q^{2}+\beta _{11}q^{3}+(1+\beta _{13})q^{4}+\cdots\)

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

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