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

• Label: 462.2.k
• Level: $462$
• Weight: $2$
• Character orbit: 462.k
• Rep. character: $\chi_{462}(89,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $7$
• Sturm bound: $192$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(192\)
Trace bound:			\(15\)
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	56	152
Cusp forms	176	56	120
Eisenstein series	32	0	32

Trace form

56 * q + 28 * q^4 + 16 * q^7 + 4 * q^9 - 8 * q^15 - 28 * q^16 + 8 * q^18 - 24 * q^19 + 16 * q^21 - 12 * q^24 - 36 * q^25 + 8 * q^28 + 24 * q^31 + 8 * q^36 - 12 * q^37 - 20 * q^39 + 36 * q^42 + 48 * q^45 + 16 * q^46 - 40 * q^49 + 4 * q^51 - 24 * q^52 - 36 * q^54 + 8 * q^57 + 12 * q^58 - 4 * q^60 - 56 * q^63 - 56 * q^64 + 32 * q^70 - 8 * q^72 + 48 * q^73 - 36 * q^75 - 20 * q^81 + 24 * q^82 - 4 * q^84 + 16 * q^85 - 36 * q^87 - 16 * q^91 - 28 * q^93 - 48 * q^94 - 12 * q^96

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.k.a	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	\(\Q(\zeta_{12})\)	None		✓			462.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.b	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	\(\Q(\zeta_{12})\)	None		✓			462.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.c	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	\(\Q(\zeta_{12})\)	None		✓			462.2.k.c	$4$	$0$	\(0\)	\(6\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(2-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.d	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	\(\Q(\zeta_{24})\)	None		✓			462.2.k.d	$4$	$0$	\(0\)	\(-12\)	\(0\)	\(4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{3}-\beta_1)q^{2}+(-\beta_{2}-1)q^{3}+\cdots\)
462.2.k.e	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	\(\Q(\zeta_{24})\)	None		✓			462.2.k.e	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}-\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
462.2.k.f	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	\(\Q(\zeta_{24})\)	None		✓			462.2.k.e	$2$	$0$	\(0\)	\(8\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
462.2.k.g	$462$	$2$	462.k	21.g	$6$	$20$	$10$	$3.689$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		462.2.k.g	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}-\beta _{12}q^{3}-\beta _{3}q^{4}+(2\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)

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

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