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

• Label: 462.2.y
• Level: $462$
• Weight: $2$
• Character orbit: 462.y
• Rep. character: $\chi_{462}(25,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $128$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	832	128	704
Cusp forms	704	128	576
Eisenstein series	128	0	128

Trace form

128 * q + 16 * q^4 + 8 * q^5 + 8 * q^6 + 8 * q^7 + 16 * q^9 + 36 * q^10 + 8 * q^11 + 16 * q^13 + 4 * q^14 + 12 * q^15 + 16 * q^16 + 12 * q^17 - 16 * q^20 - 4 * q^22 + 8 * q^23 - 4 * q^24 + 40 * q^25 + 8 * q^26 + 22 * q^28 + 24 * q^29 - 8 * q^30 - 6 * q^31 + 2 * q^33 + 32 * q^34 + 8 * q^35 - 32 * q^36 + 20 * q^37 + 8 * q^38 - 14 * q^40 - 24 * q^41 + 14 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 + 88 * q^47 + 8 * q^49 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 16 * q^54 + 12 * q^55 + 8 * q^56 + 16 * q^57 - 2 * q^58 - 32 * q^59 + 4 * q^60 + 20 * q^61 - 96 * q^62 + 20 * q^63 - 32 * q^64 - 96 * q^65 - 96 * q^67 + 12 * q^68 - 40 * q^69 - 66 * q^70 - 144 * q^71 - 32 * q^73 - 16 * q^74 + 8 * q^75 - 80 * q^76 - 64 * q^77 - 16 * q^79 - 12 * q^80 + 16 * q^81 - 24 * q^82 - 208 * q^83 - 96 * q^85 - 36 * q^86 + 4 * q^87 - 18 * q^88 - 80 * q^89 + 8 * q^90 - 36 * q^91 - 16 * q^92 + 28 * q^93 - 56 * q^94 - 12 * q^95 - 4 * q^96 - 24 * q^97 - 48 * q^98 - 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.y.a	$462$	$2$	462.y	77.m	$15$	$24$	$3$	$3.689$		None		✓			462.2.y.a	$4$	$0$	\(-3\)	\(-3\)	\(5\)	\(11\)		$\mathrm{SU}(2)[C_{15}]$
462.2.y.b	$462$	$2$	462.y	77.m	$15$	$24$	$3$	$3.689$		None		✓			462.2.y.b	$4$	$0$	\(3\)	\(3\)	\(5\)	\(-5\)		$\mathrm{SU}(2)[C_{15}]$
462.2.y.c	$462$	$2$	462.y	77.m	$15$	$40$	$5$	$3.689$		None		✓			462.2.y.c	$4$	$0$	\(-5\)	\(5\)	\(1\)	\(9\)		$\mathrm{SU}(2)[C_{15}]$
462.2.y.d	$462$	$2$	462.y	77.m	$15$	$40$	$5$	$3.689$		None		✓			462.2.y.d	$4$	$0$	\(5\)	\(-5\)	\(-3\)	\(-7\)		$\mathrm{SU}(2)[C_{15}]$

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

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