Space of modular forms of level 252, weight 3, and Character 252.bd

• Label: 252.3.bd
• Level: $252$
• Weight: $3$
• Character orbit: 252.bd
• Rep. character: $\chi_{252}(229,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(252, [\chi])\).

	Total	New	Old
Modular forms	204	32	172
Cusp forms	180	32	148
Eisenstein series	24	0	24

Trace form

32 * q + q^7 + 18 * q^9 + 6 * q^11 - 15 * q^13 + 9 * q^15 - 27 * q^17 - 48 * q^21 - 15 * q^23 + 80 * q^25 + 9 * q^27 + 24 * q^29 + 141 * q^35 + 11 * q^37 - 111 * q^39 + 90 * q^41 - 16 * q^43 - 156 * q^45 + 11 * q^49 - 57 * q^51 + 54 * q^53 + 51 * q^57 + 117 * q^63 + 66 * q^65 + 70 * q^67 - 105 * q^69 + 138 * q^71 - 75 * q^75 - 33 * q^77 - 74 * q^79 - 18 * q^81 - 378 * q^83 + 30 * q^85 - 78 * q^87 - 261 * q^89 + 45 * q^91 - 321 * q^93 + 96 * q^95 + 57 * q^97 - 45 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(252, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.3.bd.a	$252$	$3$	252.bd	63.t	$6$	$32$	$16$	$6.867$		None		✓	✓	✓	252.3.p.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)