Space of modular forms of level 252, weight 4, and Character 252.bm

• Label: 252.4.bm
• Level: $252$
• Weight: $4$
• Character orbit: 252.bm
• Rep. character: $\chi_{252}(173,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	276	48	228
Eisenstein series	24	0	24

Trace form

48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.4.bm.a	$252$	$4$	252.bm	63.s	$6$	$48$	$24$	$14.868$		None		✓	✓	✓	252.4.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)