Space of modular forms of level 252, weight 2, and Character 252.l

• Label: 252.2.l
• Level: $252$
• Weight: $2$
• Character orbit: 252.l
• Rep. character: $\chi_{252}(193,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

	Total	New	Old
Modular forms	108	16	92
Cusp forms	84	16	68
Eisenstein series	24	0	24

Trace form

16 * q + 8 * q^5 + q^7 + 4 * q^9 + 4 * q^11 - q^13 + 7 * q^15 - 5 * q^17 + 2 * q^19 + 4 * q^21 - 14 * q^23 + 16 * q^25 + 9 * q^27 + 2 * q^29 + 2 * q^31 + 5 * q^33 - 11 * q^35 - q^37 - 29 * q^39 - 24 * q^41 + 2 * q^43 - 7 * q^45 - 6 * q^47 - 11 * q^49 - q^51 - 18 * q^53 - 12 * q^55 - 3 * q^57 - 7 * q^59 - 13 * q^61 - 51 * q^63 + 9 * q^65 - 7 * q^67 - 43 * q^69 - 14 * q^71 + 14 * q^73 + q^75 + 35 * q^77 - q^79 + 40 * q^81 - 26 * q^83 - 6 * q^85 - 5 * q^87 - 21 * q^89 + 5 * q^91 + 7 * q^93 - 38 * q^95 - q^97 - 17 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.2.l.a	$252$	$2$	252.l	63.g	$3$	$2$	$1$	$2.012$	\(\Q(\sqrt{-3}) \)	None		✓			252.2.i.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
252.2.l.b	$252$	$2$	252.l	63.g	$3$	$14$	$7$	$2.012$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		252.2.i.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(-\beta _{5}+\beta _{9})q^{5}+\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

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