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

• Label: 252.2.j
• Level: $252$
• Weight: $2$
• Character orbit: 252.j
• Rep. character: $\chi_{252}(85,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
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	12	96
Cusp forms	84	12	72
Eisenstein series	24	0	24

Trace form

12 * q + 2 * q^5 + 4 * q^9 + 4 * q^11 - 2 * q^15 + 4 * q^17 + 12 * q^19 - 2 * q^21 - 8 * q^23 + 14 * q^29 + 6 * q^31 + 8 * q^33 - 8 * q^35 - 12 * q^37 - 20 * q^39 + 6 * q^41 - 6 * q^43 - 10 * q^45 - 6 * q^47 - 6 * q^49 - 22 * q^51 - 24 * q^53 - 12 * q^55 - 30 * q^57 - 28 * q^59 - 18 * q^65 + 32 * q^69 + 4 * q^71 + 12 * q^73 + 46 * q^75 + 8 * q^77 + 6 * q^79 - 32 * q^81 - 2 * q^83 + 30 * q^85 - 68 * q^87 + 36 * q^89 - 12 * q^91 + 22 * q^93 + 4 * q^95 + 24 * q^97 - 32 * 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.j.a	$252$	$2$	252.j	9.c	$3$	$6$	$3$	$2.012$	6.0.309123.1	None		✓			252.2.j.a	$2$	$0$	\(0\)	\(-2\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
252.2.j.b	$252$	$2$	252.j	9.c	$3$	$6$	$3$	$2.012$	6.0.309123.1	None		✓			252.2.j.b	$2$	$0$	\(0\)	\(2\)	\(3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)