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

• Label: 252.2.bj
• Level: $252$
• Weight: $2$
• Character orbit: 252.bj
• Rep. character: $\chi_{252}(103,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• 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.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
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	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

88 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 6 * q^6 - 8 * q^8 - 2 * q^9 - 6 * q^10 - 18 * q^12 + 12 * q^14 - 2 * q^16 - 12 * q^17 - 4 * q^18 - 24 * q^20 - 2 * q^21 + 2 * q^22 + 6 * q^24 + 30 * q^25 - 12 * q^26 - 13 * q^30 - 2 * q^32 - 6 * q^33 - 6 * q^34 - 38 * q^36 - 4 * q^37 + 27 * q^38 - 18 * q^40 - 32 * q^42 - 5 * q^44 - 18 * q^45 + 2 * q^46 + 9 * q^48 - 2 * q^49 - 31 * q^50 - 27 * q^52 - 4 * q^53 - 39 * q^54 + 54 * q^56 + 12 * q^57 - 3 * q^58 + 17 * q^60 - 8 * q^64 - 28 * q^65 + 18 * q^66 - 18 * q^68 - 18 * q^69 + 5 * q^70 + 14 * q^72 - 12 * q^73 - 17 * q^74 + 12 * q^76 - 22 * q^77 - 3 * q^78 + 51 * q^80 - 50 * q^81 - 12 * q^82 + 23 * q^84 - 14 * q^85 + 13 * q^86 - 7 * q^88 - 72 * q^89 - 75 * q^90 + 44 * q^92 - 18 * q^93 + 39 * q^96 - 5 * q^98

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.bj.a	$252$	$2$	252.bj	252.aj	$6$	$4$	$2$	$2.012$	\(\Q(\zeta_{12})\)	None		✓			252.2.n.a	$4$	$1$	\(-4\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
252.2.bj.b	$252$	$2$	252.bj	252.aj	$6$	$84$	$42$	$2.012$		None		✓	✓		252.2.n.b	$4$	$0$	\(2\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$