Space of modular forms of level 444, weight 2, and Character 444.ba

• Label: 444.2.ba
• Level: $444$
• Weight: $2$
• Character orbit: 444.ba
• Rep. character: $\chi_{444}(95,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $432$
• Newform subspaces: $1$
• Sturm bound: $152$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.ba (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 444 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(152\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(444, [\chi])\).

	Total	New	Old
Modular forms	480	480	0
Cusp forms	432	432	0
Eisenstein series	48	48	0

Trace form

432 * q - 12 * q^4 - 12 * q^9 - 6 * q^10 - 21 * q^12 - 48 * q^13 - 36 * q^16 + 15 * q^18 - 12 * q^21 + 24 * q^22 - 51 * q^24 - 24 * q^25 - 36 * q^28 - 48 * q^30 + 6 * q^33 - 12 * q^34 - 12 * q^36 - 12 * q^37 + 48 * q^40 - 51 * q^42 - 18 * q^45 - 6 * q^46 - 3 * q^48 + 12 * q^49 + 18 * q^52 - 9 * q^54 - 12 * q^57 + 36 * q^58 - 72 * q^60 + 24 * q^61 - 6 * q^64 - 81 * q^66 - 30 * q^69 - 126 * q^70 - 105 * q^72 - 48 * q^73 - 18 * q^76 - 45 * q^78 - 12 * q^81 - 108 * q^82 - 60 * q^84 + 12 * q^85 - 18 * q^88 - 72 * q^90 - 84 * q^93 - 36 * q^94 + 117 * q^96 - 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(444, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
444.2.ba.a	$444$	$2$	444.ba	444.aa	$18$	$432$	$72$	$3.545$		None		✓	✓	✓	444.2.ba.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$