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

• Label: 444.2.e
• Level: $444$
• Weight: $2$
• Character orbit: 444.e
• Rep. character: $\chi_{444}(73,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	82	8	74
Cusp forms	70	8	62
Eisenstein series	12	0	12

Trace form

8 * q + 8 * q^9 - 8 * q^11 - 8 * q^21 - 8 * q^25 + 8 * q^33 + 8 * q^37 + 24 * q^41 + 8 * q^47 + 24 * q^49 - 8 * q^53 - 32 * q^65 - 16 * q^67 - 8 * q^71 + 16 * q^73 + 8 * q^75 - 48 * q^77 + 8 * q^81 + 16 * q^83 - 64 * q^85 - 40 * q^95 - 8 * q^99

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.e.a	$444$	$2$	444.e	37.b	$2$	$4$	$4$	$3.545$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		✓			444.2.e.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
444.2.e.b	$444$	$2$	444.e	37.b	$2$	$4$	$4$	$3.545$	4.0.32448.1	None		✓			444.2.e.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(444, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(444, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)