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

• Label: 444.2.w
• Level: $444$
• Weight: $2$
• Character orbit: 444.w
• Rep. character: $\chi_{444}(29,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	328	48	280
Cusp forms	280	48	232
Eisenstein series	48	0	48

Trace form

48 * q + 2 * q^9 - 4 * q^13 - 8 * q^19 - 18 * q^21 + 40 * q^31 - 4 * q^37 + 14 * q^39 + 12 * q^43 - 54 * q^45 - 8 * q^49 + 14 * q^51 + 20 * q^55 + 46 * q^57 + 8 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 - 26 * q^81 - 32 * q^87 + 20 * q^91 + 6 * q^93 + 24 * q^97 - 12 * 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.w.a	$444$	$2$	444.w	111.m	$12$	$4$	$1$	$3.545$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			444.2.w.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1-\zeta_{12}^{2})q^{3}+(-\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
444.2.w.b	$444$	$2$	444.w	111.m	$12$	$4$	$1$	$3.545$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			444.2.w.b	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1+\zeta_{12}^{2})q^{3}+(-3\zeta_{12}+6\zeta_{12}^{3})q^{7}+\cdots\)
444.2.w.c	$444$	$2$	444.w	111.m	$12$	$40$	$10$	$3.545$		None		✓	✓		444.2.w.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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