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

• Label: 444.2.r
• Level: $444$
• Weight: $2$
• Character orbit: 444.r
• Rep. character: $\chi_{444}(85,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $152$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(152\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	164	16	148
Cusp forms	140	16	124
Eisenstein series	24	0	24

Trace form

16 * q - 8 * q^9 + 8 * q^11 - 18 * q^19 + 2 * q^21 + 20 * q^25 - 2 * q^33 + 54 * q^35 + 10 * q^37 + 24 * q^39 - 18 * q^41 + 4 * q^47 - 30 * q^49 + 26 * q^53 - 24 * q^57 - 48 * q^59 + 6 * q^61 - 22 * q^65 + 10 * q^67 + 24 * q^69 - 16 * q^71 - 28 * q^73 - 8 * q^75 - 12 * q^77 - 30 * q^79 - 8 * q^81 - 4 * q^83 - 32 * q^85 + 6 * q^87 + 42 * q^89 - 42 * q^91 - 30 * q^93 + 34 * q^95 - 4 * 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.r.a	$444$	$2$	444.r	37.e	$6$	$2$	$1$	$3.545$	\(\Q(\sqrt{-3}) \)	None		✓			444.2.r.a	$2$	$0$	\(0\)	\(-1\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{6}q^{3}+(-4+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
444.2.r.b	$444$	$2$	444.r	37.e	$6$	$2$	$1$	$3.545$	\(\Q(\sqrt{-3}) \)	None		✓			444.2.r.b	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}+2\zeta_{6}q^{7}+\cdots\)
444.2.r.c	$444$	$2$	444.r	37.e	$6$	$4$	$2$	$3.545$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			444.2.r.c	$2$	$0$	\(0\)	\(-2\)	\(9\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{3}+(3-2\beta _{2}+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
444.2.r.d	$444$	$2$	444.r	37.e	$6$	$8$	$4$	$3.545$	8.0.\(\cdots\).1	None		✓	✓		444.2.r.d	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{3})q^{3}+\beta _{5}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+\cdots\)

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

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