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

• Label: 444.2.i
• Level: $444$
• Weight: $2$
• Character orbit: 444.i
• Rep. character: $\chi_{444}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $152$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$444 = 2^{2} \cdot 3 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	444.i (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$37$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$3$
Sturm bound:			$152$
Trace bound:			$1$
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	12	152
Cusp forms	140	12	128
Eisenstein series	24	0	24

Trace form

12 * q - 2 * q^5 - 6 * q^9 + 8 * q^11 + 4 * q^13 - 6 * q^17 - 6 * q^19 + 6 * q^21 - 4 * q^23 - 12 * q^25 + 12 * q^29 - 8 * q^31 + 6 * q^33 + 10 * q^35 - 8 * q^37 + 4 * q^41 + 20 * q^43 + 4 * q^45 + 12 * q^47 + 12 * q^49 - 12 * q^51 + 30 * q^53 + 20 * q^55 - 4 * q^57 - 4 * q^59 - 30 * q^65 - 2 * q^67 - 24 * q^71 - 52 * q^73 - 8 * q^75 - 4 * q^77 - 26 * q^79 - 6 * q^81 + 8 * q^83 - 36 * q^85 + 10 * q^87 - 14 * q^91 + 2 * q^93 - 6 * q^95 + 8 * q^97 - 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.i.a	$444$	$2$	444.i	37.c	$3$	$2$	$1$	$3.545$	$\Q(\sqrt{-3})$	None		✓			444.2.i.a	$2$	$0$	$0$	$1$	$-2$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}-2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$
444.2.i.b	$444$	$2$	444.i	37.c	$3$	$4$	$2$	$3.545$	$\Q(\sqrt{-3}, \sqrt{37})$	None		✓			444.2.i.b	$2$	$0$	$0$	$2$	$1$	$-6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}-3\beta _{2}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
444.2.i.c	$444$	$2$	444.i	37.c	$3$	$6$	$3$	$3.545$	6.0.27379323.1	None		✓	✓		444.2.i.c	$2$	$0$	$0$	$-3$	$-1$	$3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots$

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}$