Space of modular forms of level 444 and weight 2

• Label: 444.2
• Level: 444
• Weight: 2
• Dimension: 2322
• Nonzero newspaces: 18
• Newform subspaces: 50
• Sturm bound: 21888
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(21888\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(444))\).

	Total	New	Old
Modular forms	5832	2458	3374
Cusp forms	5113	2322	2791
Eisenstein series	719	136	583

Trace form

2322 * q - 36 * q^4 - 18 * q^6 - 36 * q^9 - 36 * q^10 - 18 * q^12 - 72 * q^13 - 36 * q^16 - 18 * q^18 - 36 * q^21 - 36 * q^22 - 18 * q^24 - 72 * q^25 + 6 * q^27 - 36 * q^28 + 36 * q^29 - 18 * q^30 + 108 * q^31 - 36 * q^34 + 108 * q^35 - 36 * q^36 + 12 * q^37 + 42 * q^39 - 36 * q^40 + 108 * q^41 - 18 * q^42 + 72 * q^43 - 36 * q^45 - 36 * q^46 + 36 * q^47 - 18 * q^48 - 24 * q^49 - 36 * q^52 - 18 * q^54 - 36 * q^57 - 72 * q^58 - 72 * q^59 - 144 * q^60 - 162 * q^61 - 180 * q^62 - 108 * q^63 - 288 * q^64 - 162 * q^65 - 270 * q^66 - 72 * q^67 - 216 * q^68 - 180 * q^69 - 432 * q^70 - 144 * q^71 - 270 * q^72 - 288 * q^73 - 288 * q^74 - 180 * q^75 - 324 * q^76 - 144 * q^77 - 270 * q^78 - 144 * q^79 - 396 * q^80 - 180 * q^81 - 252 * q^82 - 72 * q^83 - 270 * q^84 - 234 * q^85 - 252 * q^86 - 108 * q^87 - 216 * q^88 - 90 * q^89 - 144 * q^90 - 72 * q^91 - 36 * q^92 - 90 * q^93 - 36 * q^94 - 18 * q^96 - 72 * q^97 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
444.2.a	\(\chi_{444}(1, \cdot)\)	444.2.a.a	1	1
		444.2.a.b	1
		444.2.a.c	2
		444.2.a.d	2
444.2.c	\(\chi_{444}(371, \cdot)\)	444.2.c.a	8	1
		444.2.c.b	8
		444.2.c.c	20
		444.2.c.d	36
444.2.e	\(\chi_{444}(73, \cdot)\)	444.2.e.a	4	1
		444.2.e.b	4
444.2.g	\(\chi_{444}(443, \cdot)\)	444.2.g.a	4	1
		444.2.g.b	4
		444.2.g.c	16
		444.2.g.d	48
444.2.i	\(\chi_{444}(121, \cdot)\)	444.2.i.a	2	2
		444.2.i.b	4
		444.2.i.c	6
444.2.k	\(\chi_{444}(31, \cdot)\)	444.2.k.a	2	2
		444.2.k.b	2
		444.2.k.c	36
		444.2.k.d	36
444.2.m	\(\chi_{444}(401, \cdot)\)	444.2.m.a	4	2
		444.2.m.b	4
		444.2.m.c	4
		444.2.m.d	12
444.2.p	\(\chi_{444}(11, \cdot)\)	444.2.p.a	4	2
		444.2.p.b	4
		444.2.p.c	136
444.2.r	\(\chi_{444}(85, \cdot)\)	444.2.r.a	2	2
		444.2.r.b	2
		444.2.r.c	4
		444.2.r.d	8
444.2.t	\(\chi_{444}(47, \cdot)\)	444.2.t.a	144	2
444.2.u	\(\chi_{444}(49, \cdot)\)	444.2.u.a	12	6
		444.2.u.b	18
444.2.w	\(\chi_{444}(29, \cdot)\)	444.2.w.a	4	4
		444.2.w.b	4
		444.2.w.c	40
444.2.y	\(\chi_{444}(103, \cdot)\)	444.2.y.a	8	4
		444.2.y.b	8
		444.2.y.c	68
		444.2.y.d	68
444.2.z	\(\chi_{444}(71, \cdot)\)	444.2.z.a	432	6
444.2.ba	\(\chi_{444}(95, \cdot)\)	444.2.ba.a	432	6
444.2.bb	\(\chi_{444}(25, \cdot)\)	444.2.bb.a	18	6
		444.2.bb.b	24
444.2.bg	\(\chi_{444}(5, \cdot)\)	444.2.bg.a	12	12
		444.2.bg.b	144
444.2.bh	\(\chi_{444}(19, \cdot)\)	444.2.bh.a	228	12
		444.2.bh.b	228

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(444))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(444)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)