Space of modular forms of level 1444 and weight 2

• Label: 1444.2
• Level: 1444
• Weight: 2
• Dimension: 37227
• Nonzero newspaces: 12
• Sturm bound: 259920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(259920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1444))\).

	Total	New	Old
Modular forms	66240	38163	28077
Cusp forms	63721	37227	26494
Eisenstein series	2519	936	1583

Trace form

37227 * q - 153 * q^2 - 153 * q^4 - 306 * q^5 - 153 * q^6 - 153 * q^8 - 306 * q^9 - 153 * q^10 - 153 * q^12 - 282 * q^13 - 153 * q^14 + 36 * q^15 - 153 * q^16 - 288 * q^17 - 171 * q^18 + 21 * q^19 - 297 * q^20 - 264 * q^21 - 153 * q^22 + 18 * q^23 - 153 * q^24 - 270 * q^25 - 153 * q^26 + 6 * q^27 - 207 * q^28 - 342 * q^29 - 279 * q^30 - 36 * q^31 - 243 * q^32 - 414 * q^33 - 243 * q^34 - 72 * q^35 - 333 * q^36 - 378 * q^37 - 225 * q^38 - 108 * q^39 - 279 * q^40 - 342 * q^41 - 333 * q^42 - 66 * q^43 - 243 * q^44 - 360 * q^45 - 243 * q^46 + 18 * q^47 - 279 * q^48 - 300 * q^49 - 207 * q^50 + 72 * q^51 - 153 * q^52 - 234 * q^53 - 99 * q^54 + 72 * q^55 - 171 * q^56 - 279 * q^57 - 297 * q^58 + 90 * q^59 - 171 * q^60 - 318 * q^61 - 63 * q^62 + 24 * q^63 - 9 * q^64 - 324 * q^65 - 9 * q^66 - 30 * q^67 - 27 * q^68 - 540 * q^69 + 63 * q^70 + 18 * q^71 + 117 * q^72 - 462 * q^73 - 45 * q^74 - 84 * q^75 - 72 * q^76 - 828 * q^77 - 9 * q^78 - 48 * q^79 - 9 * q^80 - 396 * q^81 + 117 * q^82 + 18 * q^83 + 63 * q^84 - 522 * q^85 - 27 * q^86 + 72 * q^87 - 9 * q^88 - 360 * q^89 - 99 * q^90 + 24 * q^91 - 63 * q^92 - 246 * q^93 - 171 * q^94 - 9 * q^95 - 441 * q^96 - 324 * q^97 - 351 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)

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
1444.2.a	\(\chi_{1444}(1, \cdot)\)	1444.2.a.a	1	1
		1444.2.a.b	1
		1444.2.a.c	1
		1444.2.a.d	2
		1444.2.a.e	2
		1444.2.a.f	2
		1444.2.a.g	6
		1444.2.a.h	6
		1444.2.a.i	8
1444.2.d	\(\chi_{1444}(1443, \cdot)\)	n/a	154	1
1444.2.e	\(\chi_{1444}(429, \cdot)\)	1444.2.e.a	2	2
		1444.2.e.b	2
		1444.2.e.c	2
		1444.2.e.d	4
		1444.2.e.e	4
		1444.2.e.f	4
		1444.2.e.g	12
		1444.2.e.h	12
		1444.2.e.i	16
1444.2.f	\(\chi_{1444}(791, \cdot)\)	n/a	308	2
1444.2.i	\(\chi_{1444}(245, \cdot)\)	n/a	168	6
1444.2.k	\(\chi_{1444}(127, \cdot)\)	n/a	924	6
1444.2.m	\(\chi_{1444}(77, \cdot)\)	n/a	558	18
1444.2.n	\(\chi_{1444}(75, \cdot)\)	n/a	3384	18
1444.2.q	\(\chi_{1444}(45, \cdot)\)	n/a	1116	36
1444.2.t	\(\chi_{1444}(27, \cdot)\)	n/a	6768	36
1444.2.u	\(\chi_{1444}(5, \cdot)\)	n/a	3456	108
1444.2.w	\(\chi_{1444}(3, \cdot)\)	n/a	20304	108

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1444)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)