Space of modular forms of level 2888 and weight 2

• Label: 2888.2
• Level: 2888
• Weight: 2
• Dimension: 144459
• Nonzero newspaces: 18
• Sturm bound: 1039680
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(1039680\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2888))\).

	Total	New	Old
Modular forms	262944	146333	116611
Cusp forms	256897	144459	112438
Eisenstein series	6047	1874	4173

Trace form

144459 * q - 306 * q^2 - 306 * q^3 - 306 * q^4 - 306 * q^6 - 306 * q^7 - 306 * q^8 - 612 * q^9 - 306 * q^10 - 306 * q^11 - 306 * q^12 - 306 * q^14 - 306 * q^15 - 306 * q^16 - 612 * q^17 - 306 * q^18 - 324 * q^19 - 594 * q^20 - 306 * q^22 - 306 * q^23 - 306 * q^24 - 612 * q^25 - 306 * q^26 - 288 * q^27 - 306 * q^28 + 36 * q^29 - 306 * q^30 - 270 * q^31 - 306 * q^32 - 504 * q^33 - 306 * q^34 - 234 * q^35 - 306 * q^36 + 36 * q^37 - 324 * q^38 - 486 * q^39 - 306 * q^40 - 576 * q^41 - 306 * q^42 - 234 * q^43 - 306 * q^44 + 108 * q^45 - 306 * q^46 - 270 * q^47 - 306 * q^48 - 576 * q^49 - 306 * q^50 - 288 * q^51 - 306 * q^52 - 414 * q^54 - 306 * q^55 - 306 * q^56 - 648 * q^57 - 594 * q^58 - 306 * q^59 - 378 * q^60 - 36 * q^61 - 486 * q^62 - 450 * q^63 - 594 * q^64 - 720 * q^65 - 594 * q^66 - 522 * q^67 - 558 * q^68 - 738 * q^70 - 414 * q^71 - 846 * q^72 - 774 * q^73 - 594 * q^74 - 594 * q^75 - 504 * q^76 - 108 * q^77 - 666 * q^78 - 558 * q^79 - 594 * q^80 - 774 * q^81 - 846 * q^82 - 414 * q^83 - 738 * q^84 - 558 * q^86 - 522 * q^87 - 594 * q^88 - 720 * q^89 - 594 * q^90 - 450 * q^91 - 486 * q^92 - 36 * q^93 - 378 * q^94 - 288 * q^95 - 594 * q^96 - 540 * q^97 - 306 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)

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
2888.2.a	\(\chi_{2888}(1, \cdot)\)	2888.2.a.a	1	1
		2888.2.a.b	1
		2888.2.a.c	1
		2888.2.a.d	1
		2888.2.a.e	1
		2888.2.a.f	1
		2888.2.a.g	2
		2888.2.a.h	2
		2888.2.a.i	2
		2888.2.a.j	2
		2888.2.a.k	2
		2888.2.a.l	2
		2888.2.a.m	3
		2888.2.a.n	3
		2888.2.a.o	3
		2888.2.a.p	3
		2888.2.a.q	3
		2888.2.a.r	3
		2888.2.a.s	3
		2888.2.a.t	6
		2888.2.a.u	6
		2888.2.a.v	8
		2888.2.a.w	8
		2888.2.a.x	9
		2888.2.a.y	9
2888.2.b	\(\chi_{2888}(1443, \cdot)\)	n/a	324	1
2888.2.c	\(\chi_{2888}(1445, \cdot)\)	n/a	324	1
2888.2.h	\(\chi_{2888}(2887, \cdot)\)	None	0	1
2888.2.i	\(\chi_{2888}(1873, \cdot)\)	n/a	170	2
2888.2.j	\(\chi_{2888}(791, \cdot)\)	None	0	2
2888.2.o	\(\chi_{2888}(2235, \cdot)\)	n/a	648	2
2888.2.p	\(\chi_{2888}(429, \cdot)\)	n/a	648	2
2888.2.q	\(\chi_{2888}(1137, \cdot)\)	n/a	510	6
2888.2.t	\(\chi_{2888}(245, \cdot)\)	n/a	1944	6
2888.2.v	\(\chi_{2888}(299, \cdot)\)	n/a	1944	6
2888.2.w	\(\chi_{2888}(127, \cdot)\)	None	0	6
2888.2.y	\(\chi_{2888}(153, \cdot)\)	n/a	1710	18
2888.2.z	\(\chi_{2888}(151, \cdot)\)	None	0	18
2888.2.be	\(\chi_{2888}(77, \cdot)\)	n/a	6804	18
2888.2.bf	\(\chi_{2888}(75, \cdot)\)	n/a	6804	18
2888.2.bg	\(\chi_{2888}(49, \cdot)\)	n/a	3420	36
2888.2.bh	\(\chi_{2888}(45, \cdot)\)	n/a	13608	36
2888.2.bi	\(\chi_{2888}(27, \cdot)\)	n/a	13608	36
2888.2.bn	\(\chi_{2888}(31, \cdot)\)	None	0	36
2888.2.bo	\(\chi_{2888}(9, \cdot)\)	n/a	10260	108
2888.2.bq	\(\chi_{2888}(15, \cdot)\)	None	0	108
2888.2.br	\(\chi_{2888}(3, \cdot)\)	n/a	40824	108
2888.2.bt	\(\chi_{2888}(5, \cdot)\)	n/a	40824	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)\(^{\oplus 1}\)