Space of modular forms of level 2898 and weight 2

• Label: 2898.2
• Level: 2898
• Weight: 2
• Dimension: 57464
• Nonzero newspaces: 40
• Sturm bound: 912384
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(912384\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2898))\).

	Total	New	Old
Modular forms	232320	57464	174856
Cusp forms	223873	57464	166409
Eisenstein series	8447	0	8447

Trace form

57464 * q - 4 * q^2 - 12 * q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 - 20 * q^7 + 8 * q^8 + 12 * q^9 - 12 * q^10 - 12 * q^11 - 12 * q^13 + 32 * q^14 + 48 * q^15 + 8 * q^16 + 28 * q^17 + 24 * q^18 + 16 * q^19 - 8 * q^20 + 84 * q^21 + 40 * q^22 - 28 * q^23 + 12 * q^24 - 8 * q^25 + 32 * q^26 + 72 * q^27 - 14 * q^28 - 20 * q^29 + 24 * q^30 - 20 * q^31 - 4 * q^32 + 12 * q^33 - 12 * q^34 + 38 * q^35 + 12 * q^36 - 104 * q^37 - 32 * q^38 + 72 * q^39 - 12 * q^40 + 16 * q^41 - 92 * q^43 - 48 * q^44 + 96 * q^45 - 48 * q^46 + 8 * q^47 + 12 * q^48 - 10 * q^49 - 100 * q^50 - 36 * q^51 + 12 * q^52 - 92 * q^53 - 20 * q^54 + 176 * q^55 + 50 * q^56 + 84 * q^57 + 288 * q^58 + 244 * q^59 - 56 * q^60 + 540 * q^61 + 196 * q^62 - 140 * q^63 + 4 * q^64 + 588 * q^65 + 160 * q^66 + 316 * q^67 + 156 * q^68 + 332 * q^69 + 300 * q^70 + 420 * q^71 + 188 * q^72 + 312 * q^73 + 400 * q^74 + 388 * q^75 + 198 * q^77 + 144 * q^78 + 476 * q^79 + 120 * q^80 + 340 * q^81 + 264 * q^82 + 292 * q^83 + 32 * q^84 + 100 * q^85 + 112 * q^86 + 216 * q^87 + 36 * q^88 + 124 * q^89 + 96 * q^90 + 88 * q^91 + 36 * q^92 + 216 * q^93 + 96 * q^94 + 156 * q^95 + 24 * q^96 - 68 * q^97 + 108 * q^98 + 312 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2898))\)

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
2898.2.a	\(\chi_{2898}(1, \cdot)\)	2898.2.a.a	1	1
		2898.2.a.b	1
		2898.2.a.c	1
		2898.2.a.d	1
		2898.2.a.e	1
		2898.2.a.f	1
		2898.2.a.g	1
		2898.2.a.h	1
		2898.2.a.i	1
		2898.2.a.j	1
		2898.2.a.k	1
		2898.2.a.l	1
		2898.2.a.m	1
		2898.2.a.n	1
		2898.2.a.o	1
		2898.2.a.p	1
		2898.2.a.q	1
		2898.2.a.r	1
		2898.2.a.s	1
		2898.2.a.t	1
		2898.2.a.u	1
		2898.2.a.v	2
		2898.2.a.w	2
		2898.2.a.x	2
		2898.2.a.y	2
		2898.2.a.z	2
		2898.2.a.ba	2
		2898.2.a.bb	2
		2898.2.a.bc	2
		2898.2.a.bd	2
		2898.2.a.be	3
		2898.2.a.bf	3
		2898.2.a.bg	3
		2898.2.a.bh	4
		2898.2.a.bi	4
2898.2.f	\(\chi_{2898}(2393, \cdot)\)	2898.2.f.a	32	1
		2898.2.f.b	32
2898.2.g	\(\chi_{2898}(2575, \cdot)\)	2898.2.g.a	4	1
		2898.2.g.b	4
		2898.2.g.c	4
		2898.2.g.d	4
		2898.2.g.e	4
		2898.2.g.f	4
		2898.2.g.g	4
		2898.2.g.h	4
		2898.2.g.i	16
		2898.2.g.j	16
		2898.2.g.k	16
2898.2.h	\(\chi_{2898}(827, \cdot)\)	2898.2.h.a	24	1
		2898.2.h.b	24
2898.2.i	\(\chi_{2898}(277, \cdot)\)	n/a	352	2
2898.2.j	\(\chi_{2898}(967, \cdot)\)	n/a	264	2
2898.2.k	\(\chi_{2898}(415, \cdot)\)	n/a	144	2
2898.2.l	\(\chi_{2898}(2209, \cdot)\)	n/a	352	2
2898.2.q	\(\chi_{2898}(137, \cdot)\)	n/a	384	2
2898.2.r	\(\chi_{2898}(1793, \cdot)\)	n/a	288	2
2898.2.s	\(\chi_{2898}(1241, \cdot)\)	n/a	128	2
2898.2.t	\(\chi_{2898}(1333, \cdot)\)	n/a	160	2
2898.2.u	\(\chi_{2898}(1151, \cdot)\)	n/a	112	2
2898.2.v	\(\chi_{2898}(229, \cdot)\)	n/a	384	2
2898.2.w	\(\chi_{2898}(1013, \cdot)\)	n/a	352	2
2898.2.x	\(\chi_{2898}(461, \cdot)\)	n/a	352	2
2898.2.y	\(\chi_{2898}(643, \cdot)\)	n/a	384	2
2898.2.bl	\(\chi_{2898}(1195, \cdot)\)	n/a	384	2
2898.2.bm	\(\chi_{2898}(47, \cdot)\)	n/a	352	2
2898.2.bn	\(\chi_{2898}(1103, \cdot)\)	n/a	384	2
2898.2.bo	\(\chi_{2898}(127, \cdot)\)	n/a	600	10
2898.2.bp	\(\chi_{2898}(701, \cdot)\)	n/a	480	10
2898.2.bq	\(\chi_{2898}(181, \cdot)\)	n/a	800	10
2898.2.br	\(\chi_{2898}(377, \cdot)\)	n/a	640	10
2898.2.bw	\(\chi_{2898}(193, \cdot)\)	n/a	3840	20
2898.2.bx	\(\chi_{2898}(163, \cdot)\)	n/a	1600	20
2898.2.by	\(\chi_{2898}(85, \cdot)\)	n/a	2880	20
2898.2.bz	\(\chi_{2898}(25, \cdot)\)	n/a	3840	20
2898.2.ca	\(\chi_{2898}(65, \cdot)\)	n/a	3840	20
2898.2.cb	\(\chi_{2898}(59, \cdot)\)	n/a	3840	20
2898.2.cc	\(\chi_{2898}(61, \cdot)\)	n/a	3840	20
2898.2.cp	\(\chi_{2898}(97, \cdot)\)	n/a	3840	20
2898.2.cq	\(\chi_{2898}(41, \cdot)\)	n/a	3840	20
2898.2.cr	\(\chi_{2898}(101, \cdot)\)	n/a	3840	20
2898.2.cs	\(\chi_{2898}(103, \cdot)\)	n/a	3840	20
2898.2.ct	\(\chi_{2898}(215, \cdot)\)	n/a	1280	20
2898.2.cu	\(\chi_{2898}(19, \cdot)\)	n/a	1600	20
2898.2.cv	\(\chi_{2898}(53, \cdot)\)	n/a	1280	20
2898.2.cw	\(\chi_{2898}(113, \cdot)\)	n/a	2880	20
2898.2.cx	\(\chi_{2898}(11, \cdot)\)	n/a	3840	20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2898))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2898)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1449))\)\(^{\oplus 2}\)