Space of modular forms of level 2900 and weight 2

• Label: 2900.2
• Level: 2900
• Weight: 2
• Dimension: 134055
• Nonzero newspaces: 40
• Sturm bound: 1008000
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(1008000\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2900))\).

	Total	New	Old
Modular forms	255920	136271	119649
Cusp forms	248081	134055	114026
Eisenstein series	7839	2216	5623

Trace form

134055 * q - 170 * q^2 - 8 * q^3 - 162 * q^4 - 418 * q^5 - 258 * q^6 + 8 * q^7 - 146 * q^8 - 320 * q^9 - 192 * q^10 - 162 * q^12 - 324 * q^13 - 162 * q^14 + 4 * q^15 - 290 * q^16 - 304 * q^17 - 186 * q^18 + 24 * q^19 - 212 * q^20 - 520 * q^21 - 162 * q^22 + 50 * q^23 - 182 * q^24 - 334 * q^25 - 502 * q^26 + 34 * q^27 - 148 * q^28 - 340 * q^29 - 428 * q^30 - 4 * q^31 - 130 * q^32 - 326 * q^33 - 162 * q^34 + 16 * q^35 - 274 * q^36 - 396 * q^37 - 222 * q^38 - 124 * q^39 - 312 * q^40 - 596 * q^41 - 362 * q^42 - 120 * q^43 - 288 * q^44 - 558 * q^45 - 308 * q^46 - 76 * q^47 - 310 * q^48 - 410 * q^49 - 412 * q^50 - 16 * q^51 - 246 * q^52 - 303 * q^53 - 296 * q^54 - 80 * q^55 - 280 * q^56 - 368 * q^57 - 58 * q^58 + 16 * q^59 - 404 * q^60 - 356 * q^61 - 164 * q^62 + 140 * q^63 - 96 * q^64 - 318 * q^65 - 242 * q^66 + 144 * q^67 - 112 * q^68 - 176 * q^69 - 204 * q^70 + 18 * q^71 - 80 * q^72 - 317 * q^73 - 168 * q^74 + 156 * q^75 - 454 * q^76 - 234 * q^77 - 222 * q^78 + 84 * q^79 - 172 * q^80 - 808 * q^81 - 18 * q^82 + 68 * q^83 - 44 * q^84 - 502 * q^85 - 124 * q^86 - 84 * q^87 - 104 * q^88 - 588 * q^89 + 108 * q^90 - 108 * q^91 + 38 * q^92 - 568 * q^93 + 158 * q^94 - 72 * q^95 - 100 * q^96 - 603 * q^97 + 64 * q^98 - 134 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2900))\)

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
2900.2.a	\(\chi_{2900}(1, \cdot)\)	2900.2.a.a	1	1
		2900.2.a.b	1
		2900.2.a.c	1
		2900.2.a.d	1
		2900.2.a.e	1
		2900.2.a.f	3
		2900.2.a.g	3
		2900.2.a.h	4
		2900.2.a.i	5
		2900.2.a.j	5
		2900.2.a.k	5
		2900.2.a.l	5
		2900.2.a.m	10
2900.2.c	\(\chi_{2900}(349, \cdot)\)	2900.2.c.a	2	1
		2900.2.c.b	2
		2900.2.c.c	2
		2900.2.c.d	2
		2900.2.c.e	2
		2900.2.c.f	6
		2900.2.c.g	6
		2900.2.c.h	10
		2900.2.c.i	10
2900.2.d	\(\chi_{2900}(1101, \cdot)\)	2900.2.d.a	2	1
		2900.2.d.b	2
		2900.2.d.c	4
		2900.2.d.d	4
		2900.2.d.e	10
		2900.2.d.f	10
		2900.2.d.g	16
2900.2.f	\(\chi_{2900}(1449, \cdot)\)	2900.2.f.a	4	1
		2900.2.f.b	4
		2900.2.f.c	8
		2900.2.f.d	8
		2900.2.f.e	20
2900.2.j	\(\chi_{2900}(1757, \cdot)\)	2900.2.j.a	2	2
		2900.2.j.b	2
		2900.2.j.c	16
		2900.2.j.d	30
		2900.2.j.e	40
2900.2.k	\(\chi_{2900}(1351, \cdot)\)	n/a	558	2
2900.2.n	\(\chi_{2900}(407, \cdot)\)	n/a	504	2
2900.2.o	\(\chi_{2900}(1043, \cdot)\)	n/a	532	2
2900.2.r	\(\chi_{2900}(99, \cdot)\)	n/a	532	2
2900.2.s	\(\chi_{2900}(157, \cdot)\)	2900.2.s.a	2	2
		2900.2.s.b	2
		2900.2.s.c	16
		2900.2.s.d	30
		2900.2.s.e	40
2900.2.u	\(\chi_{2900}(581, \cdot)\)	n/a	280	4
2900.2.v	\(\chi_{2900}(401, \cdot)\)	n/a	282	6
2900.2.x	\(\chi_{2900}(289, \cdot)\)	n/a	304	4
2900.2.z	\(\chi_{2900}(929, \cdot)\)	n/a	280	4
2900.2.bc	\(\chi_{2900}(521, \cdot)\)	n/a	296	4
2900.2.bf	\(\chi_{2900}(149, \cdot)\)	n/a	264	6
2900.2.bh	\(\chi_{2900}(701, \cdot)\)	n/a	288	6
2900.2.bi	\(\chi_{2900}(49, \cdot)\)	n/a	276	6
2900.2.bl	\(\chi_{2900}(133, \cdot)\)	n/a	600	8
2900.2.bn	\(\chi_{2900}(191, \cdot)\)	n/a	3568	8
2900.2.bp	\(\chi_{2900}(347, \cdot)\)	n/a	3568	8
2900.2.bq	\(\chi_{2900}(523, \cdot)\)	n/a	3360	8
2900.2.bs	\(\chi_{2900}(539, \cdot)\)	n/a	3568	8
2900.2.bu	\(\chi_{2900}(17, \cdot)\)	n/a	600	8
2900.2.bw	\(\chi_{2900}(193, \cdot)\)	n/a	540	12
2900.2.by	\(\chi_{2900}(599, \cdot)\)	n/a	3192	12
2900.2.cb	\(\chi_{2900}(207, \cdot)\)	n/a	3192	12
2900.2.cc	\(\chi_{2900}(7, \cdot)\)	n/a	3192	12
2900.2.cf	\(\chi_{2900}(251, \cdot)\)	n/a	3348	12
2900.2.ch	\(\chi_{2900}(657, \cdot)\)	n/a	540	12
2900.2.ci	\(\chi_{2900}(81, \cdot)\)	n/a	1824	24
2900.2.cj	\(\chi_{2900}(121, \cdot)\)	n/a	1776	24
2900.2.cm	\(\chi_{2900}(169, \cdot)\)	n/a	1776	24
2900.2.co	\(\chi_{2900}(9, \cdot)\)	n/a	1824	24
2900.2.cq	\(\chi_{2900}(73, \cdot)\)	n/a	3600	48
2900.2.ct	\(\chi_{2900}(19, \cdot)\)	n/a	21408	48
2900.2.cv	\(\chi_{2900}(23, \cdot)\)	n/a	21408	48
2900.2.cw	\(\chi_{2900}(63, \cdot)\)	n/a	21408	48
2900.2.cy	\(\chi_{2900}(11, \cdot)\)	n/a	21408	48
2900.2.db	\(\chi_{2900}(37, \cdot)\)	n/a	3600	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1450))\)\(^{\oplus 2}\)