Space of modular forms of level 1900 and weight 4

• Label: 1900.4
• Level: 1900
• Weight: 4
• Dimension: 172531
• Nonzero newspaces: 36
• Sturm bound: 864000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(864000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1900))\).

	Total	New	Old
Modular forms	326520	173927	152593
Cusp forms	321480	172531	148949
Eisenstein series	5040	1396	3644

Trace form

172531 * q - 105 * q^2 + 16 * q^3 - 97 * q^4 - 218 * q^5 - 121 * q^6 - 64 * q^7 - 273 * q^8 - 630 * q^9 - 272 * q^10 - 80 * q^11 - 417 * q^12 + 174 * q^13 - 97 * q^14 + 344 * q^15 + 583 * q^16 + 126 * q^17 + 1136 * q^18 + 250 * q^19 + 364 * q^20 - 758 * q^21 + 1343 * q^22 - 706 * q^23 - 117 * q^24 - 1534 * q^25 - 2153 * q^26 - 1679 * q^27 - 2186 * q^28 - 420 * q^29 - 2604 * q^30 - 278 * q^31 - 2940 * q^32 + 168 * q^33 - 1222 * q^34 + 1256 * q^35 - 759 * q^36 + 408 * q^37 - 1728 * q^38 - 1746 * q^39 - 552 * q^40 + 2348 * q^41 + 1613 * q^42 - 470 * q^43 + 2788 * q^44 + 4082 * q^45 + 134 * q^46 + 4148 * q^47 + 5842 * q^48 + 7674 * q^49 + 4268 * q^50 + 3539 * q^51 + 1547 * q^52 - 64 * q^53 + 7200 * q^54 + 1480 * q^55 + 8888 * q^56 + 178 * q^57 + 7414 * q^58 + 1058 * q^59 - 5764 * q^60 + 1556 * q^61 - 5852 * q^62 - 1688 * q^63 - 13861 * q^64 - 5078 * q^65 - 11409 * q^66 - 6826 * q^67 - 8612 * q^68 - 17294 * q^69 - 6204 * q^70 - 6172 * q^71 + 260 * q^72 - 2399 * q^73 + 5211 * q^74 - 7384 * q^75 + 8521 * q^76 + 9170 * q^77 + 20525 * q^78 + 12902 * q^79 + 4068 * q^80 + 23669 * q^81 + 23062 * q^82 + 3432 * q^83 + 22787 * q^84 - 7418 * q^85 - 2606 * q^86 - 16436 * q^87 - 7609 * q^88 - 12146 * q^89 - 7132 * q^90 - 15776 * q^91 - 24922 * q^92 - 28124 * q^93 - 22240 * q^94 - 7948 * q^95 + 506 * q^96 + 2778 * q^97 - 13540 * q^98 - 24505 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1900))\)

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
1900.4.a	\(\chi_{1900}(1, \cdot)\)	1900.4.a.a	1	1
		1900.4.a.b	2
		1900.4.a.c	3
		1900.4.a.d	4
		1900.4.a.e	4
		1900.4.a.f	4
		1900.4.a.g	5
		1900.4.a.h	9
		1900.4.a.i	9
		1900.4.a.j	9
		1900.4.a.k	9
		1900.4.a.l	12
		1900.4.a.m	14
1900.4.c	\(\chi_{1900}(1749, \cdot)\)	1900.4.c.a	2	1
		1900.4.c.b	4
		1900.4.c.c	6
		1900.4.c.d	8
		1900.4.c.e	8
		1900.4.c.f	8
		1900.4.c.g	10
		1900.4.c.h	18
		1900.4.c.i	18
1900.4.d	\(\chi_{1900}(1899, \cdot)\)	n/a	536	1
1900.4.f	\(\chi_{1900}(151, \cdot)\)	n/a	564	1
1900.4.i	\(\chi_{1900}(201, \cdot)\)	n/a	190	2
1900.4.k	\(\chi_{1900}(343, \cdot)\)	n/a	972	2
1900.4.l	\(\chi_{1900}(493, \cdot)\)	n/a	180	2
1900.4.n	\(\chi_{1900}(381, \cdot)\)	n/a	544	4
1900.4.o	\(\chi_{1900}(1551, \cdot)\)	n/a	1128	2
1900.4.s	\(\chi_{1900}(49, \cdot)\)	n/a	180	2
1900.4.t	\(\chi_{1900}(1399, \cdot)\)	n/a	1072	2
1900.4.v	\(\chi_{1900}(101, \cdot)\)	n/a	570	6
1900.4.x	\(\chi_{1900}(531, \cdot)\)	n/a	3584	4
1900.4.z	\(\chi_{1900}(229, \cdot)\)	n/a	536	4
1900.4.bc	\(\chi_{1900}(379, \cdot)\)	n/a	3584	4
1900.4.bd	\(\chi_{1900}(7, \cdot)\)	n/a	2144	4
1900.4.bg	\(\chi_{1900}(293, \cdot)\)	n/a	360	4
1900.4.bh	\(\chi_{1900}(121, \cdot)\)	n/a	1200	8
1900.4.bk	\(\chi_{1900}(299, \cdot)\)	n/a	3216	6
1900.4.bm	\(\chi_{1900}(149, \cdot)\)	n/a	540	6
1900.4.bn	\(\chi_{1900}(51, \cdot)\)	n/a	3384	6
1900.4.bq	\(\chi_{1900}(37, \cdot)\)	n/a	1200	8
1900.4.br	\(\chi_{1900}(267, \cdot)\)	n/a	6480	8
1900.4.bt	\(\chi_{1900}(429, \cdot)\)	n/a	1200	8
1900.4.bw	\(\chi_{1900}(179, \cdot)\)	n/a	7168	8
1900.4.by	\(\chi_{1900}(31, \cdot)\)	n/a	7168	8
1900.4.cb	\(\chi_{1900}(193, \cdot)\)	n/a	1080	12
1900.4.cd	\(\chi_{1900}(43, \cdot)\)	n/a	6432	12
1900.4.ce	\(\chi_{1900}(61, \cdot)\)	n/a	3600	24
1900.4.cf	\(\chi_{1900}(217, \cdot)\)	n/a	2400	16
1900.4.ci	\(\chi_{1900}(83, \cdot)\)	n/a	14336	16
1900.4.cj	\(\chi_{1900}(59, \cdot)\)	n/a	21504	24
1900.4.cn	\(\chi_{1900}(71, \cdot)\)	n/a	21504	24
1900.4.co	\(\chi_{1900}(9, \cdot)\)	n/a	3600	24
1900.4.cq	\(\chi_{1900}(23, \cdot)\)	n/a	43008	48
1900.4.cs	\(\chi_{1900}(13, \cdot)\)	n/a	7200	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1900))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1900)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 2}\)