Space of modular forms of level 1900 and weight 2

• Label: 1900.2
• Level: 1900
• Weight: 2
• Dimension: 57045
• Nonzero newspaces: 36
• Sturm bound: 432000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(432000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1900))\).

	Total	New	Old
Modular forms	110520	58441	52079
Cusp forms	105481	57045	48436
Eisenstein series	5039	1396	3643

Trace form

57045 * q - 105 * q^2 - 8 * q^3 - 97 * q^4 - 258 * q^5 - 153 * q^6 + 8 * q^7 - 81 * q^8 - 190 * q^9 - 112 * q^10 - 97 * q^12 - 206 * q^13 - 97 * q^14 + 4 * q^15 - 185 * q^16 - 183 * q^17 - 112 * q^18 - 9 * q^19 - 276 * q^20 - 303 * q^21 - 97 * q^22 + 55 * q^23 - 117 * q^24 - 174 * q^25 - 297 * q^26 + 73 * q^27 - 70 * q^28 - 112 * q^29 - 124 * q^30 + 42 * q^31 - 20 * q^32 - 100 * q^33 - 52 * q^34 + 16 * q^35 - 79 * q^36 - 216 * q^37 - 74 * q^38 - 42 * q^39 - 232 * q^40 - 368 * q^41 - 207 * q^42 - 87 * q^43 - 192 * q^44 - 398 * q^45 - 228 * q^46 - 113 * q^47 - 294 * q^48 - 339 * q^49 - 332 * q^50 - 108 * q^51 - 293 * q^52 - 272 * q^53 - 384 * q^54 - 80 * q^55 - 264 * q^56 - 323 * q^57 - 322 * q^58 - 57 * q^59 - 324 * q^60 - 196 * q^61 - 242 * q^62 + 16 * q^63 - 229 * q^64 - 158 * q^65 - 321 * q^66 + 103 * q^67 - 208 * q^68 + 15 * q^69 - 124 * q^70 + 23 * q^71 - 220 * q^72 - 116 * q^73 - 171 * q^74 + 156 * q^75 - 399 * q^76 - 79 * q^77 - 229 * q^78 + 280 * q^79 - 92 * q^80 - 153 * q^81 - 88 * q^82 + 331 * q^83 - 45 * q^84 - 198 * q^85 - 96 * q^86 + 512 * q^87 + 71 * q^88 - 145 * q^89 + 188 * q^90 + 252 * q^91 + 58 * q^92 + 164 * q^93 + 160 * q^94 + 72 * q^95 - 70 * q^96 - 297 * q^97 + 298 * q^98 + 447 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1900))\)

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
1900.2.a	\(\chi_{1900}(1, \cdot)\)	1900.2.a.a	1	1
		1900.2.a.b	1
		1900.2.a.c	1
		1900.2.a.d	2
		1900.2.a.e	2
		1900.2.a.f	3
		1900.2.a.g	3
		1900.2.a.h	3
		1900.2.a.i	3
		1900.2.a.j	4
		1900.2.a.k	6
1900.2.c	\(\chi_{1900}(1749, \cdot)\)	1900.2.c.a	2	1
		1900.2.c.b	2
		1900.2.c.c	2
		1900.2.c.d	4
		1900.2.c.e	4
		1900.2.c.f	6
		1900.2.c.g	6
1900.2.d	\(\chi_{1900}(1899, \cdot)\)	n/a	176	1
1900.2.f	\(\chi_{1900}(151, \cdot)\)	n/a	184	1
1900.2.i	\(\chi_{1900}(201, \cdot)\)	1900.2.i.a	2	2
		1900.2.i.b	2
		1900.2.i.c	6
		1900.2.i.d	8
		1900.2.i.e	12
		1900.2.i.f	12
		1900.2.i.g	20
1900.2.k	\(\chi_{1900}(343, \cdot)\)	n/a	324	2
1900.2.l	\(\chi_{1900}(493, \cdot)\)	1900.2.l.a	8	2
		1900.2.l.b	12
		1900.2.l.c	16
		1900.2.l.d	24
1900.2.n	\(\chi_{1900}(381, \cdot)\)	n/a	176	4
1900.2.o	\(\chi_{1900}(1551, \cdot)\)	n/a	368	2
1900.2.s	\(\chi_{1900}(49, \cdot)\)	1900.2.s.a	4	2
		1900.2.s.b	4
		1900.2.s.c	12
		1900.2.s.d	16
		1900.2.s.e	24
1900.2.t	\(\chi_{1900}(1399, \cdot)\)	n/a	352	2
1900.2.v	\(\chi_{1900}(101, \cdot)\)	n/a	192	6
1900.2.x	\(\chi_{1900}(531, \cdot)\)	n/a	1184	4
1900.2.z	\(\chi_{1900}(229, \cdot)\)	n/a	184	4
1900.2.bc	\(\chi_{1900}(379, \cdot)\)	n/a	1184	4
1900.2.bd	\(\chi_{1900}(7, \cdot)\)	n/a	704	4
1900.2.bg	\(\chi_{1900}(293, \cdot)\)	n/a	120	4
1900.2.bh	\(\chi_{1900}(121, \cdot)\)	n/a	400	8
1900.2.bk	\(\chi_{1900}(299, \cdot)\)	n/a	1056	6
1900.2.bm	\(\chi_{1900}(149, \cdot)\)	n/a	180	6
1900.2.bn	\(\chi_{1900}(51, \cdot)\)	n/a	1104	6
1900.2.bq	\(\chi_{1900}(37, \cdot)\)	n/a	400	8
1900.2.br	\(\chi_{1900}(267, \cdot)\)	n/a	2160	8
1900.2.bt	\(\chi_{1900}(429, \cdot)\)	n/a	400	8
1900.2.bw	\(\chi_{1900}(179, \cdot)\)	n/a	2368	8
1900.2.by	\(\chi_{1900}(31, \cdot)\)	n/a	2368	8
1900.2.cb	\(\chi_{1900}(193, \cdot)\)	n/a	360	12
1900.2.cd	\(\chi_{1900}(43, \cdot)\)	n/a	2112	12
1900.2.ce	\(\chi_{1900}(61, \cdot)\)	n/a	1200	24
1900.2.cf	\(\chi_{1900}(217, \cdot)\)	n/a	800	16
1900.2.ci	\(\chi_{1900}(83, \cdot)\)	n/a	4736	16
1900.2.cj	\(\chi_{1900}(59, \cdot)\)	n/a	7104	24
1900.2.cn	\(\chi_{1900}(71, \cdot)\)	n/a	7104	24
1900.2.co	\(\chi_{1900}(9, \cdot)\)	n/a	1200	24
1900.2.cq	\(\chi_{1900}(23, \cdot)\)	n/a	14208	48
1900.2.cs	\(\chi_{1900}(13, \cdot)\)	n/a	2400	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1900))\) into lower level spaces

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