Space of modular forms of level 1900 and weight 3

• Label: 1900.3
• Level: 1900
• Weight: 3
• Dimension: 114788
• Nonzero newspaces: 36
• Sturm bound: 648000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(648000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1900))\).

	Total	New	Old
Modular forms	218520	116180	102340
Cusp forms	213480	114788	98692
Eisenstein series	5040	1392	3648

Trace form

114788 * q - 105 * q^2 + 8 * q^3 - 113 * q^4 - 268 * q^5 - 217 * q^6 - 56 * q^7 - 129 * q^8 - 226 * q^9 - 112 * q^10 + 80 * q^11 + 63 * q^12 - 126 * q^13 + 127 * q^14 + 4 * q^15 + 39 * q^16 - 413 * q^17 - 18 * q^18 - 121 * q^19 - 356 * q^20 - 569 * q^21 - 417 * q^22 - 269 * q^23 - 653 * q^24 - 104 * q^25 - 745 * q^26 + 110 * q^27 - 500 * q^28 - 10 * q^29 - 44 * q^30 + 60 * q^31 + 190 * q^32 + 350 * q^33 + 392 * q^34 + 416 * q^35 + 381 * q^36 + 236 * q^37 + 446 * q^38 + 908 * q^39 + 728 * q^40 - 122 * q^41 + 1273 * q^42 + 615 * q^43 + 598 * q^44 - 48 * q^45 + 68 * q^46 + 271 * q^47 + 856 * q^48 - 463 * q^49 - 132 * q^50 + 127 * q^51 - 413 * q^52 - 1206 * q^53 - 868 * q^54 - 600 * q^55 - 426 * q^56 - 931 * q^57 - 1618 * q^58 - 1235 * q^59 - 2244 * q^60 - 1514 * q^61 - 1132 * q^62 - 2368 * q^63 - 461 * q^64 - 808 * q^65 + 239 * q^66 - 1135 * q^67 - 200 * q^68 - 221 * q^69 - 284 * q^70 + 67 * q^71 - 160 * q^72 + 961 * q^73 - 857 * q^74 + 36 * q^75 - 559 * q^76 - 367 * q^77 - 831 * q^78 - 1322 * q^79 - 412 * q^80 - 2704 * q^81 - 1938 * q^82 - 539 * q^83 - 3341 * q^84 + 832 * q^85 - 1510 * q^86 - 900 * q^87 - 3033 * q^88 + 1705 * q^89 - 3052 * q^90 - 60 * q^91 - 2742 * q^92 + 166 * q^93 - 2734 * q^94 + 332 * q^95 - 3190 * q^96 - 115 * q^97 - 1374 * q^98 + 1638 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1900))\)

We only show spaces with odd 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
1900.3.b	\(\chi_{1900}(951, \cdot)\)	n/a	342	1
1900.3.e	\(\chi_{1900}(1101, \cdot)\)	1900.3.e.a	2	1
		1900.3.e.b	2
		1900.3.e.c	4
		1900.3.e.d	4
		1900.3.e.e	12
		1900.3.e.f	12
		1900.3.e.g	14
		1900.3.e.h	14
1900.3.g	\(\chi_{1900}(949, \cdot)\)	1900.3.g.a	4	1
		1900.3.g.b	4
		1900.3.g.c	24
		1900.3.g.d	28
1900.3.h	\(\chi_{1900}(799, \cdot)\)	n/a	324	1
1900.3.j	\(\chi_{1900}(607, \cdot)\)	n/a	712	2
1900.3.m	\(\chi_{1900}(457, \cdot)\)	n/a	108	2
1900.3.p	\(\chi_{1900}(449, \cdot)\)	n/a	120	2
1900.3.q	\(\chi_{1900}(999, \cdot)\)	n/a	712	2
1900.3.r	\(\chi_{1900}(1151, \cdot)\)	n/a	748	2
1900.3.u	\(\chi_{1900}(601, \cdot)\)	n/a	128	2
1900.3.w	\(\chi_{1900}(189, \cdot)\)	n/a	400	4
1900.3.y	\(\chi_{1900}(39, \cdot)\)	n/a	2160	4
1900.3.ba	\(\chi_{1900}(191, \cdot)\)	n/a	2160	4
1900.3.bb	\(\chi_{1900}(341, \cdot)\)	n/a	400	4
1900.3.be	\(\chi_{1900}(107, \cdot)\)	n/a	1424	4
1900.3.bf	\(\chi_{1900}(657, \cdot)\)	n/a	240	4
1900.3.bi	\(\chi_{1900}(401, \cdot)\)	n/a	378	6
1900.3.bj	\(\chi_{1900}(99, \cdot)\)	n/a	2136	6
1900.3.bl	\(\chi_{1900}(249, \cdot)\)	n/a	360	6
1900.3.bo	\(\chi_{1900}(251, \cdot)\)	n/a	2244	6
1900.3.bp	\(\chi_{1900}(77, \cdot)\)	n/a	720	8
1900.3.bs	\(\chi_{1900}(227, \cdot)\)	n/a	4768	8
1900.3.bu	\(\chi_{1900}(11, \cdot)\)	n/a	4768	8
1900.3.bv	\(\chi_{1900}(141, \cdot)\)	n/a	800	8
1900.3.bx	\(\chi_{1900}(69, \cdot)\)	n/a	800	8
1900.3.bz	\(\chi_{1900}(159, \cdot)\)	n/a	4768	8
1900.3.ca	\(\chi_{1900}(93, \cdot)\)	n/a	720	12
1900.3.cc	\(\chi_{1900}(143, \cdot)\)	n/a	4272	12
1900.3.cg	\(\chi_{1900}(197, \cdot)\)	n/a	1600	16
1900.3.ch	\(\chi_{1900}(27, \cdot)\)	n/a	9536	16
1900.3.ck	\(\chi_{1900}(119, \cdot)\)	n/a	14304	24
1900.3.cl	\(\chi_{1900}(21, \cdot)\)	n/a	2400	24
1900.3.cm	\(\chi_{1900}(111, \cdot)\)	n/a	14304	24
1900.3.cp	\(\chi_{1900}(29, \cdot)\)	n/a	2400	24
1900.3.cr	\(\chi_{1900}(3, \cdot)\)	n/a	28608	48
1900.3.ct	\(\chi_{1900}(17, \cdot)\)	n/a	4800	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1900))\) into lower level spaces

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