Space of modular forms of level 2032 and weight 4

• Label: 2032.4
• Level: 2032
• Weight: 4
• Dimension: 217139
• Nonzero newspaces: 24
• Sturm bound: 1032192
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 2032 = 2^{4} \cdot 127 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1032192\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2032))\).

	Total	New	Old
Modular forms	388836	218263	170573
Cusp forms	385308	217139	168169
Eisenstein series	3528	1124	2404

Trace form

217139 * q - 248 * q^2 - 193 * q^3 - 268 * q^4 - 307 * q^5 - 188 * q^6 - 141 * q^7 - 164 * q^8 - 41 * q^9 - 116 * q^10 - 313 * q^11 - 452 * q^12 - 355 * q^13 - 628 * q^14 + 75 * q^15 - 812 * q^16 - 659 * q^17 - 600 * q^18 - 49 * q^19 + 140 * q^20 - 227 * q^21 + 924 * q^22 - 301 * q^23 + 1444 * q^24 + 179 * q^25 + 276 * q^26 - 253 * q^27 - 812 * q^28 - 307 * q^29 - 2724 * q^30 - 1245 * q^31 - 2188 * q^32 - 911 * q^33 - 1124 * q^34 - 1237 * q^35 + 940 * q^36 + 29 * q^37 + 2212 * q^38 - 365 * q^39 + 2420 * q^40 + 333 * q^41 + 1108 * q^42 + 1591 * q^43 - 1988 * q^44 - 747 * q^45 - 2516 * q^46 + 2755 * q^47 - 3788 * q^48 - 1221 * q^49 - 1704 * q^50 + 2411 * q^51 + 220 * q^52 + 925 * q^53 + 2500 * q^54 - 13 * q^55 + 724 * q^56 + 289 * q^57 - 268 * q^58 - 4937 * q^59 + 132 * q^60 - 3235 * q^61 - 92 * q^62 - 5973 * q^63 - 1276 * q^64 + 505 * q^65 + 604 * q^66 - 3697 * q^67 + 1508 * q^68 - 1923 * q^69 - 572 * q^70 + 1267 * q^71 - 2436 * q^72 - 371 * q^73 + 652 * q^74 + 6687 * q^75 + 2204 * q^76 + 2333 * q^77 + 1292 * q^78 + 7331 * q^79 + 5044 * q^80 - 909 * q^81 + 1156 * q^82 + 5407 * q^83 - 4172 * q^84 - 91 * q^85 - 7780 * q^86 - 1773 * q^87 - 3308 * q^88 - 1491 * q^89 - 4044 * q^90 - 5797 * q^91 - 1516 * q^92 + 2789 * q^93 + 6244 * q^94 - 14165 * q^95 + 8612 * q^96 + 397 * q^97 - 880 * q^98 - 9137 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2032))\)

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
2032.4.a	\(\chi_{2032}(1, \cdot)\)	2032.4.a.a	1	1
		2032.4.a.b	1
		2032.4.a.c	5
		2032.4.a.d	6
		2032.4.a.e	10
		2032.4.a.f	10
		2032.4.a.g	13
		2032.4.a.h	16
		2032.4.a.i	16
		2032.4.a.j	17
		2032.4.a.k	21
		2032.4.a.l	22
		2032.4.a.m	25
		2032.4.a.n	26
2032.4.c	\(\chi_{2032}(1017, \cdot)\)	None	0	1
2032.4.e	\(\chi_{2032}(1015, \cdot)\)	None	0	1
2032.4.g	\(\chi_{2032}(2031, \cdot)\)	n/a	192	1
2032.4.i	\(\chi_{2032}(273, \cdot)\)	n/a	382	2
2032.4.j	\(\chi_{2032}(507, \cdot)\)	n/a	1532	2
2032.4.k	\(\chi_{2032}(509, \cdot)\)	n/a	1512	2
2032.4.n	\(\chi_{2032}(655, \cdot)\)	n/a	384	2
2032.4.q	\(\chi_{2032}(361, \cdot)\)	None	0	2
2032.4.s	\(\chi_{2032}(743, \cdot)\)	None	0	2
2032.4.u	\(\chi_{2032}(129, \cdot)\)	n/a	1146	6
2032.4.v	\(\chi_{2032}(353, \cdot)\)	n/a	1146	6
2032.4.y	\(\chi_{2032}(781, \cdot)\)	n/a	3064	4
2032.4.z	\(\chi_{2032}(147, \cdot)\)	n/a	3064	4
2032.4.bb	\(\chi_{2032}(63, \cdot)\)	n/a	1152	6
2032.4.bd	\(\chi_{2032}(119, \cdot)\)	None	0	6
2032.4.bf	\(\chi_{2032}(905, \cdot)\)	None	0	6
2032.4.bh	\(\chi_{2032}(151, \cdot)\)	None	0	6
2032.4.bm	\(\chi_{2032}(1167, \cdot)\)	n/a	1152	6
2032.4.bn	\(\chi_{2032}(1369, \cdot)\)	None	0	6
2032.4.bo	\(\chi_{2032}(177, \cdot)\)	n/a	2292	12
2032.4.br	\(\chi_{2032}(389, \cdot)\)	n/a	9192	12
2032.4.bs	\(\chi_{2032}(123, \cdot)\)	n/a	9192	12
2032.4.bt	\(\chi_{2032}(37, \cdot)\)	n/a	9192	12
2032.4.bw	\(\chi_{2032}(59, \cdot)\)	n/a	9192	12
2032.4.by	\(\chi_{2032}(167, \cdot)\)	None	0	12
2032.4.ca	\(\chi_{2032}(25, \cdot)\)	None	0	12
2032.4.cd	\(\chi_{2032}(207, \cdot)\)	n/a	2304	12
2032.4.ce	\(\chi_{2032}(17, \cdot)\)	n/a	6876	36
2032.4.cf	\(\chi_{2032}(27, \cdot)\)	n/a	18384	24
2032.4.cg	\(\chi_{2032}(61, \cdot)\)	n/a	18384	24
2032.4.cl	\(\chi_{2032}(9, \cdot)\)	None	0	36
2032.4.cm	\(\chi_{2032}(175, \cdot)\)	n/a	6912	36
2032.4.cn	\(\chi_{2032}(7, \cdot)\)	None	0	36
2032.4.cq	\(\chi_{2032}(3, \cdot)\)	n/a	55152	72
2032.4.ct	\(\chi_{2032}(13, \cdot)\)	n/a	55152	72

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2032))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2032)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(254))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(508))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1016))\)\(^{\oplus 2}\)