Space of modular forms of level 1053 and weight 2

• Label: 1053.2
• Level: 1053
• Weight: 2
• Dimension: 31256
• Nonzero newspaces: 33
• Sturm bound: 163296
• Trace bound: 24

Defining parameters

Level:	\( N \)	=	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 33 \)
Sturm bound:			\(163296\)
Trace bound:			\(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1053))\).

	Total	New	Old
Modular forms	42120	32488	9632
Cusp forms	39529	31256	8273
Eisenstein series	2591	1232	1359

Trace form

31256 * q - 120 * q^2 - 180 * q^3 - 196 * q^4 - 114 * q^5 - 180 * q^6 - 194 * q^7 - 96 * q^8 - 180 * q^9 - 270 * q^10 - 102 * q^11 - 180 * q^12 - 211 * q^13 - 222 * q^14 - 180 * q^15 - 196 * q^16 - 90 * q^17 - 198 * q^18 - 302 * q^19 - 186 * q^20 - 234 * q^21 - 210 * q^22 - 186 * q^23 - 288 * q^24 - 220 * q^25 - 219 * q^26 - 450 * q^27 - 338 * q^28 - 174 * q^29 - 288 * q^30 - 218 * q^31 - 216 * q^32 - 234 * q^33 - 222 * q^34 - 138 * q^35 - 252 * q^36 - 266 * q^37 - 42 * q^38 - 198 * q^39 - 486 * q^40 - 114 * q^41 - 270 * q^42 - 194 * q^43 - 246 * q^44 - 288 * q^45 - 378 * q^46 - 246 * q^47 - 378 * q^48 - 240 * q^49 - 408 * q^50 - 306 * q^51 - 259 * q^52 - 414 * q^53 - 432 * q^54 - 378 * q^55 - 462 * q^56 - 288 * q^57 - 246 * q^58 - 258 * q^59 - 414 * q^60 - 230 * q^61 - 330 * q^62 - 288 * q^63 - 316 * q^64 - 141 * q^65 - 396 * q^66 - 218 * q^67 + 72 * q^68 - 72 * q^69 - 282 * q^70 + 90 * q^71 + 252 * q^72 - 212 * q^73 + 246 * q^74 - 290 * q^76 + 210 * q^77 - 81 * q^78 - 434 * q^79 + 516 * q^80 - 36 * q^81 - 432 * q^82 + 114 * q^83 + 270 * q^84 - 258 * q^85 + 282 * q^86 + 108 * q^87 - 306 * q^88 + 36 * q^89 - 18 * q^90 - 314 * q^91 - 78 * q^92 - 216 * q^93 - 282 * q^94 - 246 * q^95 - 162 * q^96 - 338 * q^97 - 540 * q^98 - 324 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)

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
1053.2.a	\(\chi_{1053}(1, \cdot)\)	1053.2.a.a	1	1
		1053.2.a.b	1
		1053.2.a.c	1
		1053.2.a.d	1
		1053.2.a.e	2
		1053.2.a.f	2
		1053.2.a.g	3
		1053.2.a.h	3
		1053.2.a.i	4
		1053.2.a.j	5
		1053.2.a.k	5
		1053.2.a.l	6
		1053.2.a.m	6
		1053.2.a.n	8
1053.2.b	\(\chi_{1053}(649, \cdot)\)	1053.2.b.a	2	1
		1053.2.b.b	2
		1053.2.b.c	2
		1053.2.b.d	2
		1053.2.b.e	2
		1053.2.b.f	2
		1053.2.b.g	4
		1053.2.b.h	4
		1053.2.b.i	10
		1053.2.b.j	10
		1053.2.b.k	12
1053.2.e	\(\chi_{1053}(352, \cdot)\)	1053.2.e.a	2	2
		1053.2.e.b	2
		1053.2.e.c	2
		1053.2.e.d	2
		1053.2.e.e	4
		1053.2.e.f	4
		1053.2.e.g	4
		1053.2.e.h	4
		1053.2.e.i	4
		1053.2.e.j	4
		1053.2.e.k	4
		1053.2.e.l	4
		1053.2.e.m	4
		1053.2.e.n	6
		1053.2.e.o	6
		1053.2.e.p	8
		1053.2.e.q	8
		1053.2.e.r	8
		1053.2.e.s	16
1053.2.f	\(\chi_{1053}(217, \cdot)\)	n/a	108	2
1053.2.g	\(\chi_{1053}(406, \cdot)\)	n/a	104	2
1053.2.h	\(\chi_{1053}(55, \cdot)\)	n/a	108	2
1053.2.i	\(\chi_{1053}(161, \cdot)\)	n/a	104	2
1053.2.l	\(\chi_{1053}(433, \cdot)\)	n/a	108	2
1053.2.q	\(\chi_{1053}(82, \cdot)\)	n/a	104	2
1053.2.r	\(\chi_{1053}(595, \cdot)\)	n/a	108	2
1053.2.t	\(\chi_{1053}(298, \cdot)\)	n/a	108	2
1053.2.w	\(\chi_{1053}(118, \cdot)\)	n/a	216	6
1053.2.x	\(\chi_{1053}(289, \cdot)\)	n/a	240	6
1053.2.y	\(\chi_{1053}(100, \cdot)\)	n/a	240	6
1053.2.ba	\(\chi_{1053}(215, \cdot)\)	n/a	216	4
1053.2.bc	\(\chi_{1053}(512, \cdot)\)	n/a	216	4
1053.2.bd	\(\chi_{1053}(80, \cdot)\)	n/a	208	4
1053.2.bf	\(\chi_{1053}(188, \cdot)\)	n/a	216	4
1053.2.bl	\(\chi_{1053}(64, \cdot)\)	n/a	240	6
1053.2.bn	\(\chi_{1053}(127, \cdot)\)	n/a	240	6
1053.2.bo	\(\chi_{1053}(10, \cdot)\)	n/a	240	6
1053.2.bq	\(\chi_{1053}(40, \cdot)\)	n/a	1944	18
1053.2.br	\(\chi_{1053}(16, \cdot)\)	n/a	2232	18
1053.2.bs	\(\chi_{1053}(61, \cdot)\)	n/a	2232	18
1053.2.bt	\(\chi_{1053}(206, \cdot)\)	n/a	480	12
1053.2.bw	\(\chi_{1053}(8, \cdot)\)	n/a	480	12
1053.2.by	\(\chi_{1053}(71, \cdot)\)	n/a	480	12
1053.2.bz	\(\chi_{1053}(43, \cdot)\)	n/a	2232	18
1053.2.cd	\(\chi_{1053}(25, \cdot)\)	n/a	2232	18
1053.2.ce	\(\chi_{1053}(4, \cdot)\)	n/a	2232	18
1053.2.cl	\(\chi_{1053}(5, \cdot)\)	n/a	4464	36
1053.2.cm	\(\chi_{1053}(20, \cdot)\)	n/a	4464	36
1053.2.cn	\(\chi_{1053}(2, \cdot)\)	n/a	4464	36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1053))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1053)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)