Space of modular forms of level 1083 and weight 2

• Label: 1083.2
• Level: 1083
• Weight: 2
• Dimension: 31843
• Nonzero newspaces: 12
• Sturm bound: 173280
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(173280\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1083))\).

	Total	New	Old
Modular forms	44328	32779	11549
Cusp forms	42313	31843	10470
Eisenstein series	2015	936	1079

Trace form

31843 * q + 3 * q^2 - 152 * q^3 - 299 * q^4 + 6 * q^5 - 150 * q^6 - 298 * q^7 + 15 * q^8 - 152 * q^9 - 288 * q^10 + 12 * q^11 - 170 * q^12 - 340 * q^13 - 48 * q^14 - 183 * q^15 - 419 * q^16 - 18 * q^17 - 168 * q^18 - 366 * q^19 - 102 * q^20 - 187 * q^21 - 378 * q^22 - 12 * q^23 - 210 * q^24 - 347 * q^25 - 30 * q^26 - 176 * q^27 - 406 * q^28 - 42 * q^29 - 261 * q^30 - 346 * q^31 - 117 * q^32 - 249 * q^33 - 432 * q^34 - 96 * q^35 - 290 * q^36 - 376 * q^37 - 126 * q^38 - 391 * q^39 - 540 * q^40 - 30 * q^41 - 309 * q^42 - 406 * q^43 - 96 * q^44 - 201 * q^45 - 414 * q^46 - 24 * q^47 - 122 * q^48 - 321 * q^49 - 15 * q^50 - 63 * q^51 - 208 * q^52 + 54 * q^53 - 42 * q^54 - 234 * q^55 + 120 * q^56 - 117 * q^57 - 504 * q^58 + 60 * q^59 + 15 * q^60 - 364 * q^61 - 84 * q^62 - 97 * q^63 - 467 * q^64 - 132 * q^65 - 117 * q^66 - 526 * q^67 - 126 * q^68 - 219 * q^69 - 594 * q^70 - 72 * q^71 - 264 * q^72 - 556 * q^73 - 174 * q^74 - 308 * q^75 - 504 * q^76 - 300 * q^77 - 399 * q^78 - 634 * q^79 - 318 * q^80 - 224 * q^81 - 864 * q^82 - 168 * q^83 - 529 * q^84 - 630 * q^85 - 264 * q^86 - 411 * q^87 - 774 * q^88 - 234 * q^89 - 261 * q^90 - 530 * q^91 - 300 * q^92 - 325 * q^93 - 558 * q^94 - 54 * q^95 - 378 * q^96 - 316 * q^97 - 117 * q^98 - 159 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)

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
1083.2.a	\(\chi_{1083}(1, \cdot)\)	1083.2.a.a	1	1
		1083.2.a.b	1
		1083.2.a.c	1
		1083.2.a.d	1
		1083.2.a.e	1
		1083.2.a.f	2
		1083.2.a.g	2
		1083.2.a.h	2
		1083.2.a.i	2
		1083.2.a.j	2
		1083.2.a.k	2
		1083.2.a.l	3
		1083.2.a.m	3
		1083.2.a.n	3
		1083.2.a.o	3
		1083.2.a.p	6
		1083.2.a.q	6
		1083.2.a.r	8
		1083.2.a.s	8
1083.2.d	\(\chi_{1083}(1082, \cdot)\)	1083.2.d.a	6	1
		1083.2.d.b	8
		1083.2.d.c	12
		1083.2.d.d	24
		1083.2.d.e	48
1083.2.e	\(\chi_{1083}(292, \cdot)\)	n/a	112	2
1083.2.f	\(\chi_{1083}(293, \cdot)\)	n/a	196	2
1083.2.i	\(\chi_{1083}(28, \cdot)\)	n/a	342	6
1083.2.j	\(\chi_{1083}(116, \cdot)\)	n/a	582	6
1083.2.m	\(\chi_{1083}(58, \cdot)\)	n/a	1152	18
1083.2.n	\(\chi_{1083}(56, \cdot)\)	n/a	2232	18
1083.2.q	\(\chi_{1083}(7, \cdot)\)	n/a	2304	36
1083.2.t	\(\chi_{1083}(8, \cdot)\)	n/a	4464	36
1083.2.u	\(\chi_{1083}(4, \cdot)\)	n/a	6804	108
1083.2.x	\(\chi_{1083}(2, \cdot)\)	n/a	13500	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1083))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1083)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)