Space of modular forms of level 1089 and weight 2

• Label: 1089.2
• Level: 1089
• Weight: 2
• Dimension: 33285
• Nonzero newspaces: 16
• Sturm bound: 174240
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(174240\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1089))\).

	Total	New	Old
Modular forms	44840	34550	10290
Cusp forms	42281	33285	8996
Eisenstein series	2559	1265	1294

Trace form

33285 * q - 135 * q^2 - 180 * q^3 - 135 * q^4 - 135 * q^5 - 180 * q^6 - 125 * q^7 - 115 * q^8 - 180 * q^9 - 375 * q^10 - 145 * q^11 - 340 * q^12 - 125 * q^13 - 105 * q^14 - 180 * q^15 - 75 * q^16 - 105 * q^17 - 180 * q^18 - 375 * q^19 - 145 * q^20 - 180 * q^21 - 120 * q^22 - 265 * q^23 - 240 * q^24 - 155 * q^25 - 205 * q^26 - 240 * q^27 - 535 * q^28 - 205 * q^29 - 300 * q^30 - 175 * q^31 - 355 * q^32 - 250 * q^33 - 335 * q^34 - 245 * q^35 - 320 * q^36 - 425 * q^37 - 265 * q^38 - 240 * q^39 - 205 * q^40 - 165 * q^41 - 300 * q^42 - 125 * q^43 - 140 * q^44 - 360 * q^45 - 275 * q^46 - 65 * q^47 - 260 * q^48 - 25 * q^49 - 175 * q^50 - 200 * q^51 - 125 * q^52 - 185 * q^53 - 340 * q^54 - 470 * q^55 - 435 * q^56 - 340 * q^57 - 285 * q^58 - 315 * q^59 - 460 * q^60 - 205 * q^61 - 525 * q^62 - 340 * q^63 - 705 * q^64 - 345 * q^65 - 330 * q^66 - 445 * q^67 - 485 * q^68 - 340 * q^69 - 345 * q^70 - 315 * q^71 - 480 * q^72 - 435 * q^73 - 465 * q^74 - 320 * q^75 - 185 * q^76 - 225 * q^77 - 540 * q^78 - 125 * q^79 + 75 * q^80 - 180 * q^81 - 475 * q^82 + 55 * q^83 - 5 * q^85 + 155 * q^86 + 20 * q^87 - 70 * q^88 - 25 * q^89 + 220 * q^90 - 415 * q^91 + 275 * q^92 + 20 * q^93 + 15 * q^94 + 255 * q^95 + 400 * q^96 - 15 * q^97 + 385 * q^98 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)

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
1089.2.a	\(\chi_{1089}(1, \cdot)\)	1089.2.a.a	1	1
		1089.2.a.b	1
		1089.2.a.c	1
		1089.2.a.d	1
		1089.2.a.e	1
		1089.2.a.f	1
		1089.2.a.g	1
		1089.2.a.h	1
		1089.2.a.i	1
		1089.2.a.j	1
		1089.2.a.k	1
		1089.2.a.l	2
		1089.2.a.m	2
		1089.2.a.n	2
		1089.2.a.o	2
		1089.2.a.p	2
		1089.2.a.q	2
		1089.2.a.r	2
		1089.2.a.s	2
		1089.2.a.t	2
		1089.2.a.u	4
		1089.2.a.v	4
		1089.2.a.w	4
1089.2.d	\(\chi_{1089}(1088, \cdot)\)	1089.2.d.a	2	1
		1089.2.d.b	2
		1089.2.d.c	4
		1089.2.d.d	4
		1089.2.d.e	4
		1089.2.d.f	4
		1089.2.d.g	16
1089.2.e	\(\chi_{1089}(364, \cdot)\)	1089.2.e.a	2	2
		1089.2.e.b	2
		1089.2.e.c	2
		1089.2.e.d	4
		1089.2.e.e	4
		1089.2.e.f	4
		1089.2.e.g	4
		1089.2.e.h	6
		1089.2.e.i	8
		1089.2.e.j	12
		1089.2.e.k	16
		1089.2.e.l	20
		1089.2.e.m	20
		1089.2.e.n	24
		1089.2.e.o	36
		1089.2.e.p	36
1089.2.f	\(\chi_{1089}(487, \cdot)\)	n/a	164	4
1089.2.g	\(\chi_{1089}(362, \cdot)\)	n/a	200	2
1089.2.j	\(\chi_{1089}(161, \cdot)\)	n/a	144	4
1089.2.m	\(\chi_{1089}(100, \cdot)\)	n/a	540	10
1089.2.n	\(\chi_{1089}(124, \cdot)\)	n/a	800	8
1089.2.o	\(\chi_{1089}(98, \cdot)\)	n/a	440	10
1089.2.t	\(\chi_{1089}(239, \cdot)\)	n/a	800	8
1089.2.u	\(\chi_{1089}(34, \cdot)\)	n/a	2600	20
1089.2.v	\(\chi_{1089}(37, \cdot)\)	n/a	2160	40
1089.2.y	\(\chi_{1089}(32, \cdot)\)	n/a	2600	20
1089.2.bb	\(\chi_{1089}(8, \cdot)\)	n/a	1760	40
1089.2.bc	\(\chi_{1089}(4, \cdot)\)	n/a	10400	80
1089.2.bd	\(\chi_{1089}(2, \cdot)\)	n/a	10400	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1089))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1089)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)