Space of modular forms of level 1089 and weight 4

• Label: 1089.4
• Level: 1089
• Weight: 4
• Dimension: 101120
• Nonzero newspaces: 16
• Sturm bound: 348480
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(348480\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1089))\).

	Total	New	Old
Modular forms	131960	102385	29575
Cusp forms	129400	101120	28280
Eisenstein series	2560	1265	1295

Trace form

101120 * q - 138 * q^2 - 183 * q^3 - 148 * q^4 - 150 * q^5 - 171 * q^6 - 102 * q^7 - 149 * q^8 - 135 * q^9 - 583 * q^10 - 200 * q^11 - 496 * q^12 - 234 * q^13 + 195 * q^14 - 153 * q^15 + 696 * q^16 + 363 * q^17 + 36 * q^18 - 953 * q^19 - 1313 * q^20 - 159 * q^21 - 780 * q^22 - 2408 * q^23 - 2679 * q^24 - 1939 * q^25 - 1913 * q^26 - 492 * q^27 + 2977 * q^28 + 2416 * q^29 + 3228 * q^30 + 3310 * q^31 + 8758 * q^32 + 1400 * q^33 + 4928 * q^34 + 4931 * q^35 + 2395 * q^36 + 285 * q^37 + 136 * q^38 - 21 * q^39 - 6249 * q^40 - 6087 * q^41 - 5466 * q^42 - 5573 * q^43 - 5035 * q^44 - 3495 * q^45 - 2723 * q^46 - 1714 * q^47 - 1481 * q^48 - 1545 * q^49 - 4886 * q^50 - 2783 * q^51 - 15235 * q^52 - 10627 * q^53 - 9685 * q^54 - 2450 * q^55 - 7461 * q^56 - 2521 * q^57 + 395 * q^58 + 2877 * q^59 + 9584 * q^60 + 6168 * q^61 + 26703 * q^62 + 9863 * q^63 + 26149 * q^64 + 18630 * q^65 + 8250 * q^66 + 16337 * q^67 + 26822 * q^68 + 9191 * q^69 + 20857 * q^70 + 12861 * q^71 + 7611 * q^72 + 6415 * q^73 - 1941 * q^74 - 4043 * q^75 - 13844 * q^76 - 8640 * q^77 - 19530 * q^78 - 16088 * q^79 - 29193 * q^80 + 1893 * q^81 - 44815 * q^82 - 3118 * q^83 + 29442 * q^84 - 13129 * q^85 + 5812 * q^86 + 6467 * q^87 - 5790 * q^88 - 5747 * q^89 - 11336 * q^90 + 3873 * q^91 - 10307 * q^92 - 13993 * q^93 + 10815 * q^94 - 17043 * q^95 - 58520 * q^96 + 3769 * q^97 - 22351 * q^98 - 15880 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1089))\)

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
1089.4.a	\(\chi_{1089}(1, \cdot)\)	1089.4.a.a	1	1
		1089.4.a.b	1
		1089.4.a.c	1
		1089.4.a.d	1
		1089.4.a.e	1
		1089.4.a.f	1
		1089.4.a.g	1
		1089.4.a.h	1
		1089.4.a.i	1
		1089.4.a.j	1
		1089.4.a.k	2
		1089.4.a.l	2
		1089.4.a.m	2
		1089.4.a.n	2
		1089.4.a.o	2
		1089.4.a.p	2
		1089.4.a.q	2
		1089.4.a.r	2
		1089.4.a.s	2
		1089.4.a.t	2
		1089.4.a.u	2
		1089.4.a.v	2
		1089.4.a.w	2
		1089.4.a.x	2
		1089.4.a.y	4
		1089.4.a.z	4
		1089.4.a.ba	4
		1089.4.a.bb	4
		1089.4.a.bc	4
		1089.4.a.bd	4
		1089.4.a.be	4
		1089.4.a.bf	4
		1089.4.a.bg	4
		1089.4.a.bh	4
		1089.4.a.bi	6
		1089.4.a.bj	6
		1089.4.a.bk	6
		1089.4.a.bl	12
		1089.4.a.bm	12
		1089.4.a.bn	12
1089.4.d	\(\chi_{1089}(1088, \cdot)\)	n/a	108	1
1089.4.e	\(\chi_{1089}(364, \cdot)\)	n/a	636	2
1089.4.f	\(\chi_{1089}(487, \cdot)\)	n/a	524	4
1089.4.g	\(\chi_{1089}(362, \cdot)\)	n/a	632	2
1089.4.j	\(\chi_{1089}(161, \cdot)\)	n/a	432	4
1089.4.m	\(\chi_{1089}(100, \cdot)\)	n/a	1640	10
1089.4.n	\(\chi_{1089}(124, \cdot)\)	n/a	2528	8
1089.4.o	\(\chi_{1089}(98, \cdot)\)	n/a	1320	10
1089.4.t	\(\chi_{1089}(239, \cdot)\)	n/a	2528	8
1089.4.u	\(\chi_{1089}(34, \cdot)\)	n/a	7880	20
1089.4.v	\(\chi_{1089}(37, \cdot)\)	n/a	6560	40
1089.4.y	\(\chi_{1089}(32, \cdot)\)	n/a	7880	20
1089.4.bb	\(\chi_{1089}(8, \cdot)\)	n/a	5280	40
1089.4.bc	\(\chi_{1089}(4, \cdot)\)	n/a	31520	80
1089.4.bd	\(\chi_{1089}(2, \cdot)\)	n/a	31520	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1089))\) into lower level spaces

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