Space of modular forms of level 121 and weight 8

• Label: 121.8
• Level: 121
• Weight: 8
• Dimension: 4095
• Nonzero newspaces: 4
• Sturm bound: 9680
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 121 = 11^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(9680\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(121))\).

	Total	New	Old
Modular forms	4315	4236	79
Cusp forms	4155	4095	60
Eisenstein series	160	141	19

Trace form

4095 * q - 45 * q^2 - 45 * q^3 - 45 * q^4 - 45 * q^5 - 3485 * q^6 + 1925 * q^7 + 8915 * q^8 - 5785 * q^9 - 20035 * q^10 - 3345 * q^11 + 33195 * q^12 + 23885 * q^13 + 89505 * q^14 - 123925 * q^15 - 119365 * q^16 + 39465 * q^17 + 375985 * q^18 + 10425 * q^19 - 283715 * q^20 - 370475 * q^21 - 235640 * q^22 + 193505 * q^23 - 161905 * q^24 + 371775 * q^25 + 1174545 * q^26 + 911775 * q^27 + 796685 * q^28 - 364195 * q^29 - 2134695 * q^30 - 547445 * q^31 + 499345 * q^32 - 1227280 * q^33 - 3025405 * q^34 - 593835 * q^35 + 4113105 * q^36 + 3171775 * q^37 + 6376985 * q^38 + 4389065 * q^39 + 249465 * q^40 - 3873195 * q^41 - 10006075 * q^42 - 7715795 * q^43 - 4880515 * q^44 - 2530865 * q^45 + 1344005 * q^46 + 5058145 * q^47 + 21048465 * q^48 + 13056185 * q^49 + 11902975 * q^50 + 12814605 * q^51 - 6340955 * q^52 - 17746015 * q^53 - 48110275 * q^54 - 10381350 * q^55 - 10736745 * q^56 + 17790605 * q^57 + 32392665 * q^58 + 19200295 * q^59 + 42434545 * q^60 + 19807165 * q^61 - 1008075 * q^62 - 17440495 * q^63 - 43818165 * q^64 - 33612375 * q^65 - 23581835 * q^66 - 26279275 * q^67 - 8399075 * q^68 + 22070935 * q^69 + 69868065 * q^70 + 51021215 * q^71 + 57320955 * q^72 - 23790755 * q^73 + 9545285 * q^74 - 45012495 * q^75 - 49916675 * q^76 - 12044305 * q^77 - 33921985 * q^78 + 17217845 * q^79 + 20824465 * q^80 + 68286245 * q^81 + 68917975 * q^82 + 21950165 * q^83 - 13964975 * q^84 - 58065275 * q^85 - 29623405 * q^86 - 55088695 * q^87 - 26444770 * q^88 - 4611915 * q^89 - 1391155 * q^90 + 29174305 * q^91 + 12587325 * q^92 - 16350865 * q^93 + 9954685 * q^94 + 59715425 * q^95 - 47859055 * q^96 + 45353855 * q^97 + 53624945 * q^98 + 22506970 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.8.a	\(\chi_{121}(1, \cdot)\)	121.8.a.a	1	1
		121.8.a.b	2
		121.8.a.c	4
		121.8.a.d	5
		121.8.a.e	5
		121.8.a.f	6
		121.8.a.g	12
		121.8.a.h	12
		121.8.a.i	12
121.8.c	\(\chi_{121}(3, \cdot)\)	n/a	236	4
121.8.e	\(\chi_{121}(12, \cdot)\)	n/a	760	10
121.8.g	\(\chi_{121}(4, \cdot)\)	n/a	3040	40

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)