Space of modular forms of level 121 and weight 6

• Label: 121.6
• Level: 121
• Weight: 6
• Dimension: 2905
• Nonzero newspaces: 4
• Sturm bound: 7260
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 121 = 11^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(7260\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(121))\).

	Total	New	Old
Modular forms	3105	3046	59
Cusp forms	2945	2905	40
Eisenstein series	160	141	19

Trace form

2905 * q - 45 * q^2 - 45 * q^3 - 45 * q^4 - 45 * q^5 - 5 * q^6 - 635 * q^7 - 365 * q^8 + 1055 * q^9 + 1965 * q^10 + 395 * q^11 + 555 * q^12 - 1055 * q^13 + 945 * q^14 - 7525 * q^15 - 16325 * q^16 - 3555 * q^17 + 5545 * q^18 + 4425 * q^19 + 17325 * q^20 + 17605 * q^21 + 12520 * q^22 + 20305 * q^23 + 2735 * q^24 - 25785 * q^25 - 65935 * q^26 - 46905 * q^27 - 64835 * q^28 - 8495 * q^29 + 42585 * q^30 + 50555 * q^31 + 152625 * q^32 + 42560 * q^33 + 8675 * q^34 - 37955 * q^35 - 137535 * q^36 - 68905 * q^37 - 120935 * q^38 - 61975 * q^39 - 66775 * q^40 + 20625 * q^41 + 234245 * q^42 + 109165 * q^43 + 92805 * q^44 + 157255 * q^45 - 37675 * q^46 - 60655 * q^47 - 190335 * q^48 - 128195 * q^49 - 125985 * q^50 - 85155 * q^51 + 195125 * q^52 - 18195 * q^53 - 93955 * q^54 - 12310 * q^55 - 60585 * q^56 + 28145 * q^57 - 5655 * q^58 - 121265 * q^59 - 56255 * q^60 + 59825 * q^61 + 295125 * q^62 + 39425 * q^63 - 52085 * q^64 + 54225 * q^65 - 15875 * q^66 + 163805 * q^67 + 235325 * q^68 + 165955 * q^69 + 452705 * q^70 + 228095 * q^71 + 226395 * q^72 - 31255 * q^73 - 822235 * q^74 - 532335 * q^75 - 569795 * q^76 - 393655 * q^77 - 834145 * q^78 - 429275 * q^79 + 525745 * q^80 + 801305 * q^81 + 1130975 * q^82 + 585285 * q^83 - 148175 * q^84 + 106265 * q^85 - 564245 * q^86 - 28855 * q^87 - 120450 * q^88 - 118015 * q^89 + 490205 * q^90 + 759065 * q^91 + 909005 * q^92 + 614855 * q^93 + 317885 * q^94 + 39185 * q^95 - 657535 * q^96 - 1121825 * q^97 - 1628055 * q^98 - 726350 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.6.a	\(\chi_{121}(1, \cdot)\)	121.6.a.a	1	1
		121.6.a.b	1
		121.6.a.c	2
		121.6.a.d	3
		121.6.a.e	5
		121.6.a.f	5
		121.6.a.g	8
		121.6.a.h	8
		121.6.a.i	8
121.6.c	\(\chi_{121}(3, \cdot)\)	n/a	164	4
121.6.e	\(\chi_{121}(12, \cdot)\)	n/a	540	10
121.6.g	\(\chi_{121}(4, \cdot)\)	n/a	2160	40

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)