Space of modular forms of level 121 and weight 4

• Label: 121.4
• Level: 121
• Weight: 4
• Dimension: 1715
• Nonzero newspaces: 4
• Newform subspaces: 20
• Sturm bound: 4840
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 121 = 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(4840\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(121))\).

	Total	New	Old
Modular forms	1895	1856	39
Cusp forms	1735	1715	20
Eisenstein series	160	141	19

Trace form

1715 * q - 45 * q^2 - 45 * q^3 - 45 * q^4 - 45 * q^5 + 55 * q^6 - 25 * q^7 - 125 * q^8 - 205 * q^9 - 235 * q^10 - 100 * q^11 - 405 * q^12 - 85 * q^13 + 345 * q^14 + 575 * q^15 + 715 * q^16 + 255 * q^17 - 35 * q^18 - 495 * q^19 - 915 * q^20 - 875 * q^21 - 680 * q^22 + 115 * q^23 + 335 * q^24 + 75 * q^25 + 305 * q^26 + 165 * q^27 + 285 * q^28 + 55 * q^29 + 705 * q^30 + 735 * q^31 - 495 * q^32 + 155 * q^33 + 595 * q^34 - 185 * q^35 - 135 * q^36 - 325 * q^37 - 815 * q^38 - 1585 * q^39 - 135 * q^40 - 1065 * q^41 - 115 * q^42 + 1365 * q^43 + 1065 * q^44 - 1865 * q^45 - 1835 * q^46 - 1225 * q^47 - 2895 * q^48 - 2025 * q^49 - 225 * q^50 + 765 * q^51 + 2245 * q^52 + 3915 * q^53 + 6365 * q^54 + 1550 * q^55 + 2775 * q^56 + 2765 * q^57 - 2455 * q^58 - 2675 * q^59 - 3455 * q^60 - 685 * q^61 - 5235 * q^62 - 415 * q^63 - 1445 * q^64 - 1875 * q^65 - 1355 * q^66 - 1785 * q^67 - 2755 * q^68 - 1895 * q^69 - 335 * q^70 - 985 * q^71 - 405 * q^72 + 5055 * q^73 + 2885 * q^74 + 1305 * q^75 - 435 * q^76 + 2180 * q^77 + 3455 * q^78 + 1035 * q^79 + 6865 * q^80 + 2585 * q^81 + 5915 * q^82 - 1095 * q^83 + 1585 * q^84 - 5725 * q^85 - 1865 * q^86 - 7075 * q^87 - 4730 * q^88 - 3985 * q^89 + 245 * q^90 - 2885 * q^91 + 4925 * q^92 + 5375 * q^93 + 525 * q^94 - 3325 * q^95 - 655 * q^96 - 1755 * q^97 - 3795 * q^98 - 1670 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.4.a	\(\chi_{121}(1, \cdot)\)	121.4.a.a	1	1
		121.4.a.b	2
		121.4.a.c	2
		121.4.a.d	2
		121.4.a.e	2
		121.4.a.f	4
		121.4.a.g	4
		121.4.a.h	6
121.4.c	\(\chi_{121}(3, \cdot)\)	121.4.c.a	4	4
		121.4.c.b	8
		121.4.c.c	8
		121.4.c.d	8
		121.4.c.e	8
		121.4.c.f	8
		121.4.c.g	8
		121.4.c.h	8
		121.4.c.i	8
		121.4.c.j	24
121.4.e	\(\chi_{121}(12, \cdot)\)	121.4.e.a	320	10
121.4.g	\(\chi_{121}(4, \cdot)\)	121.4.g.a	1280	40

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)