Space of modular forms of level 55 and weight 2

• Label: 55.2
• Level: 55
• Weight: 2
• Dimension: 79
• Nonzero newspaces: 6
• Newform subspaces: 9
• Sturm bound: 480
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(55))\).

	Total	New	Old
Modular forms	160	135	25
Cusp forms	81	79	2
Eisenstein series	79	56	23

Trace form

79 * q - 13 * q^2 - 14 * q^3 - 17 * q^4 - 16 * q^5 - 32 * q^6 - 8 * q^7 - 5 * q^8 - 3 * q^9 - 3 * q^10 - 31 * q^11 - 8 * q^12 - 14 * q^13 - 4 * q^14 + q^15 - q^16 + 2 * q^17 + 11 * q^18 + 13 * q^20 - 12 * q^21 + 17 * q^22 - 14 * q^23 + 40 * q^24 + 14 * q^25 + 18 * q^26 + 10 * q^27 + 44 * q^28 + 10 * q^29 + 38 * q^30 - 22 * q^31 + 27 * q^32 + 26 * q^33 + 6 * q^34 + 22 * q^35 + 59 * q^36 + 12 * q^37 + 40 * q^38 + 44 * q^39 - 25 * q^40 + 18 * q^41 + 44 * q^42 - 4 * q^43 - 27 * q^44 - 33 * q^45 - 52 * q^46 - 48 * q^47 - 64 * q^48 - 57 * q^49 - 43 * q^50 - 52 * q^51 - 98 * q^52 - 14 * q^53 - 60 * q^54 - 46 * q^55 - 120 * q^56 - 20 * q^57 - 90 * q^58 - 30 * q^59 - 38 * q^60 - 82 * q^61 + 24 * q^62 - 24 * q^63 - 37 * q^64 - 14 * q^65 + 8 * q^66 - 18 * q^67 + 34 * q^68 + 34 * q^69 + 56 * q^70 + 38 * q^71 + 55 * q^72 + 46 * q^73 + 106 * q^74 + 71 * q^75 + 100 * q^76 + 72 * q^77 + 112 * q^78 + 80 * q^79 + 139 * q^80 + 79 * q^81 + 74 * q^82 + 76 * q^83 + 116 * q^84 + 72 * q^85 + 68 * q^86 + 100 * q^87 + 145 * q^88 + 20 * q^89 - 9 * q^90 + 48 * q^91 + 52 * q^92 + 2 * q^93 + 16 * q^94 - 52 * q^96 - 28 * q^97 - 81 * q^98 - 73 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.2.a	\(\chi_{55}(1, \cdot)\)	55.2.a.a	1	1
		55.2.a.b	2
55.2.b	\(\chi_{55}(34, \cdot)\)	55.2.b.a	4	1
55.2.e	\(\chi_{55}(32, \cdot)\)	55.2.e.a	4	2
		55.2.e.b	4
55.2.g	\(\chi_{55}(16, \cdot)\)	55.2.g.a	8	4
		55.2.g.b	8
55.2.j	\(\chi_{55}(4, \cdot)\)	55.2.j.a	16	4
55.2.l	\(\chi_{55}(2, \cdot)\)	55.2.l.a	32	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 1}\)