Space of modular forms of level 53 and weight 2

• Label: 53.2
• Level: 53
• Weight: 2
• Dimension: 92
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 468
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(468\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(53))\).

	Total	New	Old
Modular forms	143	143	0
Cusp forms	92	92	0
Eisenstein series	51	51	0

Trace form

92 * q - 23 * q^2 - 22 * q^3 - 19 * q^4 - 20 * q^5 - 14 * q^6 - 18 * q^7 - 11 * q^8 - 13 * q^9 - 8 * q^10 - 14 * q^11 + 2 * q^12 - 12 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 - 8 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 + 6 * q^21 + 10 * q^22 - 2 * q^23 + 34 * q^24 + 5 * q^25 + 16 * q^26 + 14 * q^27 + 30 * q^28 + 4 * q^29 + 46 * q^30 + 6 * q^31 + 37 * q^32 + 22 * q^33 + 28 * q^34 + 22 * q^35 + 65 * q^36 + 12 * q^37 + 34 * q^38 + 30 * q^39 + 25 * q^40 - 10 * q^41 - 34 * q^42 - 34 * q^43 - 46 * q^44 - 78 * q^45 - 6 * q^46 - 4 * q^47 - 162 * q^48 - 21 * q^49 - 50 * q^50 - 58 * q^51 - 110 * q^52 - 51 * q^53 - 88 * q^54 - 32 * q^55 - 62 * q^56 - 50 * q^57 - 53 * q^58 - 18 * q^59 - 118 * q^60 + 10 * q^61 + 18 * q^62 - 52 * q^63 - 3 * q^64 + 6 * q^65 + 14 * q^66 + 16 * q^67 + 61 * q^68 + 70 * q^69 + 118 * q^70 + 46 * q^71 + 169 * q^72 + 48 * q^73 + 88 * q^74 + 98 * q^75 + 114 * q^76 + 70 * q^77 + 142 * q^78 + 54 * q^79 + 160 * q^80 + 95 * q^81 + 100 * q^82 + 58 * q^83 + 198 * q^84 + 82 * q^85 + 106 * q^86 + 42 * q^87 + 24 * q^88 - q^89 - 18 * q^91 - 92 * q^92 - 2 * q^93 - 194 * q^94 - 10 * q^95 - 34 * q^96 - 149 * q^97 - 63 * q^98 - 130 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)

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
53.2.a	\(\chi_{53}(1, \cdot)\)	53.2.a.a	1	1
		53.2.a.b	3
53.2.b	\(\chi_{53}(52, \cdot)\)	53.2.b.a	4	1
53.2.d	\(\chi_{53}(10, \cdot)\)	53.2.d.a	36	12
53.2.e	\(\chi_{53}(4, \cdot)\)	53.2.e.a	48	12