Space of modular forms of level 159 and weight 2

• Label: 159.2
• Level: 159
• Weight: 2
• Dimension: 649
• Nonzero newspaces: 6
• Newform subspaces: 8
• Sturm bound: 3744
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 159 = 3 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(3744\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(159))\).

	Total	New	Old
Modular forms	1040	753	287
Cusp forms	833	649	184
Eisenstein series	207	104	103

Trace form

649 * q - 3 * q^2 - 27 * q^3 - 59 * q^4 - 6 * q^5 - 29 * q^6 - 60 * q^7 - 15 * q^8 - 27 * q^9 - 70 * q^10 - 12 * q^11 - 33 * q^12 - 66 * q^13 - 24 * q^14 - 32 * q^15 - 83 * q^16 - 18 * q^17 - 29 * q^18 - 72 * q^19 - 42 * q^20 - 34 * q^21 - 88 * q^22 - 24 * q^23 - 41 * q^24 - 83 * q^25 - 42 * q^26 - 27 * q^27 - 108 * q^28 - 30 * q^29 - 44 * q^30 - 84 * q^31 - 63 * q^32 - 38 * q^33 - 106 * q^34 - 48 * q^35 - 33 * q^36 - 90 * q^37 - 60 * q^38 - 40 * q^39 - 64 * q^40 + 10 * q^41 + 54 * q^42 + 8 * q^43 + 124 * q^44 + 98 * q^45 - 20 * q^46 + 4 * q^47 + 203 * q^48 - 5 * q^49 + 141 * q^50 + 60 * q^51 + 214 * q^52 + 103 * q^53 + 101 * q^54 + 32 * q^55 + 192 * q^56 + 58 * q^57 + 92 * q^58 + 44 * q^59 + 192 * q^60 - 62 * q^61 + 8 * q^62 + 96 * q^63 + 29 * q^64 + 20 * q^65 + 42 * q^66 - 68 * q^67 - 48 * q^68 - 50 * q^69 - 196 * q^70 - 72 * q^71 - 41 * q^72 - 126 * q^73 - 114 * q^74 - 57 * q^75 - 192 * q^76 - 96 * q^77 - 68 * q^78 - 132 * q^79 - 186 * q^80 - 27 * q^81 - 178 * q^82 - 84 * q^83 - 82 * q^84 - 160 * q^85 - 132 * q^86 - 4 * q^87 + 28 * q^88 + 40 * q^89 + 8 * q^90 + 44 * q^91 + 300 * q^92 + 46 * q^93 + 428 * q^94 + 88 * q^95 + 171 * q^96 + 292 * q^97 + 245 * q^98 + 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)

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
159.2.a	\(\chi_{159}(1, \cdot)\)	159.2.a.a	4	1
		159.2.a.b	5
159.2.c	\(\chi_{159}(52, \cdot)\)	159.2.c.a	8	1
159.2.f	\(\chi_{159}(23, \cdot)\)	159.2.f.a	32	2
159.2.g	\(\chi_{159}(10, \cdot)\)	159.2.g.a	60	12
		159.2.g.b	60
159.2.i	\(\chi_{159}(4, \cdot)\)	159.2.i.a	96	12
159.2.k	\(\chi_{159}(2, \cdot)\)	159.2.k.a	384	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(159))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(159)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)