Space of modular forms of level 531 and weight 2

• Label: 531.2
• Level: 531
• Weight: 2
• Dimension: 8004
• Nonzero newspaces: 8
• Newform subspaces: 20
• Sturm bound: 41760
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(41760\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(531))\).

	Total	New	Old
Modular forms	10904	8516	2388
Cusp forms	9977	8004	1973
Eisenstein series	927	512	415

Trace form

8004 * q - 87 * q^2 - 116 * q^3 - 87 * q^4 - 87 * q^5 - 116 * q^6 - 87 * q^7 - 87 * q^8 - 116 * q^9 - 261 * q^10 - 87 * q^11 - 116 * q^12 - 87 * q^13 - 87 * q^14 - 116 * q^15 - 87 * q^16 - 87 * q^17 - 116 * q^18 - 261 * q^19 - 87 * q^20 - 116 * q^21 - 87 * q^22 - 87 * q^23 - 116 * q^24 - 87 * q^25 - 87 * q^26 - 116 * q^27 - 261 * q^28 - 87 * q^29 - 116 * q^30 - 87 * q^31 - 87 * q^32 - 116 * q^33 - 87 * q^34 - 87 * q^35 - 116 * q^36 - 261 * q^37 - 87 * q^38 - 116 * q^39 - 87 * q^40 - 87 * q^41 - 116 * q^42 - 87 * q^43 - 87 * q^44 - 116 * q^45 - 319 * q^46 - 116 * q^47 - 116 * q^48 - 145 * q^49 - 203 * q^50 - 116 * q^51 - 203 * q^52 - 145 * q^53 - 116 * q^54 - 348 * q^55 - 319 * q^56 - 116 * q^57 - 174 * q^58 - 145 * q^59 - 232 * q^60 - 145 * q^61 - 145 * q^62 - 116 * q^63 - 493 * q^64 - 174 * q^65 - 116 * q^66 - 145 * q^67 - 203 * q^68 - 116 * q^69 - 203 * q^70 - 145 * q^71 - 116 * q^72 - 290 * q^73 - 145 * q^74 - 116 * q^75 - 87 * q^76 - 87 * q^77 - 116 * q^78 - 87 * q^79 - 87 * q^80 - 116 * q^81 - 261 * q^82 - 87 * q^83 - 116 * q^84 - 87 * q^85 - 87 * q^86 - 116 * q^87 - 87 * q^88 - 87 * q^89 - 116 * q^90 - 261 * q^91 - 87 * q^92 - 116 * q^93 - 87 * q^94 - 87 * q^95 - 116 * q^96 - 87 * q^97 - 174 * q^98 - 116 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)

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
531.2.a	\(\chi_{531}(1, \cdot)\)	531.2.a.a	2	1
		531.2.a.b	2
		531.2.a.c	2
		531.2.a.d	3
		531.2.a.e	5
		531.2.a.f	5
		531.2.a.g	5
531.2.d	\(\chi_{531}(530, \cdot)\)	531.2.d.a	20	1
531.2.e	\(\chi_{531}(178, \cdot)\)	531.2.e.a	4	2
		531.2.e.b	42
		531.2.e.c	70
531.2.f	\(\chi_{531}(176, \cdot)\)	531.2.f.a	12	2
		531.2.f.b	104
531.2.i	\(\chi_{531}(19, \cdot)\)	531.2.i.a	112	28
		531.2.i.b	140
		531.2.i.c	140
		531.2.i.d	280
531.2.j	\(\chi_{531}(8, \cdot)\)	531.2.j.a	560	28
531.2.m	\(\chi_{531}(4, \cdot)\)	531.2.m.a	3248	56
531.2.p	\(\chi_{531}(2, \cdot)\)	531.2.p.a	3248	56

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(531)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)