Space of modular forms of level 529 and weight 2

• Label: 529.2
• Level: 529
• Weight: 2
• Dimension: 11241
• Nonzero newspaces: 4
• Newform subspaces: 30
• Sturm bound: 46552
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 529 = 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(46552\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(529))\).

	Total	New	Old
Modular forms	12012	11946	66
Cusp forms	11265	11241	24
Eisenstein series	747	705	42

Trace form

11241 * q - 234 * q^2 - 235 * q^3 - 238 * q^4 - 237 * q^5 - 243 * q^6 - 239 * q^7 - 246 * q^8 - 244 * q^9 - 249 * q^10 - 243 * q^11 - 259 * q^12 - 245 * q^13 - 255 * q^14 - 233 * q^15 - 218 * q^16 - 227 * q^17 - 182 * q^18 - 229 * q^19 - 185 * q^20 - 197 * q^21 - 201 * q^22 - 220 * q^23 - 379 * q^24 - 218 * q^25 - 229 * q^26 - 205 * q^27 - 199 * q^28 - 239 * q^29 - 215 * q^30 - 241 * q^31 - 250 * q^32 - 257 * q^33 - 241 * q^34 - 235 * q^35 - 212 * q^36 - 181 * q^37 - 181 * q^38 - 199 * q^39 - 145 * q^40 - 229 * q^41 - 107 * q^42 - 187 * q^43 - 117 * q^44 - 155 * q^45 - 154 * q^46 - 411 * q^47 - 135 * q^48 - 156 * q^49 - 170 * q^50 - 215 * q^51 - 109 * q^52 - 241 * q^53 - 131 * q^54 - 171 * q^55 - 109 * q^56 - 157 * q^57 - 123 * q^58 - 159 * q^59 - 135 * q^60 - 205 * q^61 - 195 * q^62 - 225 * q^63 - 182 * q^64 - 161 * q^65 - 133 * q^66 - 255 * q^67 - 71 * q^68 - 187 * q^69 - 419 * q^70 - 193 * q^71 - 96 * q^72 - 261 * q^73 - 147 * q^74 - 113 * q^75 - 85 * q^76 - 129 * q^77 - 47 * q^78 - 135 * q^79 + q^80 - 137 * q^82 - 161 * q^83 - 15 * q^84 - 75 * q^85 - 99 * q^86 - 87 * q^87 - 147 * q^88 - 189 * q^89 - 3 * q^90 - 145 * q^91 - 143 * q^92 - 315 * q^93 - 133 * q^94 - 153 * q^95 + 111 * q^96 - 131 * q^97 - 138 * q^98 - 13 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)

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
529.2.a	\(\chi_{529}(1, \cdot)\)	529.2.a.a	2	1
		529.2.a.b	2
		529.2.a.c	2
		529.2.a.d	2
		529.2.a.e	2
		529.2.a.f	3
		529.2.a.g	4
		529.2.a.h	4
		529.2.a.i	5
		529.2.a.j	5
529.2.c	\(\chi_{529}(118, \cdot)\)	529.2.c.a	10	10
		529.2.c.b	10
		529.2.c.c	10
		529.2.c.d	10
		529.2.c.e	10
		529.2.c.f	10
		529.2.c.g	10
		529.2.c.h	10
		529.2.c.i	10
		529.2.c.j	20
		529.2.c.k	20
		529.2.c.l	20
		529.2.c.m	20
		529.2.c.n	20
		529.2.c.o	20
		529.2.c.p	30
		529.2.c.q	40
		529.2.c.r	40
529.2.e	\(\chi_{529}(24, \cdot)\)	529.2.e.a	990	22
529.2.g	\(\chi_{529}(2, \cdot)\)	529.2.g.a	9900	220

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(529))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(529)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)