Space of modular forms of level 643 and weight 2

• Label: 643.2
• Level: 643
• Weight: 2
• Dimension: 16907
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 68908
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 643 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(68908\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(643))\).

	Total	New	Old
Modular forms	17548	17548	0
Cusp forms	16907	16907	0
Eisenstein series	641	641	0

Trace form

16907 * q - 318 * q^2 - 317 * q^3 - 314 * q^4 - 315 * q^5 - 309 * q^6 - 313 * q^7 - 306 * q^8 - 308 * q^9 - 303 * q^10 - 309 * q^11 - 293 * q^12 - 307 * q^13 - 297 * q^14 - 297 * q^15 - 290 * q^16 - 303 * q^17 - 282 * q^18 - 301 * q^19 - 279 * q^20 - 289 * q^21 - 285 * q^22 - 297 * q^23 - 261 * q^24 - 290 * q^25 - 279 * q^26 - 281 * q^27 - 265 * q^28 - 291 * q^29 - 249 * q^30 - 289 * q^31 - 258 * q^32 - 273 * q^33 - 267 * q^34 - 273 * q^35 - 230 * q^36 - 283 * q^37 - 261 * q^38 - 265 * q^39 - 231 * q^40 - 279 * q^41 - 225 * q^42 - 277 * q^43 - 237 * q^44 - 243 * q^45 - 249 * q^46 - 273 * q^47 - 197 * q^48 - 264 * q^49 - 228 * q^50 - 249 * q^51 - 223 * q^52 - 267 * q^53 - 201 * q^54 - 249 * q^55 - 201 * q^56 - 241 * q^57 - 231 * q^58 - 261 * q^59 - 153 * q^60 - 259 * q^61 - 225 * q^62 - 217 * q^63 - 194 * q^64 - 237 * q^65 - 177 * q^66 - 253 * q^67 - 195 * q^68 - 225 * q^69 - 177 * q^70 - 249 * q^71 - 126 * q^72 - 247 * q^73 - 207 * q^74 - 197 * q^75 - 181 * q^76 - 225 * q^77 - 153 * q^78 - 241 * q^79 - 135 * q^80 - 200 * q^81 - 195 * q^82 - 237 * q^83 - 97 * q^84 - 213 * q^85 - 189 * q^86 - 201 * q^87 - 141 * q^88 - 231 * q^89 - 87 * q^90 - 209 * q^91 - 153 * q^92 - 193 * q^93 - 177 * q^94 - 201 * q^95 - 69 * q^96 - 223 * q^97 - 150 * q^98 - 165 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(643))\)

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
643.2.a	\(\chi_{643}(1, \cdot)\)	643.2.a.a	1	1
		643.2.a.b	24
		643.2.a.c	28
643.2.c	\(\chi_{643}(177, \cdot)\)	643.2.c.a	106	2
643.2.e	\(\chi_{643}(4, \cdot)\)	643.2.e.a	5512	106
643.2.g	\(\chi_{643}(7, \cdot)\)	643.2.g.a	11236	212