Space of modular forms of level 667 and weight 2

• Label: 667.2
• Level: 667
• Weight: 2
• Dimension: 17797
• Nonzero newspaces: 12
• Newform subspaces: 22
• Sturm bound: 73920
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(73920\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(667))\).

	Total	New	Old
Modular forms	19096	18933	163
Cusp forms	17865	17797	68
Eisenstein series	1231	1136	95

Trace form

17797 * q - 267 * q^2 - 270 * q^3 - 279 * q^4 - 276 * q^5 - 294 * q^6 - 282 * q^7 - 303 * q^8 - 297 * q^9 - 312 * q^10 - 294 * q^11 - 342 * q^12 - 300 * q^13 - 330 * q^14 - 308 * q^15 - 307 * q^16 - 290 * q^17 - 287 * q^18 - 296 * q^19 - 254 * q^20 - 232 * q^21 - 244 * q^22 - 261 * q^23 - 424 * q^24 - 251 * q^25 - 270 * q^26 - 228 * q^27 - 198 * q^28 - 261 * q^29 - 498 * q^30 - 276 * q^31 - 291 * q^32 - 296 * q^33 - 306 * q^34 - 302 * q^35 - 253 * q^36 - 256 * q^37 - 272 * q^38 - 282 * q^39 - 310 * q^40 - 340 * q^41 - 326 * q^42 - 302 * q^43 - 284 * q^44 - 268 * q^45 - 167 * q^46 - 544 * q^47 - 186 * q^48 - 185 * q^49 - 187 * q^50 - 274 * q^51 - 108 * q^52 - 250 * q^53 - 146 * q^54 - 118 * q^55 - 124 * q^56 - 204 * q^57 - 11 * q^58 - 530 * q^59 - 106 * q^60 - 244 * q^61 - 218 * q^62 - 236 * q^63 - 211 * q^64 - 230 * q^65 - 224 * q^66 - 306 * q^67 - 154 * q^68 - 294 * q^69 - 520 * q^70 - 224 * q^71 - 205 * q^72 - 310 * q^73 - 206 * q^74 - 248 * q^75 - 168 * q^76 - 208 * q^77 - 186 * q^78 - 266 * q^79 - 6 * q^80 - 45 * q^81 - 304 * q^82 - 244 * q^83 - 70 * q^84 - 150 * q^85 - 82 * q^86 - 233 * q^87 - 478 * q^88 - 256 * q^89 - 134 * q^90 - 228 * q^91 - 235 * q^92 - 552 * q^93 - 336 * q^94 - 196 * q^95 + 56 * q^96 - 200 * q^97 - 143 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)

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
667.2.a	\(\chi_{667}(1, \cdot)\)	667.2.a.a	10	1
		667.2.a.b	12
		667.2.a.c	13
		667.2.a.d	16
667.2.c	\(\chi_{667}(231, \cdot)\)	667.2.c.a	24	1
		667.2.c.b	30
667.2.f	\(\chi_{667}(505, \cdot)\)	667.2.f.a	12	2
		667.2.f.b	104
667.2.g	\(\chi_{667}(24, \cdot)\)	667.2.g.a	6	6
		667.2.g.b	144
		667.2.g.c	186
667.2.h	\(\chi_{667}(59, \cdot)\)	667.2.h.a	280	10
		667.2.h.b	280
667.2.j	\(\chi_{667}(93, \cdot)\)	667.2.j.a	144	6
		667.2.j.b	180
667.2.m	\(\chi_{667}(144, \cdot)\)	667.2.m.a	580	10
667.2.o	\(\chi_{667}(68, \cdot)\)	667.2.o.a	72	12
		667.2.o.b	624
667.2.q	\(\chi_{667}(17, \cdot)\)	667.2.q.a	1160	20
667.2.s	\(\chi_{667}(16, \cdot)\)	667.2.s.a	3480	60
667.2.u	\(\chi_{667}(4, \cdot)\)	667.2.u.a	3480	60
667.2.x	\(\chi_{667}(10, \cdot)\)	667.2.x.a	6960	120

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)