Space of modular forms of level 637 and weight 2

• Label: 637.2
• Level: 637
• Weight: 2
• Dimension: 15079
• Nonzero newspaces: 30
• Newform subspaces: 142
• Sturm bound: 65856
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 142 \)
Sturm bound:			\(65856\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(637))\).

	Total	New	Old
Modular forms	17184	16145	1039
Cusp forms	15745	15079	666
Eisenstein series	1439	1066	373

Trace form

15079 * q - 150 * q^2 - 152 * q^3 - 158 * q^4 - 156 * q^5 - 168 * q^6 - 188 * q^7 - 291 * q^8 - 178 * q^9 - 195 * q^10 - 174 * q^11 - 226 * q^12 - 191 * q^13 - 432 * q^14 - 312 * q^15 - 226 * q^16 - 189 * q^17 - 255 * q^18 - 204 * q^19 - 261 * q^20 - 230 * q^21 - 354 * q^22 - 204 * q^23 - 324 * q^24 - 227 * q^25 - 237 * q^26 - 446 * q^27 - 272 * q^28 - 339 * q^29 - 360 * q^30 - 234 * q^31 - 336 * q^32 - 282 * q^33 - 300 * q^34 - 258 * q^35 - 410 * q^36 - 181 * q^37 - 222 * q^38 - 204 * q^39 - 330 * q^40 - 189 * q^41 - 174 * q^42 - 302 * q^43 - 138 * q^44 - 165 * q^45 - 120 * q^46 - 198 * q^47 - 150 * q^48 - 104 * q^49 - 573 * q^50 - 198 * q^51 - 192 * q^52 - 402 * q^53 - 234 * q^54 - 144 * q^55 - 132 * q^56 - 402 * q^57 - 231 * q^58 - 222 * q^59 - 390 * q^60 - 227 * q^61 - 336 * q^62 - 300 * q^63 - 485 * q^64 - 330 * q^65 - 750 * q^66 - 336 * q^67 - 519 * q^68 - 414 * q^69 - 426 * q^70 - 456 * q^71 - 288 * q^72 - 336 * q^73 - 351 * q^74 - 346 * q^75 - 180 * q^76 - 234 * q^77 - 237 * q^78 - 262 * q^79 - 9 * q^80 - 10 * q^81 + 279 * q^82 - 6 * q^83 + 232 * q^84 + 39 * q^85 + 48 * q^86 + 264 * q^87 + 648 * q^88 + 36 * q^89 + 756 * q^90 - 53 * q^91 - 192 * q^92 + 282 * q^93 + 522 * q^94 + 132 * q^95 + 768 * q^96 + 222 * q^97 + 264 * q^98 - 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)

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
637.2.a	\(\chi_{637}(1, \cdot)\)	637.2.a.a	1	1
		637.2.a.b	1
		637.2.a.c	1
		637.2.a.d	1
		637.2.a.e	2
		637.2.a.f	2
		637.2.a.g	2
		637.2.a.h	3
		637.2.a.i	3
		637.2.a.j	3
		637.2.a.k	5
		637.2.a.l	5
		637.2.a.m	6
		637.2.a.n	6
637.2.c	\(\chi_{637}(246, \cdot)\)	637.2.c.a	2	1
		637.2.c.b	2
		637.2.c.c	2
		637.2.c.d	6
		637.2.c.e	8
		637.2.c.f	8
		637.2.c.g	16
637.2.e	\(\chi_{637}(79, \cdot)\)	637.2.e.a	2	2
		637.2.e.b	2
		637.2.e.c	2
		637.2.e.d	2
		637.2.e.e	2
		637.2.e.f	4
		637.2.e.g	4
		637.2.e.h	4
		637.2.e.i	6
		637.2.e.j	6
		637.2.e.k	6
		637.2.e.l	6
		637.2.e.m	10
		637.2.e.n	12
		637.2.e.o	12
637.2.f	\(\chi_{637}(295, \cdot)\)	637.2.f.a	2	2
		637.2.f.b	2
		637.2.f.c	4
		637.2.f.d	4
		637.2.f.e	4
		637.2.f.f	4
		637.2.f.g	8
		637.2.f.h	8
		637.2.f.i	8
		637.2.f.j	12
		637.2.f.k	12
		637.2.f.l	16
637.2.g	\(\chi_{637}(263, \cdot)\)	637.2.g.a	2	2
		637.2.g.b	4
		637.2.g.c	4
		637.2.g.d	4
		637.2.g.e	4
		637.2.g.f	4
		637.2.g.g	4
		637.2.g.h	8
		637.2.g.i	8
		637.2.g.j	8
		637.2.g.k	8
		637.2.g.l	12
		637.2.g.m	16
637.2.h	\(\chi_{637}(165, \cdot)\)	637.2.h.a	2	2
		637.2.h.b	4
		637.2.h.c	4
		637.2.h.d	4
		637.2.h.e	4
		637.2.h.f	4
		637.2.h.g	4
		637.2.h.h	8
		637.2.h.i	8
		637.2.h.j	8
		637.2.h.k	8
		637.2.h.l	12
		637.2.h.m	16
637.2.i	\(\chi_{637}(489, \cdot)\)	637.2.i.a	32	2
		637.2.i.b	56
637.2.k	\(\chi_{637}(459, \cdot)\)	637.2.k.a	2	2
		637.2.k.b	2
		637.2.k.c	2
		637.2.k.d	4
		637.2.k.e	4
		637.2.k.f	4
		637.2.k.g	12
		637.2.k.h	12
		637.2.k.i	12
		637.2.k.j	32
637.2.q	\(\chi_{637}(491, \cdot)\)	637.2.q.a	2	2
		637.2.q.b	2
		637.2.q.c	2
		637.2.q.d	4
		637.2.q.e	4
		637.2.q.f	4
		637.2.q.g	12
		637.2.q.h	12
		637.2.q.i	12
		637.2.q.j	32
637.2.r	\(\chi_{637}(116, \cdot)\)	637.2.r.a	4	2
		637.2.r.b	4
		637.2.r.c	4
		637.2.r.d	12
		637.2.r.e	12
		637.2.r.f	16
		637.2.r.g	32
637.2.u	\(\chi_{637}(30, \cdot)\)	637.2.u.a	2	2
		637.2.u.b	2
		637.2.u.c	2
		637.2.u.d	4
		637.2.u.e	4
		637.2.u.f	4
		637.2.u.g	12
		637.2.u.h	12
		637.2.u.i	12
		637.2.u.j	32
637.2.w	\(\chi_{637}(92, \cdot)\)	637.2.w.a	162	6
		637.2.w.b	174
637.2.x	\(\chi_{637}(19, \cdot)\)	637.2.x.a	28	4
		637.2.x.b	32
		637.2.x.c	112
637.2.bb	\(\chi_{637}(227, \cdot)\)	637.2.bb.a	28	4
		637.2.bb.b	32
		637.2.bb.c	112
637.2.bc	\(\chi_{637}(31, \cdot)\)	637.2.bc.a	24	4
		637.2.bc.b	32
		637.2.bc.c	112
637.2.bd	\(\chi_{637}(97, \cdot)\)	637.2.bd.a	28	4
		637.2.bd.b	28
		637.2.bd.c	112
637.2.bg	\(\chi_{637}(64, \cdot)\)	637.2.bg.a	372	6
637.2.bi	\(\chi_{637}(16, \cdot)\)	637.2.bi.a	756	12
637.2.bj	\(\chi_{637}(9, \cdot)\)	637.2.bj.a	756	12
637.2.bk	\(\chi_{637}(22, \cdot)\)	637.2.bk.a	768	12
637.2.bl	\(\chi_{637}(53, \cdot)\)	637.2.bl.a	324	12
		637.2.bl.b	348
637.2.bn	\(\chi_{637}(34, \cdot)\)	637.2.bn.a	744	12
637.2.bp	\(\chi_{637}(88, \cdot)\)	637.2.bp.a	756	12
637.2.bs	\(\chi_{637}(25, \cdot)\)	637.2.bs.a	768	12
637.2.bt	\(\chi_{637}(36, \cdot)\)	637.2.bt.a	768	12
637.2.bz	\(\chi_{637}(4, \cdot)\)	637.2.bz.a	756	12
637.2.cb	\(\chi_{637}(6, \cdot)\)	637.2.cb.a	1536	24
637.2.cc	\(\chi_{637}(5, \cdot)\)	637.2.cc.a	1536	24
637.2.cd	\(\chi_{637}(45, \cdot)\)	637.2.cd.a	1512	24
637.2.ch	\(\chi_{637}(24, \cdot)\)	637.2.ch.a	1512	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(637))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(637)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 1}\)