Space of modular forms of level 627 and weight 2

• Label: 627.2
• Level: 627
• Weight: 2
• Dimension: 10259
• Nonzero newspaces: 24
• Newform subspaces: 49
• Sturm bound: 57600
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 49 \)
Sturm bound:			\(57600\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(627))\).

	Total	New	Old
Modular forms	15120	10867	4253
Cusp forms	13681	10259	3422
Eisenstein series	1439	608	831

Trace form

10259 * q + 9 * q^2 - 59 * q^3 - 103 * q^4 + 18 * q^5 - 63 * q^6 - 120 * q^7 + 5 * q^8 - 79 * q^9 - 130 * q^10 + 3 * q^11 - 185 * q^12 - 150 * q^13 - 60 * q^14 - 120 * q^15 - 295 * q^16 - 42 * q^17 - 101 * q^18 - 209 * q^19 - 118 * q^20 - 130 * q^21 - 247 * q^22 - 4 * q^23 - 139 * q^24 - 183 * q^25 - 46 * q^26 - 53 * q^27 - 212 * q^28 - 22 * q^29 - 144 * q^30 - 140 * q^31 - 31 * q^32 - 82 * q^33 - 382 * q^34 - 80 * q^35 - 195 * q^36 - 198 * q^37 - 185 * q^38 - 250 * q^39 - 398 * q^40 - 66 * q^41 - 240 * q^42 - 276 * q^43 - 149 * q^44 - 268 * q^45 - 348 * q^46 - 68 * q^47 - 119 * q^48 - 245 * q^49 - 49 * q^50 - 46 * q^51 - 90 * q^52 + 22 * q^53 + 25 * q^54 - 164 * q^55 + 120 * q^56 + 67 * q^57 - 178 * q^58 + 120 * q^59 + 140 * q^60 - 158 * q^61 - 12 * q^62 + 40 * q^63 - 231 * q^64 - 84 * q^65 + 8 * q^66 - 468 * q^67 - 74 * q^68 - 100 * q^69 - 424 * q^70 - 48 * q^71 - 133 * q^72 - 406 * q^73 - 126 * q^74 - 245 * q^75 - 411 * q^76 - 194 * q^77 - 404 * q^78 - 552 * q^79 - 366 * q^80 - 151 * q^81 - 650 * q^82 - 260 * q^83 - 456 * q^84 - 492 * q^85 - 280 * q^86 - 390 * q^87 - 441 * q^88 - 214 * q^89 - 264 * q^90 - 344 * q^91 - 304 * q^92 - 330 * q^93 - 388 * q^94 - 24 * q^95 - 219 * q^96 - 178 * q^97 - 215 * q^98 - 117 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)

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
627.2.a	\(\chi_{627}(1, \cdot)\)	627.2.a.a	1	1
		627.2.a.b	1
		627.2.a.c	3
		627.2.a.d	3
		627.2.a.e	3
		627.2.a.f	3
		627.2.a.g	3
		627.2.a.h	4
		627.2.a.i	5
		627.2.a.j	5
627.2.f	\(\chi_{627}(362, \cdot)\)	627.2.f.a	72	1
627.2.g	\(\chi_{627}(56, \cdot)\)	627.2.g.a	68	1
627.2.h	\(\chi_{627}(208, \cdot)\)	627.2.h.a	16	1
		627.2.h.b	24
627.2.i	\(\chi_{627}(463, \cdot)\)	627.2.i.a	2	2
		627.2.i.b	2
		627.2.i.c	4
		627.2.i.d	10
		627.2.i.e	14
		627.2.i.f	16
		627.2.i.g	16
627.2.j	\(\chi_{627}(58, \cdot)\)	627.2.j.a	24	4
		627.2.j.b	32
		627.2.j.c	40
		627.2.j.d	48
627.2.k	\(\chi_{627}(274, \cdot)\)	627.2.k.a	80	2
627.2.l	\(\chi_{627}(197, \cdot)\)	627.2.l.a	152	2
627.2.m	\(\chi_{627}(122, \cdot)\)	627.2.m.a	136	2
627.2.r	\(\chi_{627}(100, \cdot)\)	627.2.r.a	42	6
		627.2.r.b	48
		627.2.r.c	54
		627.2.r.d	60
627.2.s	\(\chi_{627}(94, \cdot)\)	627.2.s.a	160	4
627.2.t	\(\chi_{627}(113, \cdot)\)	627.2.t.a	304	4
627.2.u	\(\chi_{627}(134, \cdot)\)	627.2.u.a	288	4
627.2.z	\(\chi_{627}(49, \cdot)\)	627.2.z.a	8	8
		627.2.z.b	152
		627.2.z.c	160
627.2.ba	\(\chi_{627}(89, \cdot)\)	627.2.ba.a	396	6
627.2.bd	\(\chi_{627}(131, \cdot)\)	627.2.bd.a	456	6
627.2.be	\(\chi_{627}(10, \cdot)\)	627.2.be.a	240	6
627.2.bl	\(\chi_{627}(179, \cdot)\)	627.2.bl.a	608	8
627.2.bm	\(\chi_{627}(68, \cdot)\)	627.2.bm.a	608	8
627.2.bn	\(\chi_{627}(46, \cdot)\)	627.2.bn.a	320	8
627.2.bo	\(\chi_{627}(4, \cdot)\)	627.2.bo.a	480	24
		627.2.bo.b	480
627.2.br	\(\chi_{627}(13, \cdot)\)	627.2.br.a	960	24
627.2.bs	\(\chi_{627}(17, \cdot)\)	627.2.bs.a	1824	24
627.2.bv	\(\chi_{627}(14, \cdot)\)	627.2.bv.a	1824	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(627))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(627)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 2}\)