Space of modular forms of level 627 and weight 4

• Label: 627.4
• Level: 627
• Weight: 4
• Dimension: 31376
• Nonzero newspaces: 24
• Sturm bound: 115200
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(115200\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(627))\).

	Total	New	Old
Modular forms	43920	31984	11936
Cusp forms	42480	31376	11104
Eisenstein series	1440	608	832

Trace form

31376 * q - 62 * q^3 - 124 * q^4 - 162 * q^6 - 164 * q^7 + 160 * q^8 + 98 * q^9 + 256 * q^10 + 200 * q^11 - 398 * q^12 - 620 * q^13 - 924 * q^14 - 466 * q^15 + 84 * q^16 - 24 * q^17 - 360 * q^18 + 1828 * q^19 + 4204 * q^20 + 1272 * q^21 + 2702 * q^22 + 688 * q^23 + 1094 * q^24 - 1132 * q^25 - 2636 * q^26 - 1760 * q^27 - 11404 * q^28 - 3920 * q^29 - 6326 * q^30 - 3244 * q^31 - 2300 * q^32 - 2763 * q^33 + 456 * q^34 + 2144 * q^35 + 3942 * q^36 + 2584 * q^37 + 9974 * q^38 + 5786 * q^39 + 10460 * q^40 + 6240 * q^41 + 7868 * q^42 + 1184 * q^43 + 1090 * q^44 + 7250 * q^45 - 2844 * q^46 - 1456 * q^47 - 3114 * q^48 - 3004 * q^49 - 9992 * q^50 - 2922 * q^51 + 4656 * q^52 - 640 * q^53 - 4392 * q^54 - 2942 * q^55 - 720 * q^56 - 5952 * q^57 + 3112 * q^58 + 2040 * q^59 - 22382 * q^60 - 18644 * q^61 - 24780 * q^62 - 11274 * q^63 - 28540 * q^64 - 14280 * q^65 - 12993 * q^66 - 6100 * q^67 - 4972 * q^68 + 3460 * q^69 + 9096 * q^70 + 4200 * q^71 + 15736 * q^72 + 11312 * q^73 + 17124 * q^74 + 14670 * q^75 + 30856 * q^76 + 11124 * q^77 + 13978 * q^78 + 17732 * q^79 + 10404 * q^80 + 9242 * q^81 + 34288 * q^82 + 14072 * q^83 + 20280 * q^84 + 20932 * q^85 + 6268 * q^86 + 7632 * q^87 + 20114 * q^88 - 9200 * q^89 - 4562 * q^90 - 24396 * q^91 - 32216 * q^92 - 12894 * q^93 - 18412 * q^94 + 6552 * q^95 + 25864 * q^96 - 2560 * q^97 + 13496 * q^98 + 1628 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(627))\)

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
627.4.a	\(\chi_{627}(1, \cdot)\)	627.4.a.a	10	1
		627.4.a.b	10
		627.4.a.c	10
		627.4.a.d	10
		627.4.a.e	12
		627.4.a.f	12
		627.4.a.g	12
		627.4.a.h	12
627.4.f	\(\chi_{627}(362, \cdot)\)	n/a	216	1
627.4.g	\(\chi_{627}(56, \cdot)\)	n/a	200	1
627.4.h	\(\chi_{627}(208, \cdot)\)	n/a	120	1
627.4.i	\(\chi_{627}(463, \cdot)\)	n/a	200	2
627.4.j	\(\chi_{627}(58, \cdot)\)	n/a	432	4
627.4.k	\(\chi_{627}(274, \cdot)\)	n/a	240	2
627.4.l	\(\chi_{627}(197, \cdot)\)	n/a	472	2
627.4.m	\(\chi_{627}(122, \cdot)\)	n/a	400	2
627.4.r	\(\chi_{627}(100, \cdot)\)	n/a	600	6
627.4.s	\(\chi_{627}(94, \cdot)\)	n/a	480	4
627.4.t	\(\chi_{627}(113, \cdot)\)	n/a	944	4
627.4.u	\(\chi_{627}(134, \cdot)\)	n/a	864	4
627.4.z	\(\chi_{627}(49, \cdot)\)	n/a	960	8
627.4.ba	\(\chi_{627}(89, \cdot)\)	n/a	1200	6
627.4.bd	\(\chi_{627}(131, \cdot)\)	n/a	1416	6
627.4.be	\(\chi_{627}(10, \cdot)\)	n/a	720	6
627.4.bl	\(\chi_{627}(179, \cdot)\)	n/a	1888	8
627.4.bm	\(\chi_{627}(68, \cdot)\)	n/a	1888	8
627.4.bn	\(\chi_{627}(46, \cdot)\)	n/a	960	8
627.4.bo	\(\chi_{627}(4, \cdot)\)	n/a	2880	24
627.4.br	\(\chi_{627}(13, \cdot)\)	n/a	2880	24
627.4.bs	\(\chi_{627}(17, \cdot)\)	n/a	5664	24
627.4.bv	\(\chi_{627}(14, \cdot)\)	n/a	5664	24

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(627))\) into lower level spaces

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