Space of modular forms of level 529 and weight 4

• Label: 529.4
• Level: 529
• Weight: 4
• Dimension: 34430
• Nonzero newspaces: 4
• Sturm bound: 93104
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 529 = 23^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(93104\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(529))\).

	Total	New	Old
Modular forms	35288	35135	153
Cusp forms	34540	34430	110
Eisenstein series	748	705	43

Trace form

34430 * q - 231 * q^2 - 231 * q^3 - 231 * q^4 - 231 * q^5 - 231 * q^6 - 231 * q^7 - 231 * q^8 - 231 * q^9 - 231 * q^10 - 231 * q^11 - 231 * q^12 - 231 * q^13 - 231 * q^14 + 517 * q^15 + 649 * q^16 - 55 * q^17 - 407 * q^18 - 451 * q^19 - 1639 * q^20 - 1551 * q^21 - 1177 * q^22 - 726 * q^23 - 3091 * q^24 - 935 * q^25 - 671 * q^26 - 363 * q^27 + 473 * q^28 + 209 * q^29 + 2761 * q^30 + 869 * q^31 + 2761 * q^32 + 1705 * q^33 + 3597 * q^34 + 2629 * q^35 + 4719 * q^36 + 2145 * q^37 + 979 * q^38 - 495 * q^39 - 2871 * q^40 - 1331 * q^41 - 7491 * q^42 - 3663 * q^43 - 6677 * q^44 - 6149 * q^45 - 4202 * q^46 - 4235 * q^47 - 6919 * q^48 - 4587 * q^49 - 4081 * q^50 - 1551 * q^51 - 891 * q^52 + 253 * q^53 + 10769 * q^54 + 8745 * q^55 + 18535 * q^56 + 11649 * q^57 + 15675 * q^58 + 7733 * q^59 + 7909 * q^60 - 1287 * q^61 - 3663 * q^62 - 4411 * q^63 - 8679 * q^64 - 8855 * q^65 - 10549 * q^66 - 3135 * q^67 - 18161 * q^68 - 3982 * q^69 - 12067 * q^70 - 7051 * q^71 - 14421 * q^72 - 2343 * q^73 - 2189 * q^74 + 11693 * q^75 + 14047 * q^76 + 10681 * q^77 + 22693 * q^78 + 9185 * q^79 + 21967 * q^80 + 12529 * q^81 + 9669 * q^82 + 7469 * q^83 + 11693 * q^84 - 2035 * q^85 - 3179 * q^86 - 18975 * q^87 - 12727 * q^88 - 11451 * q^89 - 37257 * q^90 - 16225 * q^91 - 9251 * q^92 - 23947 * q^93 - 16885 * q^94 - 8283 * q^95 - 8437 * q^96 + 4389 * q^97 + 5049 * q^98 + 4389 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(529))\)

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
529.4.a	\(\chi_{529}(1, \cdot)\)	529.4.a.a	1	1
		529.4.a.b	1
		529.4.a.c	2
		529.4.a.d	2
		529.4.a.e	2
		529.4.a.f	2
		529.4.a.g	4
		529.4.a.h	5
		529.4.a.i	5
		529.4.a.j	6
		529.4.a.k	12
		529.4.a.l	24
		529.4.a.m	25
		529.4.a.n	25
529.4.c	\(\chi_{529}(118, \cdot)\)	n/a	1160	10
529.4.e	\(\chi_{529}(24, \cdot)\)	n/a	3014	22
529.4.g	\(\chi_{529}(2, \cdot)\)	n/a	30140	220

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(529))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(529)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)