Space of modular forms of level 52 and weight 4

• Label: 52.4
• Level: 52
• Weight: 4
• Dimension: 135
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 672
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(672\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(52))\).

	Total	New	Old
Modular forms	282	159	123
Cusp forms	222	135	87
Eisenstein series	60	24	36

Trace form

135 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 36 * q^7 - 6 * q^8 - 12 * q^9 - 6 * q^10 + 60 * q^11 + 132 * q^13 - 12 * q^14 + 72 * q^15 - 6 * q^16 + 81 * q^17 + 552 * q^18 - 36 * q^19 + 114 * q^20 - 252 * q^21 - 396 * q^22 - 228 * q^23 - 1110 * q^24 - 375 * q^25 - 756 * q^26 - 828 * q^27 - 576 * q^28 - 831 * q^29 - 246 * q^30 - 192 * q^31 + 504 * q^32 + 876 * q^33 + 1122 * q^34 + 1560 * q^35 + 1362 * q^36 + 813 * q^37 + 1332 * q^39 - 1956 * q^40 + 2703 * q^41 - 1248 * q^42 + 588 * q^43 - 156 * q^44 - 537 * q^45 + 1254 * q^46 - 984 * q^47 + 1866 * q^48 - 4440 * q^49 + 2688 * q^50 - 4056 * q^51 + 2748 * q^52 - 2604 * q^53 + 2472 * q^54 - 1404 * q^55 + 1668 * q^56 - 1368 * q^57 + 426 * q^58 + 672 * q^59 - 516 * q^60 + 2367 * q^61 + 1158 * q^62 + 7092 * q^63 + 8691 * q^65 - 528 * q^66 + 2940 * q^67 + 1008 * q^68 + 1656 * q^69 - 2268 * q^70 - 1416 * q^71 - 3672 * q^72 - 3324 * q^73 - 5466 * q^74 - 7740 * q^75 - 4506 * q^76 - 7008 * q^77 - 8784 * q^78 - 4560 * q^79 - 8100 * q^80 - 5304 * q^81 - 3426 * q^82 - 2208 * q^83 - 5004 * q^84 + 423 * q^85 - 5268 * q^86 + 3432 * q^87 - 1740 * q^88 + 2796 * q^89 + 4860 * q^91 + 6924 * q^92 + 7872 * q^93 + 7638 * q^94 + 7176 * q^95 + 9840 * q^96 + 336 * q^97 + 5994 * q^98 - 2772 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)

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
52.4.a	\(\chi_{52}(1, \cdot)\)	52.4.a.a	1	1
		52.4.a.b	2
52.4.d	\(\chi_{52}(25, \cdot)\)	52.4.d.a	2	1
		52.4.d.b	2
52.4.e	\(\chi_{52}(9, \cdot)\)	52.4.e.a	6	2
52.4.f	\(\chi_{52}(31, \cdot)\)	52.4.f.a	2	2
		52.4.f.b	36
52.4.h	\(\chi_{52}(17, \cdot)\)	52.4.h.a	8	2
52.4.l	\(\chi_{52}(7, \cdot)\)	52.4.l.a	4	4
		52.4.l.b	72

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(52))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(52)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)