Space of modular forms of level 50 and weight 4

• Label: 50.4
• Level: 50
• Weight: 4
• Dimension: 69
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 600
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(600\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	253	69	184
Cusp forms	197	69	128
Eisenstein series	56	0	56

Trace form

69 * q - 4 * q^2 + 16 * q^3 + 8 * q^4 + 5 * q^5 + 16 * q^6 + 8 * q^7 - 16 * q^8 - 166 * q^9 - 50 * q^10 + 88 * q^11 + 64 * q^12 + 116 * q^13 + 224 * q^14 + 80 * q^15 - 96 * q^16 + 508 * q^17 + 302 * q^18 + 200 * q^19 - 80 * q^20 - 752 * q^21 - 768 * q^22 - 1144 * q^23 - 288 * q^24 - 1315 * q^25 - 304 * q^26 - 920 * q^27 - 208 * q^28 + 380 * q^29 + 360 * q^30 + 928 * q^31 + 96 * q^32 + 2112 * q^33 + 874 * q^34 + 1220 * q^35 + 72 * q^36 + 603 * q^37 + 400 * q^38 + 1608 * q^39 + 120 * q^40 + 368 * q^41 - 128 * q^42 - 344 * q^43 - 544 * q^44 - 2275 * q^45 - 64 * q^46 - 1312 * q^47 + 256 * q^48 - 219 * q^49 + 350 * q^50 - 1252 * q^51 + 464 * q^52 - 2109 * q^53 - 480 * q^54 - 1100 * q^55 - 768 * q^56 - 1040 * q^57 + 360 * q^58 + 4040 * q^59 + 2720 * q^60 + 2008 * q^61 + 4312 * q^62 + 11416 * q^63 + 128 * q^64 + 3085 * q^65 + 712 * q^66 + 608 * q^67 - 2448 * q^68 - 4512 * q^69 - 4800 * q^70 - 1312 * q^71 - 592 * q^72 - 6484 * q^73 - 5376 * q^74 - 12040 * q^75 - 1120 * q^76 - 10784 * q^77 - 8056 * q^78 - 6880 * q^79 + 80 * q^80 - 3526 * q^81 + 312 * q^82 + 3036 * q^83 + 1536 * q^84 + 6605 * q^85 + 456 * q^86 + 9040 * q^87 - 192 * q^88 + 10075 * q^89 + 8670 * q^90 + 5128 * q^91 + 3584 * q^92 + 5512 * q^93 + 2624 * q^94 - 2060 * q^95 + 256 * q^96 - 4072 * q^97 + 1308 * q^98 - 4252 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.4.a	\(\chi_{50}(1, \cdot)\)	50.4.a.a	1	1
		50.4.a.b	1
		50.4.a.c	1
		50.4.a.d	1
		50.4.a.e	1
50.4.b	\(\chi_{50}(49, \cdot)\)	50.4.b.a	2	1
		50.4.b.b	2
50.4.d	\(\chi_{50}(11, \cdot)\)	50.4.d.a	12	4
		50.4.d.b	16
50.4.e	\(\chi_{50}(9, \cdot)\)	50.4.e.a	32	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)