Space of modular forms of level 50 and weight 3

• Label: 50.3
• Level: 50
• Weight: 3
• Dimension: 46
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 450
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(450\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	178	46	132
Cusp forms	122	46	76
Eisenstein series	56	0	56

Trace form

46 * q + 4 * q^2 + 8 * q^3 - 16 * q^6 - 8 * q^7 - 8 * q^8 + 10 * q^10 + 32 * q^11 + 16 * q^12 - 12 * q^13 - 20 * q^15 + 16 * q^16 - 168 * q^17 - 154 * q^18 - 200 * q^19 - 40 * q^20 - 88 * q^21 - 112 * q^22 - 32 * q^23 + 110 * q^25 + 64 * q^26 + 260 * q^27 + 96 * q^28 + 200 * q^29 + 240 * q^30 + 72 * q^31 + 24 * q^32 + 296 * q^33 + 250 * q^34 + 200 * q^35 + 8 * q^36 - 48 * q^37 + 80 * q^38 - 400 * q^39 + 20 * q^40 - 128 * q^41 - 32 * q^42 - 72 * q^43 - 330 * q^45 - 16 * q^46 - 8 * q^47 - 32 * q^48 - 50 * q^50 + 232 * q^51 - 24 * q^52 - 32 * q^53 + 240 * q^55 - 32 * q^56 + 480 * q^57 - 160 * q^58 + 100 * q^59 - 240 * q^60 - 88 * q^61 - 512 * q^62 - 532 * q^63 - 790 * q^65 - 352 * q^66 - 808 * q^67 - 304 * q^68 - 700 * q^69 - 280 * q^70 - 128 * q^71 - 8 * q^72 + 108 * q^73 + 60 * q^75 - 80 * q^76 + 544 * q^77 + 352 * q^78 + 400 * q^79 + 276 * q^81 + 608 * q^82 + 868 * q^83 + 600 * q^84 + 460 * q^85 + 384 * q^86 + 1140 * q^87 + 64 * q^88 + 1450 * q^89 + 970 * q^90 + 312 * q^91 + 376 * q^92 + 556 * q^93 + 40 * q^95 + 64 * q^96 + 212 * q^97 + 164 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)

We only show spaces with odd 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
50.3.c	\(\chi_{50}(7, \cdot)\)	50.3.c.a	2	2
		50.3.c.b	2
		50.3.c.c	2
50.3.f	\(\chi_{50}(3, \cdot)\)	50.3.f.a	16	8
		50.3.f.b	24

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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