Space of modular forms of level 50 and weight 9

• Label: 50.9
• Level: 50
• Weight: 9
• Dimension: 184
• Nonzero newspaces: 2
• Newform subspaces: 8
• Sturm bound: 1350
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1350\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	628	184	444
Cusp forms	572	184	388
Eisenstein series	56	0	56

Trace form

184 * q - 280 * q^3 + 780 * q^5 - 1024 * q^6 - 9080 * q^7 + 6400 * q^10 + 69168 * q^11 - 35840 * q^12 - 238560 * q^13 + 252580 * q^15 + 262144 * q^16 + 336180 * q^17 - 317440 * q^18 - 1437800 * q^19 - 161280 * q^20 + 598328 * q^21 + 1940480 * q^22 + 1391520 * q^23 - 3015940 * q^25 - 927744 * q^26 - 3183580 * q^27 + 1059840 * q^28 + 3913800 * q^29 + 5352960 * q^30 + 1696008 * q^31 - 4164520 * q^33 - 10304000 * q^34 - 2665680 * q^35 + 1236992 * q^36 + 3982080 * q^37 + 10152960 * q^38 + 22510400 * q^39 - 1146880 * q^40 - 21657552 * q^41 - 26301440 * q^42 - 38495640 * q^43 + 48565500 * q^45 + 34820096 * q^46 + 44007720 * q^47 + 4587520 * q^48 - 5414400 * q^50 - 61195472 * q^51 - 30535680 * q^52 - 100767360 * q^53 + 41350200 * q^55 + 28311552 * q^56 + 171395520 * q^57 + 48389120 * q^58 - 96239100 * q^59 + 11627520 * q^60 + 7546088 * q^61 - 7088640 * q^62 - 206014900 * q^63 - 173478540 * q^65 + 55903232 * q^66 + 11911160 * q^67 + 78927360 * q^68 + 256837700 * q^69 + 115673600 * q^70 - 24006432 * q^71 - 40632320 * q^72 + 265225440 * q^73 - 262176540 * q^75 - 33336320 * q^76 - 237209520 * q^77 - 214607360 * q^78 - 277012400 * q^79 - 12779520 * q^80 - 240206736 * q^81 - 19701760 * q^82 + 594720900 * q^83 + 387110400 * q^84 + 648719080 * q^85 + 353865216 * q^86 - 240100860 * q^87 + 10485760 * q^88 - 999182700 * q^89 - 739278080 * q^90 + 111682008 * q^91 + 89986560 * q^92 + 842135020 * q^93 + 582691440 * q^95 + 16777216 * q^96 - 216146800 * q^97 - 230338560 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.9.c	\(\chi_{50}(7, \cdot)\)	50.9.c.a	4	2
		50.9.c.b	4
		50.9.c.c	4
		50.9.c.d	4
		50.9.c.e	4
		50.9.c.f	4
50.9.f	\(\chi_{50}(3, \cdot)\)	50.9.f.a	80	8
		50.9.f.b	80

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)