Space of modular forms of level 50 and weight 6

• Label: 50.6
• Level: 50
• Weight: 6
• Dimension: 115
• Nonzero newspaces: 4
• Newform subspaces: 14
• Sturm bound: 900
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(900\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	403	115	288
Cusp forms	347	115	232
Eisenstein series	56	0	56

Trace form

115 * q + 8 * q^2 - 8 * q^3 - 32 * q^4 - 85 * q^5 + 160 * q^6 + 624 * q^7 + 128 * q^8 - 1306 * q^9 + 180 * q^10 + 1480 * q^11 - 128 * q^12 - 228 * q^13 - 3136 * q^14 - 820 * q^15 - 2560 * q^16 + 1984 * q^17 - 316 * q^18 - 6400 * q^19 + 640 * q^20 - 2120 * q^21 + 2816 * q^22 + 12152 * q^23 + 6912 * q^24 + 25335 * q^25 + 1760 * q^26 + 15820 * q^27 + 3904 * q^28 - 34420 * q^29 - 30000 * q^30 - 22520 * q^31 - 3072 * q^32 - 63336 * q^33 - 13716 * q^34 + 60860 * q^35 - 14880 * q^36 + 64409 * q^37 + 34720 * q^38 + 60888 * q^39 + 320 * q^40 - 37120 * q^41 - 22784 * q^42 - 86288 * q^43 + 4736 * q^44 + 1835 * q^45 - 19840 * q^46 - 22456 * q^47 - 2048 * q^48 + 153531 * q^49 + 11300 * q^50 + 26780 * q^51 - 3648 * q^52 + 112257 * q^53 + 64320 * q^54 - 66180 * q^55 + 30720 * q^56 - 221840 * q^57 - 74640 * q^58 - 44860 * q^59 + 112640 * q^60 + 160880 * q^61 - 90704 * q^62 - 127508 * q^63 - 8192 * q^64 - 337865 * q^65 - 110480 * q^66 - 258296 * q^67 - 114816 * q^68 - 333372 * q^69 + 47360 * q^70 + 97280 * q^71 + 124544 * q^72 + 428212 * q^73 + 570624 * q^74 + 892460 * q^75 + 89600 * q^76 + 685888 * q^77 + 34448 * q^78 + 379120 * q^79 - 21760 * q^80 - 110410 * q^81 - 368624 * q^82 - 326088 * q^83 - 210624 * q^84 - 834505 * q^85 - 360240 * q^86 - 1636820 * q^87 - 105984 * q^88 - 509375 * q^89 + 244020 * q^90 - 186320 * q^91 + 379712 * q^92 + 525124 * q^93 + 316544 * q^94 + 379540 * q^95 + 40960 * q^96 + 614584 * q^97 - 5304 * q^98 + 1272548 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.6.a	\(\chi_{50}(1, \cdot)\)	50.6.a.a	1	1
		50.6.a.b	1
		50.6.a.c	1
		50.6.a.d	1
		50.6.a.e	1
		50.6.a.f	1
		50.6.a.g	1
50.6.b	\(\chi_{50}(49, \cdot)\)	50.6.b.a	2	1
		50.6.b.b	2
		50.6.b.c	2
		50.6.b.d	2
50.6.d	\(\chi_{50}(11, \cdot)\)	50.6.d.a	24	4
		50.6.d.b	28
50.6.e	\(\chi_{50}(9, \cdot)\)	50.6.e.a	48	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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