Space of modular forms of level 50 and weight 7

• Label: 50.7
• Level: 50
• Weight: 7
• Dimension: 138
• Nonzero newspaces: 2
• Newform subspaces: 8
• Sturm bound: 1050
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1050\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	478	138	340
Cusp forms	422	138	284
Eisenstein series	56	0	56

Trace form

138 * q - 16 * q^2 + 128 * q^3 - 180 * q^5 - 448 * q^6 + 1392 * q^7 + 512 * q^8 - 2280 * q^10 - 944 * q^11 + 4096 * q^12 + 9228 * q^13 - 3320 * q^15 + 12288 * q^16 - 26148 * q^17 + 24296 * q^18 + 38400 * q^19 + 6400 * q^20 + 15056 * q^21 - 48192 * q^22 - 139072 * q^23 + 116910 * q^25 - 34048 * q^26 + 146960 * q^27 + 20736 * q^28 + 49600 * q^29 - 12480 * q^30 - 32544 * q^31 - 24576 * q^32 - 35344 * q^33 - 33000 * q^34 + 85480 * q^35 - 278656 * q^36 - 224688 * q^37 - 115520 * q^38 + 414800 * q^39 + 49920 * q^40 + 138416 * q^41 + 734848 * q^42 + 274128 * q^43 - 1097610 * q^45 - 497088 * q^46 - 1242928 * q^47 - 131072 * q^48 + 86600 * q^50 + 946696 * q^51 + 295296 * q^52 + 1052288 * q^53 + 907080 * q^55 + 149504 * q^56 - 858720 * q^57 - 946560 * q^58 - 3653200 * q^59 - 422400 * q^60 + 162816 * q^61 + 2025728 * q^62 + 4281008 * q^63 + 2608810 * q^65 + 13184 * q^66 - 228288 * q^67 - 811904 * q^68 - 5605600 * q^69 - 3852960 * q^70 - 781984 * q^71 - 777728 * q^72 - 2584332 * q^73 + 1393560 * q^75 + 806400 * q^76 + 6551024 * q^77 + 7349632 * q^78 + 4579200 * q^79 + 184320 * q^80 + 104028 * q^81 + 647808 * q^82 + 2969648 * q^83 - 1459200 * q^84 - 1132260 * q^85 + 1189632 * q^86 - 1320960 * q^87 - 1314816 * q^88 - 8476150 * q^89 - 3327080 * q^90 - 4548864 * q^91 + 1473536 * q^92 - 3126944 * q^93 - 2700760 * q^95 + 458752 * q^96 + 676092 * q^97 + 2572144 * q^98

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.7.c	\(\chi_{50}(7, \cdot)\)	50.7.c.a	2	2
		50.7.c.b	2
		50.7.c.c	2
		50.7.c.d	4
		50.7.c.e	4
		50.7.c.f	4
50.7.f	\(\chi_{50}(3, \cdot)\)	50.7.f.a	56	8
		50.7.f.b	64

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)