Space of modular forms of level 50 and weight 5

• Label: 50.5
• Level: 50
• Weight: 5
• Dimension: 92
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 750
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(750\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	328	92	236
Cusp forms	272	92	180
Eisenstein series	56	0	56

Trace form

92 * q - 40 * q^3 + 60 * q^5 + 128 * q^6 - 40 * q^7 - 160 * q^10 - 336 * q^11 - 320 * q^12 + 120 * q^13 - 20 * q^15 + 512 * q^16 - 60 * q^17 + 1280 * q^18 + 2600 * q^19 + 480 * q^20 + 2024 * q^21 + 640 * q^22 - 1440 * q^23 - 2240 * q^25 + 768 * q^26 - 8740 * q^27 - 2880 * q^28 - 6600 * q^29 - 6720 * q^30 - 1416 * q^31 + 8840 * q^33 + 8000 * q^34 + 13440 * q^35 - 64 * q^36 - 2160 * q^37 - 1920 * q^38 - 8800 * q^39 - 1280 * q^40 - 8016 * q^41 + 4480 * q^42 + 10680 * q^43 + 17280 * q^45 - 4352 * q^46 + 3960 * q^47 + 2560 * q^48 + 4800 * q^50 + 9664 * q^51 + 960 * q^52 - 6480 * q^53 - 15240 * q^55 - 6144 * q^56 - 42240 * q^57 - 7040 * q^58 - 39300 * q^59 - 16320 * q^60 - 5096 * q^61 - 6720 * q^62 + 29300 * q^63 + 46560 * q^65 + 12416 * q^66 + 30280 * q^67 + 19680 * q^68 + 79100 * q^69 + 38080 * q^70 + 20064 * q^71 + 10240 * q^72 + 37320 * q^73 - 10740 * q^75 - 1600 * q^76 - 40560 * q^77 - 44480 * q^78 - 53200 * q^79 - 3840 * q^80 - 65208 * q^81 - 58880 * q^82 - 135300 * q^83 - 40800 * q^84 - 68800 * q^85 + 9408 * q^86 - 15780 * q^87 + 20480 * q^88 + 74400 * q^89 + 63520 * q^90 + 79464 * q^91 + 24480 * q^92 + 98260 * q^93 + 37440 * q^95 - 8192 * q^96 + 34600 * q^97 - 7680 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.5.c	\(\chi_{50}(7, \cdot)\)	50.5.c.a	2	2
		50.5.c.b	2
		50.5.c.c	4
		50.5.c.d	4
50.5.f	\(\chi_{50}(3, \cdot)\)	50.5.f.a	40	8
		50.5.f.b	40

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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