Space of modular forms of level 50 and weight 2

• Label: 50.2
• Level: 50
• Weight: 2
• Dimension: 24
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 300
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(300\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(50))\).

	Total	New	Old
Modular forms	103	24	79
Cusp forms	48	24	24
Eisenstein series	55	0	55

Trace form

24 * q - q^2 - 4 * q^3 - q^4 - 5 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 5 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 20 * q^15 - q^16 + 2 * q^17 + 12 * q^18 + 20 * q^19 + 8 * q^21 + 28 * q^22 + 16 * q^23 + 16 * q^24 + 35 * q^25 + 6 * q^26 + 20 * q^27 + 12 * q^28 + 10 * q^29 + 20 * q^30 + 8 * q^31 + 4 * q^32 - 8 * q^33 + 7 * q^34 - 20 * q^35 - 13 * q^36 - 33 * q^37 - 20 * q^38 - 16 * q^39 - 5 * q^40 - 22 * q^41 - 32 * q^42 - 4 * q^43 - 12 * q^44 + 15 * q^45 - 24 * q^46 - 8 * q^47 - 4 * q^48 - 12 * q^49 - 25 * q^50 - 12 * q^51 - 14 * q^52 - 9 * q^53 - 40 * q^54 - 20 * q^55 - 8 * q^56 - 30 * q^58 - 2 * q^61 + 28 * q^62 + 36 * q^63 - q^64 + 35 * q^65 + 12 * q^66 + 12 * q^67 + 42 * q^68 + 44 * q^69 + 40 * q^70 + 8 * q^71 - 13 * q^72 + 6 * q^73 + 62 * q^74 + 60 * q^75 + 20 * q^76 + 64 * q^77 + 44 * q^78 - 5 * q^80 - 41 * q^81 + 38 * q^82 + 76 * q^83 + 28 * q^84 + 15 * q^85 + 16 * q^86 + 20 * q^87 - 12 * q^88 + 15 * q^89 - 5 * q^90 - 32 * q^91 - 4 * q^92 - 68 * q^93 - 48 * q^94 - 60 * q^95 - 4 * q^96 - 78 * q^97 - 57 * q^98 - 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.2.a	\(\chi_{50}(1, \cdot)\)	50.2.a.a	1	1
		50.2.a.b	1
50.2.b	\(\chi_{50}(49, \cdot)\)	50.2.b.a	2	1
50.2.d	\(\chi_{50}(11, \cdot)\)	50.2.d.a	4	4
		50.2.d.b	8
50.2.e	\(\chi_{50}(9, \cdot)\)	50.2.e.a	8	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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