Space of modular forms of level 100 and weight 2

• Label: 100.2
• Level: 100
• Weight: 2
• Dimension: 141
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 1200
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1200\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(100))\).

	Total	New	Old
Modular forms	370	181	189
Cusp forms	231	141	90
Eisenstein series	139	40	99

Trace form

141 * q - 6 * q^2 + 4 * q^3 - 10 * q^4 - 15 * q^5 - 18 * q^6 - 4 * q^7 - 18 * q^8 - 22 * q^9 - 16 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^14 - 2 * q^15 - 2 * q^16 - 30 * q^17 + 2 * q^18 - 12 * q^19 - 6 * q^20 - 48 * q^21 - 10 * q^22 - 32 * q^23 - 57 * q^25 - 36 * q^26 - 38 * q^27 - 10 * q^28 - 52 * q^29 - 10 * q^30 - 12 * q^31 - 26 * q^32 - 40 * q^33 - 10 * q^34 - 8 * q^35 - 10 * q^36 + 9 * q^37 + 20 * q^38 + 48 * q^39 + 44 * q^40 + 4 * q^41 + 90 * q^42 + 60 * q^43 + 60 * q^44 + 55 * q^45 + 42 * q^46 + 52 * q^47 + 120 * q^48 + 51 * q^49 + 94 * q^50 + 36 * q^51 + 88 * q^52 + q^53 + 120 * q^54 + 40 * q^55 + 42 * q^56 + 44 * q^57 + 44 * q^58 + 6 * q^59 + 90 * q^60 - 88 * q^61 + 40 * q^62 - 14 * q^63 + 20 * q^64 - 65 * q^65 + 30 * q^66 - 44 * q^67 + 14 * q^68 - 66 * q^69 - 10 * q^70 - 16 * q^71 - 16 * q^72 - 20 * q^73 - 78 * q^75 - 60 * q^76 - 100 * q^77 + 20 * q^78 - 56 * q^79 - 26 * q^80 + 54 * q^81 - 82 * q^82 - 62 * q^83 - 90 * q^84 + 27 * q^85 - 78 * q^86 + 14 * q^87 - 130 * q^88 + 77 * q^89 - 166 * q^90 + 12 * q^91 - 110 * q^92 + 74 * q^93 - 170 * q^94 + 36 * q^95 - 118 * q^96 + 144 * q^97 - 158 * q^98 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.2.a	\(\chi_{100}(1, \cdot)\)	100.2.a.a	1	1
100.2.c	\(\chi_{100}(49, \cdot)\)	100.2.c.a	2	1
100.2.e	\(\chi_{100}(7, \cdot)\)	100.2.e.a	2	2
		100.2.e.b	2
		100.2.e.c	2
		100.2.e.d	8
100.2.g	\(\chi_{100}(21, \cdot)\)	100.2.g.a	12	4
100.2.i	\(\chi_{100}(9, \cdot)\)	100.2.i.a	8	4
100.2.l	\(\chi_{100}(3, \cdot)\)	100.2.l.a	8	8
		100.2.l.b	96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)