Space of modular forms of level 75 and weight 2

• Label: 75.2
• Level: 75
• Weight: 2
• Dimension: 119
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 800
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(800\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(75))\).

	Total	New	Old
Modular forms	256	159	97
Cusp forms	145	119	26
Eisenstein series	111	40	71

Trace form

119 * q - q^2 - 9 * q^3 - 25 * q^4 - 6 * q^5 - 23 * q^6 - 28 * q^7 - 21 * q^8 - 13 * q^9 - 34 * q^10 - 4 * q^11 - 19 * q^12 - 30 * q^13 - 24 * q^14 - 14 * q^15 - 33 * q^16 - 2 * q^17 - q^18 - 8 * q^19 + 36 * q^20 - 6 * q^21 + 16 * q^22 + 16 * q^23 + 51 * q^24 + 14 * q^25 - 6 * q^26 - 9 * q^27 + 44 * q^28 + 14 * q^29 + 14 * q^30 - 28 * q^31 + 17 * q^32 - 10 * q^33 - 20 * q^34 - 20 * q^35 + 9 * q^36 - 28 * q^37 + 8 * q^38 + 12 * q^39 + 2 * q^40 - 22 * q^41 + 66 * q^42 + 8 * q^43 + 48 * q^44 + 64 * q^45 + 12 * q^46 + 16 * q^47 + 67 * q^48 + 47 * q^49 + 106 * q^50 + 18 * q^51 + 98 * q^52 + 56 * q^53 + 115 * q^54 + 4 * q^55 + 58 * q^57 + 26 * q^58 + 28 * q^59 + 14 * q^60 - 54 * q^61 + 4 * q^62 - 28 * q^63 - 101 * q^64 - 58 * q^65 - 58 * q^66 - 112 * q^67 - 122 * q^68 - 104 * q^69 - 140 * q^70 - 56 * q^71 - 171 * q^72 - 114 * q^73 - 134 * q^74 - 114 * q^75 - 124 * q^76 - 96 * q^77 - 118 * q^78 - 100 * q^79 - 154 * q^80 - 61 * q^81 - 46 * q^82 - 28 * q^83 - 106 * q^84 + 38 * q^85 - 4 * q^86 - 14 * q^87 + 64 * q^88 + 72 * q^89 - 24 * q^90 + 12 * q^91 + 32 * q^92 + 68 * q^93 + 172 * q^94 + 56 * q^95 + 33 * q^96 + 158 * q^97 + 95 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.2.a	\(\chi_{75}(1, \cdot)\)	75.2.a.a	1	1
		75.2.a.b	1
		75.2.a.c	1
75.2.b	\(\chi_{75}(49, \cdot)\)	75.2.b.a	2	1
		75.2.b.b	2
75.2.e	\(\chi_{75}(32, \cdot)\)	75.2.e.a	4	2
		75.2.e.b	4
75.2.g	\(\chi_{75}(16, \cdot)\)	75.2.g.a	4	4
		75.2.g.b	8
		75.2.g.c	12
75.2.i	\(\chi_{75}(4, \cdot)\)	75.2.i.a	16	4
75.2.l	\(\chi_{75}(2, \cdot)\)	75.2.l.a	64	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)