Space of modular forms of level 127 and weight 4

• Label: 127.4
• Level: 127
• Weight: 4
• Dimension: 1953
• Nonzero newspaces: 6
• Newform subspaces: 8
• Sturm bound: 5376
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 127 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(5376\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(127))\).

	Total	New	Old
Modular forms	2079	2077	2
Cusp forms	1953	1953	0
Eisenstein series	126	124	2

Trace form

1953 * q - 63 * q^2 - 63 * q^3 - 63 * q^4 - 63 * q^5 - 63 * q^6 - 63 * q^7 - 63 * q^8 - 63 * q^9 - 63 * q^10 - 63 * q^11 - 63 * q^12 - 63 * q^13 - 63 * q^14 - 63 * q^15 - 63 * q^16 - 63 * q^17 - 63 * q^18 - 63 * q^19 - 63 * q^20 - 63 * q^21 - 63 * q^22 - 63 * q^23 - 63 * q^24 - 63 * q^25 - 63 * q^26 - 63 * q^27 - 63 * q^28 - 63 * q^29 - 63 * q^30 - 63 * q^31 - 63 * q^32 - 63 * q^33 - 63 * q^34 - 63 * q^35 - 63 * q^36 - 63 * q^37 - 63 * q^38 - 63 * q^39 - 63 * q^40 - 63 * q^41 - 63 * q^42 - 63 * q^43 - 63 * q^44 - 63 * q^45 - 63 * q^46 - 63 * q^47 - 63 * q^48 - 63 * q^49 - 63 * q^50 - 63 * q^51 - 63 * q^52 - 63 * q^53 - 63 * q^54 - 63 * q^55 - 63 * q^56 - 63 * q^57 - 63 * q^58 - 63 * q^59 - 63 * q^60 - 63 * q^61 - 63 * q^62 - 63 * q^63 - 63 * q^64 - 63 * q^65 - 63 * q^66 - 63 * q^67 - 63 * q^68 - 63 * q^69 - 63 * q^70 - 63 * q^71 - 63 * q^72 - 63 * q^73 - 63 * q^74 - 63 * q^75 - 63 * q^76 - 63 * q^77 - 63 * q^78 - 63 * q^79 - 63 * q^80 - 63 * q^81 - 63 * q^82 - 63 * q^83 - 63 * q^84 - 63 * q^85 - 63 * q^86 - 63 * q^87 - 63 * q^88 - 63 * q^89 - 63 * q^90 - 63 * q^91 - 63 * q^92 - 63 * q^93 - 63 * q^94 - 63 * q^95 - 63 * q^96 - 63 * q^97 - 63 * q^98 - 63 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(127))\)

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
127.4.a	\(\chi_{127}(1, \cdot)\)	127.4.a.a	1	1
		127.4.a.b	13
		127.4.a.c	17
127.4.c	\(\chi_{127}(19, \cdot)\)	127.4.c.a	62	2
127.4.e	\(\chi_{127}(2, \cdot)\)	127.4.e.a	186	6
127.4.f	\(\chi_{127}(22, \cdot)\)	127.4.f.a	186	6
127.4.i	\(\chi_{127}(25, \cdot)\)	127.4.i.a	372	12
127.4.k	\(\chi_{127}(9, \cdot)\)	127.4.k.a	1116	36