Space of modular forms of level 126 and weight 2

• Label: 126.2
• Level: 126
• Weight: 2
• Dimension: 110
• Nonzero newspaces: 9
• Newform subspaces: 22
• Sturm bound: 1728
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1728\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	528	110	418
Cusp forms	337	110	227
Eisenstein series	191	0	191

Trace form

110 * q + 2 * q^2 + 6 * q^3 + 4 * q^4 + 6 * q^5 - 6 * q^6 + 10 * q^7 - 4 * q^8 - 6 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^13 - 16 * q^14 - 24 * q^15 - 4 * q^16 - 36 * q^17 - 12 * q^18 - 30 * q^19 - 18 * q^20 - 42 * q^21 - 42 * q^22 - 60 * q^23 - 6 * q^24 - 40 * q^25 - 38 * q^26 - 36 * q^27 - 4 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 + 2 * q^32 - 6 * q^33 + 6 * q^34 - 30 * q^35 - 6 * q^36 + 8 * q^37 + 16 * q^38 - 36 * q^39 + 6 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 48 * q^45 + 48 * q^46 - 48 * q^47 - 6 * q^48 - 28 * q^49 + 50 * q^50 + 18 * q^51 - 6 * q^52 + 24 * q^53 + 54 * q^54 + 8 * q^56 + 90 * q^57 - 12 * q^58 + 120 * q^59 + 72 * q^60 - 6 * q^61 + 100 * q^62 + 180 * q^63 - 2 * q^64 + 168 * q^65 + 96 * q^66 - 26 * q^67 + 54 * q^68 + 108 * q^69 - 18 * q^70 + 120 * q^71 - 6 * q^72 - 24 * q^73 + 64 * q^74 + 114 * q^75 + 66 * q^77 + 60 * q^78 + 4 * q^79 + 6 * q^80 + 6 * q^81 + 30 * q^83 + 6 * q^84 + 60 * q^85 + 10 * q^86 - 108 * q^87 - 18 * q^88 - 84 * q^89 - 48 * q^90 - 66 * q^91 - 36 * q^92 - 108 * q^93 - 48 * q^94 - 144 * q^95 - 12 * q^96 - 54 * q^97 - 76 * q^98 - 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.2.a	\(\chi_{126}(1, \cdot)\)	126.2.a.a	1	1
		126.2.a.b	1
126.2.d	\(\chi_{126}(125, \cdot)\)	None	0	1
126.2.e	\(\chi_{126}(25, \cdot)\)	126.2.e.a	2	2
		126.2.e.b	2
		126.2.e.c	6
		126.2.e.d	6
126.2.f	\(\chi_{126}(43, \cdot)\)	126.2.f.a	2	2
		126.2.f.b	2
		126.2.f.c	4
		126.2.f.d	4
126.2.g	\(\chi_{126}(37, \cdot)\)	126.2.g.a	2	2
		126.2.g.b	2
		126.2.g.c	2
		126.2.g.d	2
126.2.h	\(\chi_{126}(67, \cdot)\)	126.2.h.a	2	2
		126.2.h.b	2
		126.2.h.c	6
		126.2.h.d	6
126.2.k	\(\chi_{126}(17, \cdot)\)	126.2.k.a	8	2
126.2.l	\(\chi_{126}(5, \cdot)\)	126.2.l.a	16	2
126.2.m	\(\chi_{126}(41, \cdot)\)	126.2.m.a	16	2
126.2.t	\(\chi_{126}(47, \cdot)\)	126.2.t.a	16	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)