Space of modular forms of level 126 and weight 4

• Label: 126.4
• Level: 126
• Weight: 4
• Dimension: 328
• Nonzero newspaces: 10
• Newform subspaces: 28
• Sturm bound: 3456
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(3456\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	1392	328	1064
Cusp forms	1200	328	872
Eisenstein series	192	0	192

Trace form

328 * q - 8 * q^2 - 6 * q^3 + 16 * q^4 - 48 * q^5 + 36 * q^6 - 44 * q^7 + 16 * q^8 + 210 * q^9 + 60 * q^10 - 12 * q^11 - 48 * q^12 - 250 * q^13 - 464 * q^14 - 420 * q^15 + 64 * q^16 + 330 * q^17 + 24 * q^18 + 488 * q^19 + 264 * q^20 + 756 * q^21 + 732 * q^22 + 1578 * q^23 + 144 * q^24 + 826 * q^25 + 500 * q^26 - 792 * q^27 - 8 * q^28 - 1164 * q^29 - 264 * q^30 - 1978 * q^31 - 128 * q^32 - 2274 * q^33 - 1092 * q^34 - 1920 * q^35 - 1032 * q^36 + 158 * q^37 - 616 * q^38 + 2424 * q^39 + 240 * q^40 + 3642 * q^41 + 816 * q^42 + 1202 * q^43 + 888 * q^44 + 2796 * q^45 - 504 * q^46 + 1902 * q^47 + 288 * q^48 - 3224 * q^49 + 1408 * q^50 + 3582 * q^51 - 760 * q^52 - 2046 * q^53 - 1188 * q^54 + 900 * q^55 - 224 * q^56 - 5046 * q^57 + 1632 * q^58 - 3930 * q^59 - 2160 * q^60 + 5720 * q^61 + 824 * q^62 - 8622 * q^63 - 512 * q^64 - 7092 * q^65 - 5376 * q^66 - 4648 * q^67 - 3072 * q^68 - 6912 * q^69 - 804 * q^70 - 1608 * q^71 + 48 * q^72 - 3034 * q^73 + 1304 * q^74 + 5214 * q^75 - 256 * q^76 + 8622 * q^77 + 8280 * q^78 + 4382 * q^79 + 960 * q^80 + 294 * q^81 + 5016 * q^82 + 5262 * q^83 - 744 * q^84 + 5424 * q^85 - 4492 * q^86 + 1692 * q^87 - 2352 * q^88 - 4950 * q^89 - 4224 * q^90 - 6970 * q^91 + 528 * q^92 + 2748 * q^93 - 3000 * q^94 + 1374 * q^95 - 384 * q^96 - 2470 * q^97 + 3172 * q^98 + 1032 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.4.a	\(\chi_{126}(1, \cdot)\)	126.4.a.a	1	1
		126.4.a.b	1
		126.4.a.c	1
		126.4.a.d	1
		126.4.a.e	1
		126.4.a.f	1
		126.4.a.g	1
		126.4.a.h	1
126.4.d	\(\chi_{126}(125, \cdot)\)	126.4.d.a	8	1
126.4.e	\(\chi_{126}(25, \cdot)\)	126.4.e.a	24	2
		126.4.e.b	24
126.4.f	\(\chi_{126}(43, \cdot)\)	126.4.f.a	6	2
		126.4.f.b	8
		126.4.f.c	10
		126.4.f.d	12
126.4.g	\(\chi_{126}(37, \cdot)\)	126.4.g.a	2	2
		126.4.g.b	2
		126.4.g.c	2
		126.4.g.d	2
		126.4.g.e	4
		126.4.g.f	4
		126.4.g.g	4
126.4.h	\(\chi_{126}(67, \cdot)\)	126.4.h.a	24	2
		126.4.h.b	24
126.4.k	\(\chi_{126}(17, \cdot)\)	126.4.k.a	16	2
126.4.l	\(\chi_{126}(5, \cdot)\)	126.4.l.a	48	2
126.4.m	\(\chi_{126}(41, \cdot)\)	126.4.m.a	48	2
126.4.t	\(\chi_{126}(47, \cdot)\)	126.4.t.a	48	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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