Space of modular forms of level 126 and weight 10

• Label: 126.10
• Level: 126
• Weight: 10
• Dimension: 982
• Nonzero newspaces: 10
• Sturm bound: 8640
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(8640\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	3984	982	3002
Cusp forms	3792	982	2810
Eisenstein series	192	0	192

Trace form

982 * q + 32 * q^2 - 150 * q^3 + 2560 * q^4 + 4740 * q^5 + 6048 * q^6 - 10628 * q^7 - 16384 * q^8 - 27114 * q^9 + 110688 * q^10 + 54636 * q^11 - 150528 * q^12 + 56582 * q^13 + 832256 * q^14 + 516252 * q^15 + 655360 * q^16 + 749682 * q^17 + 552768 * q^18 - 449560 * q^19 - 1230336 * q^20 - 4406220 * q^21 + 1063776 * q^22 + 12456426 * q^23 + 1548288 * q^24 - 1727696 * q^25 - 14167136 * q^26 - 31353624 * q^27 + 644608 * q^28 + 20330736 * q^29 + 33504576 * q^30 + 14517374 * q^31 + 2097152 * q^32 - 83008374 * q^33 - 18204576 * q^34 - 21909288 * q^35 + 625152 * q^36 + 68749814 * q^37 + 12651520 * q^38 + 112055160 * q^39 + 28336128 * q^40 + 35374362 * q^41 - 6302208 * q^42 - 127485814 * q^43 - 117004800 * q^44 - 174472716 * q^45 + 30249984 * q^46 + 450440358 * q^47 + 48365568 * q^48 - 85331810 * q^49 - 315210976 * q^50 - 271206450 * q^51 - 41840128 * q^52 + 52034946 * q^53 - 54935712 * q^54 - 242773884 * q^55 + 91062272 * q^56 + 312807918 * q^57 + 743691072 * q^58 + 924426750 * q^59 + 227902464 * q^60 - 1566870556 * q^61 - 134037440 * q^62 + 1307308914 * q^63 - 436207616 * q^64 + 1108359060 * q^65 + 516189696 * q^66 + 2301920312 * q^67 - 1004497920 * q^68 - 3164474736 * q^69 - 640782624 * q^70 - 3546367080 * q^71 + 35364864 * q^72 + 909876926 * q^73 + 2787569152 * q^74 + 5186203950 * q^75 + 729743360 * q^76 - 1142774502 * q^77 - 3204850752 * q^78 + 1103465198 * q^79 + 445120512 * q^80 - 2957824974 * q^81 - 4356016128 * q^82 - 1926363570 * q^83 + 56787456 * q^84 - 1579988616 * q^85 + 1050114208 * q^86 + 4902196428 * q^87 + 1966989312 * q^88 + 5659127754 * q^89 - 673533696 * q^90 - 5303440210 * q^91 - 3104013312 * q^92 - 5403997644 * q^93 - 4468732416 * q^94 - 6289076034 * q^95 + 994050048 * q^96 + 8249846378 * q^97 + 10066346816 * q^98 + 8347246728 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.10.a	\(\chi_{126}(1, \cdot)\)	126.10.a.a	1	1
		126.10.a.b	1
		126.10.a.c	1
		126.10.a.d	1
		126.10.a.e	1
		126.10.a.f	1
		126.10.a.g	1
		126.10.a.h	1
		126.10.a.i	2
		126.10.a.j	2
		126.10.a.k	2
		126.10.a.l	2
		126.10.a.m	2
		126.10.a.n	2
		126.10.a.o	2
126.10.d	\(\chi_{126}(125, \cdot)\)	126.10.d.a	24	1
126.10.e	\(\chi_{126}(25, \cdot)\)	n/a	144	2
126.10.f	\(\chi_{126}(43, \cdot)\)	n/a	108	2
126.10.g	\(\chi_{126}(37, \cdot)\)	126.10.g.a	2	2
		126.10.g.b	4
		126.10.g.c	4
		126.10.g.d	6
		126.10.g.e	6
		126.10.g.f	6
		126.10.g.g	8
		126.10.g.h	12
		126.10.g.i	12
126.10.h	\(\chi_{126}(67, \cdot)\)	n/a	144	2
126.10.k	\(\chi_{126}(17, \cdot)\)	126.10.k.a	48	2
126.10.l	\(\chi_{126}(5, \cdot)\)	n/a	144	2
126.10.m	\(\chi_{126}(41, \cdot)\)	n/a	144	2
126.10.t	\(\chi_{126}(47, \cdot)\)	n/a	144	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)