Space of modular forms of level 126 and weight 12

• Label: 126.12
• Level: 126
• Weight: 12
• Dimension: 1200
• Nonzero newspaces: 10
• Sturm bound: 10368
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(10368\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	4848	1200	3648
Cusp forms	4656	1200	3456
Eisenstein series	192	0	192

Trace form

1200 * q - 128 * q^2 + 486 * q^3 + 10240 * q^4 - 5898 * q^5 + 6720 * q^6 + 127810 * q^7 + 65536 * q^8 - 30642 * q^9 - 183360 * q^10 - 208362 * q^11 + 2113536 * q^12 - 2270522 * q^13 - 14249216 * q^14 - 673080 * q^15 + 18874368 * q^16 + 13521696 * q^17 - 25067136 * q^18 - 34642022 * q^19 + 36009984 * q^20 + 132788058 * q^21 - 89282112 * q^22 - 495634524 * q^23 + 6881280 * q^24 + 592595826 * q^25 + 290990912 * q^26 - 204371028 * q^27 - 266760192 * q^28 - 506055072 * q^29 + 509041536 * q^30 + 483872908 * q^31 - 134217728 * q^32 - 68795538 * q^33 - 6665280 * q^34 + 2527303650 * q^35 - 13092864 * q^36 - 2720372140 * q^37 - 1015064704 * q^38 - 5003841252 * q^39 - 187760640 * q^40 + 7008747954 * q^41 + 786374400 * q^42 + 441945674 * q^43 - 2464555008 * q^44 + 993424416 * q^45 + 3170005632 * q^46 + 1796606184 * q^47 - 2673868800 * q^48 - 1437202782 * q^49 - 13289111552 * q^50 + 22404599154 * q^51 + 196274176 * q^52 + 12786193860 * q^53 - 27080350272 * q^54 + 12879457920 * q^55 - 7030046720 * q^56 + 18055322430 * q^57 - 29860563456 * q^58 + 2384479560 * q^59 - 11027865600 * q^60 + 63361325290 * q^61 + 14462605184 * q^62 - 85037831100 * q^63 - 34359738368 * q^64 - 29546622792 * q^65 + 71668875264 * q^66 - 167007656082 * q^67 + 32550844416 * q^68 + 32341463892 * q^69 + 81174576576 * q^70 - 83961121128 * q^71 + 29538582528 * q^72 + 199036609036 * q^73 + 21661740416 * q^74 + 64812365874 * q^75 - 96369115136 * q^76 - 287355595194 * q^77 - 156587842176 * q^78 + 5411213028 * q^79 + 45455769600 * q^80 + 467282720274 * q^81 + 14042167680 * q^82 + 217046646942 * q^83 - 118614472704 * q^84 - 409178787396 * q^85 - 203177285824 * q^86 + 390832950564 * q^87 + 81126555648 * q^88 + 157396443192 * q^89 - 7700865024 * q^90 + 147143211286 * q^91 - 64272175104 * q^92 - 161956213860 * q^93 + 360214259328 * q^94 + 302684933184 * q^95 - 32614907904 * q^96 + 184681917754 * q^97 - 576120224192 * q^98 + 271154108148 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.12.a	\(\chi_{126}(1, \cdot)\)	126.12.a.a	1	1
		126.12.a.b	1
		126.12.a.c	1
		126.12.a.d	1
		126.12.a.e	1
		126.12.a.f	1
		126.12.a.g	1
		126.12.a.h	1
		126.12.a.i	2
		126.12.a.j	2
		126.12.a.k	2
		126.12.a.l	2
		126.12.a.m	3
		126.12.a.n	3
		126.12.a.o	3
		126.12.a.p	3
126.12.d	\(\chi_{126}(125, \cdot)\)	126.12.d.a	32	1
126.12.e	\(\chi_{126}(25, \cdot)\)	n/a	176	2
126.12.f	\(\chi_{126}(43, \cdot)\)	n/a	132	2
126.12.g	\(\chi_{126}(37, \cdot)\)	126.12.g.a	6	2
		126.12.g.b	6
		126.12.g.c	8
		126.12.g.d	8
		126.12.g.e	8
		126.12.g.f	8
		126.12.g.g	14
		126.12.g.h	14
126.12.h	\(\chi_{126}(67, \cdot)\)	n/a	176	2
126.12.k	\(\chi_{126}(17, \cdot)\)	126.12.k.a	56	2
126.12.l	\(\chi_{126}(5, \cdot)\)	n/a	176	2
126.12.m	\(\chi_{126}(41, \cdot)\)	n/a	176	2
126.12.t	\(\chi_{126}(47, \cdot)\)	n/a	176	2

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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