Space of modular forms of level 126 and weight 7

• Label: 126.7
• Level: 126
• Weight: 7
• Dimension: 656
• Nonzero newspaces: 10
• Newform subspaces: 17
• Sturm bound: 6048
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(6048\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	2688	656	2032
Cusp forms	2496	656	1840
Eisenstein series	192	0	192

Trace form

656 * q + 84 * q^3 - 256 * q^4 - 1200 * q^5 + 288 * q^6 + 1688 * q^7 - 4380 * q^9 + 1920 * q^10 - 6552 * q^11 - 768 * q^12 + 3328 * q^13 - 9504 * q^14 - 2256 * q^15 + 8192 * q^16 + 55272 * q^17 + 39552 * q^18 + 7108 * q^19 - 27648 * q^20 - 69516 * q^21 - 42816 * q^22 + 7512 * q^23 - 9216 * q^24 + 6308 * q^25 + 116256 * q^26 - 76608 * q^27 + 2048 * q^28 - 107976 * q^29 - 152544 * q^30 + 7276 * q^31 + 284196 * q^33 + 55008 * q^34 - 15780 * q^35 - 76416 * q^36 + 194692 * q^37 - 39696 * q^38 + 200352 * q^39 - 61440 * q^40 + 821124 * q^41 + 222144 * q^42 - 968132 * q^43 - 185472 * q^44 - 690024 * q^45 + 33456 * q^46 - 880356 * q^47 - 110592 * q^48 + 318788 * q^49 - 56064 * q^50 + 2036196 * q^51 + 256384 * q^52 + 2492700 * q^53 + 911520 * q^54 - 1462752 * q^55 + 112128 * q^56 - 1197996 * q^57 + 928320 * q^58 - 3086940 * q^59 - 1078272 * q^60 - 315164 * q^61 + 2062008 * q^63 + 1310720 * q^64 + 5434428 * q^65 + 1675968 * q^66 - 1951724 * q^67 + 225408 * q^68 - 1698840 * q^69 - 1999680 * q^70 - 3733032 * q^71 + 749568 * q^72 + 1620412 * q^73 - 104064 * q^74 - 3471108 * q^75 + 1900672 * q^76 + 3128832 * q^77 + 4270464 * q^78 + 3239008 * q^79 + 344064 * q^80 + 3298236 * q^81 - 2917824 * q^82 - 793800 * q^83 - 1441536 * q^84 - 5108832 * q^85 - 2651136 * q^86 - 5188680 * q^87 - 2072064 * q^88 - 11305476 * q^89 - 1296768 * q^90 - 8622920 * q^91 + 2489088 * q^92 + 1266096 * q^93 + 5958096 * q^94 + 15618144 * q^95 + 786432 * q^96 + 14125732 * q^97 + 11116128 * q^98 + 3335640 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(126))\)

We only show spaces with odd 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
126.7.b	\(\chi_{126}(71, \cdot)\)	126.7.b.a	4	1
		126.7.b.b	8
126.7.c	\(\chi_{126}(55, \cdot)\)	126.7.c.a	4	1
		126.7.c.b	8
		126.7.c.c	8
126.7.i	\(\chi_{126}(65, \cdot)\)	126.7.i.a	96	2
126.7.j	\(\chi_{126}(31, \cdot)\)	126.7.j.a	96	2
126.7.n	\(\chi_{126}(19, \cdot)\)	126.7.n.a	8	2
		126.7.n.b	8
		126.7.n.c	8
		126.7.n.d	16
126.7.o	\(\chi_{126}(13, \cdot)\)	126.7.o.a	96	2
126.7.p	\(\chi_{126}(103, \cdot)\)	126.7.p.a	96	2
126.7.q	\(\chi_{126}(29, \cdot)\)	126.7.q.a	72	2
126.7.r	\(\chi_{126}(11, \cdot)\)	126.7.r.a	96	2
126.7.s	\(\chi_{126}(53, \cdot)\)	126.7.s.a	16	2
		126.7.s.b	16

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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