Space of modular forms of level 126 and weight 3

• Label: 126.3
• Level: 126
• Weight: 3
• Dimension: 216
• Nonzero newspaces: 10
• Newform subspaces: 14
• Sturm bound: 2592
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(2592\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	960	216	744
Cusp forms	768	216	552
Eisenstein series	192	0	192

Trace form

216 * q - 4 * q^4 + 30 * q^5 + 24 * q^6 + 14 * q^7 - 24 * q^9 - 18 * q^11 - 24 * q^12 + 44 * q^13 + 72 * q^14 + 84 * q^15 + 24 * q^16 + 186 * q^17 + 96 * q^18 + 206 * q^19 + 72 * q^20 + 6 * q^21 + 48 * q^22 - 222 * q^23 - 48 * q^24 - 312 * q^25 - 264 * q^26 - 252 * q^27 - 108 * q^28 - 420 * q^29 - 264 * q^30 - 142 * q^31 + 84 * q^33 - 120 * q^34 + 390 * q^35 - 24 * q^36 + 10 * q^37 + 132 * q^38 + 276 * q^39 + 252 * q^41 + 48 * q^42 + 148 * q^43 + 36 * q^44 - 84 * q^45 - 12 * q^46 - 366 * q^47 - 48 * q^48 - 66 * q^49 - 384 * q^50 - 1008 * q^51 + 152 * q^52 - 1194 * q^53 - 648 * q^54 - 72 * q^55 - 24 * q^56 - 768 * q^57 + 240 * q^58 - 510 * q^59 - 72 * q^60 - 274 * q^61 - 54 * q^63 + 128 * q^64 - 12 * q^65 + 528 * q^66 - 210 * q^67 + 132 * q^68 + 972 * q^69 - 240 * q^70 + 984 * q^71 + 192 * q^72 + 350 * q^73 + 384 * q^74 + 1872 * q^75 - 328 * q^76 + 1044 * q^77 + 480 * q^78 + 270 * q^79 + 24 * q^80 + 528 * q^81 - 144 * q^82 + 756 * q^83 + 144 * q^84 - 132 * q^85 + 672 * q^86 + 576 * q^87 + 120 * q^88 + 1278 * q^89 + 672 * q^90 + 476 * q^91 + 384 * q^92 + 240 * q^93 + 300 * q^94 + 474 * q^95 + 164 * q^97 + 744 * q^98 - 156 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.3.b	\(\chi_{126}(71, \cdot)\)	126.3.b.a	4	1
126.3.c	\(\chi_{126}(55, \cdot)\)	126.3.c.a	4	1
		126.3.c.b	4
126.3.i	\(\chi_{126}(65, \cdot)\)	126.3.i.a	32	2
126.3.j	\(\chi_{126}(31, \cdot)\)	126.3.j.a	32	2
126.3.n	\(\chi_{126}(19, \cdot)\)	126.3.n.a	4	2
		126.3.n.b	4
		126.3.n.c	4
126.3.o	\(\chi_{126}(13, \cdot)\)	126.3.o.a	32	2
126.3.p	\(\chi_{126}(103, \cdot)\)	126.3.p.a	32	2
126.3.q	\(\chi_{126}(29, \cdot)\)	126.3.q.a	24	2
126.3.r	\(\chi_{126}(11, \cdot)\)	126.3.r.a	32	2
126.3.s	\(\chi_{126}(53, \cdot)\)	126.3.s.a	4	2
		126.3.s.b	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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