Space of modular forms of level 272 and weight 3

• Label: 272.3
• Level: 272
• Weight: 3
• Dimension: 2506
• Nonzero newspaces: 13
• Newform subspaces: 28
• Sturm bound: 13824
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 13 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(13824\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(272))\).

	Total	New	Old
Modular forms	4832	2642	2190
Cusp forms	4384	2506	1878
Eisenstein series	448	136	312

Trace form

2506 * q - 28 * q^2 - 20 * q^3 - 16 * q^4 - 24 * q^5 - 16 * q^6 - 16 * q^7 - 40 * q^8 - 26 * q^9 - 104 * q^10 + 12 * q^11 - 136 * q^12 - 56 * q^13 - 56 * q^14 - 24 * q^15 + 48 * q^16 - 38 * q^17 + 84 * q^18 - 84 * q^19 + 136 * q^20 + 72 * q^22 - 144 * q^23 - 128 * q^24 - 30 * q^25 - 224 * q^26 - 152 * q^27 - 144 * q^28 - 88 * q^29 - 136 * q^30 - 24 * q^31 - 48 * q^32 - 56 * q^33 + 44 * q^34 + 152 * q^35 + 72 * q^36 + 8 * q^37 - 112 * q^38 + 368 * q^39 - 112 * q^40 - 44 * q^41 + 16 * q^42 + 204 * q^43 - 72 * q^44 - 64 * q^45 - 88 * q^46 - 24 * q^47 + 16 * q^48 - 78 * q^49 - 124 * q^50 - 180 * q^51 - 264 * q^52 - 152 * q^53 - 96 * q^54 + 48 * q^55 + 304 * q^56 + 632 * q^57 + 320 * q^58 - 52 * q^59 + 288 * q^60 + 328 * q^61 + 256 * q^62 + 552 * q^63 - 160 * q^64 + 152 * q^65 - 424 * q^66 + 420 * q^67 - 144 * q^68 - 104 * q^69 + 304 * q^71 - 136 * q^72 - 172 * q^73 + 152 * q^74 - 700 * q^75 + 344 * q^76 - 256 * q^77 + 136 * q^78 - 600 * q^79 - 496 * q^80 - 1302 * q^81 - 640 * q^82 - 1428 * q^83 - 496 * q^84 - 296 * q^85 - 600 * q^86 - 912 * q^87 - 16 * q^88 + 148 * q^89 + 288 * q^90 - 400 * q^91 + 304 * q^92 + 24 * q^93 - 128 * q^94 - 24 * q^95 + 128 * q^96 - 324 * q^97 - 52 * q^98 + 356 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.3.d	\(\chi_{272}(239, \cdot)\)	272.3.d.a	4	1
		272.3.d.b	12
272.3.e	\(\chi_{272}(135, \cdot)\)	None	0	1
272.3.f	\(\chi_{272}(103, \cdot)\)	None	0	1
272.3.g	\(\chi_{272}(271, \cdot)\)	272.3.g.a	2	1
		272.3.g.b	2
		272.3.g.c	2
		272.3.g.d	12
272.3.i	\(\chi_{272}(251, \cdot)\)	272.3.i.a	140	2
272.3.k	\(\chi_{272}(67, \cdot)\)	272.3.k.a	140	2
272.3.n	\(\chi_{272}(55, \cdot)\)	None	0	2
272.3.p	\(\chi_{272}(47, \cdot)\)	272.3.p.a	2	2
		272.3.p.b	2
		272.3.p.c	4
		272.3.p.d	4
		272.3.p.e	24
272.3.q	\(\chi_{272}(35, \cdot)\)	272.3.q.a	128	2
272.3.t	\(\chi_{272}(115, \cdot)\)	272.3.t.a	140	2
272.3.u	\(\chi_{272}(15, \cdot)\)	272.3.u.a	24	4
		272.3.u.b	48
272.3.x	\(\chi_{272}(155, \cdot)\)	272.3.x.a	280	4
272.3.z	\(\chi_{272}(19, \cdot)\)	272.3.z.a	280	4
272.3.bb	\(\chi_{272}(87, \cdot)\)	None	0	4
272.3.bc	\(\chi_{272}(29, \cdot)\)	272.3.bc.a	560	8
272.3.be	\(\chi_{272}(41, \cdot)\)	None	0	8
272.3.bh	\(\chi_{272}(65, \cdot)\)	272.3.bh.a	8	8
		272.3.bh.b	8
		272.3.bh.c	8
		272.3.bh.d	16
		272.3.bh.e	24
		272.3.bh.f	32
		272.3.bh.g	40
272.3.bi	\(\chi_{272}(5, \cdot)\)	272.3.bi.a	560	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(272)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)