Space of modular forms of level 272 and weight 4

• Label: 272.4
• Level: 272
• Weight: 4
• Dimension: 3794
• Nonzero newspaces: 13
• Sturm bound: 18432
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 13 \)
Sturm bound:			\(18432\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(272))\).

	Total	New	Old
Modular forms	7136	3928	3208
Cusp forms	6688	3794	2894
Eisenstein series	448	134	314

Trace form

3794 * q - 28 * q^2 - 28 * q^3 - 48 * q^4 - 32 * q^5 + 32 * q^6 + 24 * q^7 + 56 * q^8 + 14 * q^9 + 104 * q^10 - 148 * q^11 - 232 * q^12 - 80 * q^13 - 408 * q^14 + 240 * q^15 - 592 * q^16 - 118 * q^17 - 412 * q^18 + 116 * q^19 + 360 * q^20 + 48 * q^21 + 1144 * q^22 - 136 * q^23 + 1664 * q^24 + 234 * q^25 + 496 * q^26 - 88 * q^27 - 592 * q^28 - 32 * q^29 - 2504 * q^30 - 1080 * q^31 - 1968 * q^32 - 424 * q^33 - 468 * q^34 - 1096 * q^35 + 1160 * q^36 + 304 * q^37 + 2432 * q^38 - 200 * q^39 + 2640 * q^40 + 388 * q^41 + 1328 * q^42 + 1756 * q^43 - 1768 * q^44 - 472 * q^45 - 2296 * q^46 + 2920 * q^47 - 3568 * q^48 - 726 * q^49 - 1484 * q^50 + 1276 * q^51 + 408 * q^52 - 1088 * q^53 + 2720 * q^54 - 4120 * q^55 + 944 * q^56 - 2408 * q^57 - 48 * q^58 - 5012 * q^59 + 352 * q^60 - 1360 * q^61 + 128 * q^62 + 960 * q^63 - 1056 * q^64 + 4904 * q^65 + 824 * q^66 - 308 * q^67 + 848 * q^68 + 6632 * q^69 - 352 * q^70 + 4072 * q^71 - 2216 * q^72 + 2052 * q^73 + 872 * q^74 + 8436 * q^75 + 2424 * q^76 + 1136 * q^77 + 1512 * q^78 + 4376 * q^79 + 5264 * q^80 - 7774 * q^81 + 1376 * q^82 - 2732 * q^83 - 3952 * q^84 - 3752 * q^85 - 7592 * q^86 - 1608 * q^87 - 3088 * q^88 - 1436 * q^89 - 3824 * q^90 - 5632 * q^91 - 1296 * q^92 + 3064 * q^93 + 6464 * q^94 - 14000 * q^95 + 8832 * q^96 + 892 * q^97 - 660 * q^98 - 8756 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.4.a	\(\chi_{272}(1, \cdot)\)	272.4.a.a	1	1
		272.4.a.b	1
		272.4.a.c	1
		272.4.a.d	1
		272.4.a.e	2
		272.4.a.f	2
		272.4.a.g	3
		272.4.a.h	3
		272.4.a.i	3
		272.4.a.j	3
		272.4.a.k	4
272.4.b	\(\chi_{272}(33, \cdot)\)	272.4.b.a	2	1
		272.4.b.b	2
		272.4.b.c	4
		272.4.b.d	4
		272.4.b.e	6
		272.4.b.f	8
272.4.c	\(\chi_{272}(137, \cdot)\)	None	0	1
272.4.h	\(\chi_{272}(169, \cdot)\)	None	0	1
272.4.j	\(\chi_{272}(13, \cdot)\)	n/a	212	2
272.4.l	\(\chi_{272}(69, \cdot)\)	n/a	192	2
272.4.m	\(\chi_{272}(89, \cdot)\)	None	0	2
272.4.o	\(\chi_{272}(81, \cdot)\)	272.4.o.a	2	2
		272.4.o.b	2
		272.4.o.c	6
		272.4.o.d	6
		272.4.o.e	8
		272.4.o.f	14
		272.4.o.g	14
272.4.r	\(\chi_{272}(101, \cdot)\)	n/a	212	2
272.4.s	\(\chi_{272}(149, \cdot)\)	n/a	212	2
272.4.v	\(\chi_{272}(49, \cdot)\)	n/a	104	4
272.4.w	\(\chi_{272}(189, \cdot)\)	n/a	424	4
272.4.y	\(\chi_{272}(53, \cdot)\)	n/a	424	4
272.4.ba	\(\chi_{272}(9, \cdot)\)	None	0	4
272.4.bd	\(\chi_{272}(3, \cdot)\)	n/a	848	8
272.4.bf	\(\chi_{272}(31, \cdot)\)	n/a	216	8
272.4.bg	\(\chi_{272}(7, \cdot)\)	None	0	8
272.4.bj	\(\chi_{272}(107, \cdot)\)	n/a	848	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

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