Space of modular forms of level 275 and weight 4

• Label: 275.4
• Level: 275
• Weight: 4
• Dimension: 7972
• Nonzero newspaces: 21
• Sturm bound: 24000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 21 \)
Sturm bound:			\(24000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(275))\).

	Total	New	Old
Modular forms	9280	8340	940
Cusp forms	8720	7972	748
Eisenstein series	560	368	192

Trace form

7972 * q - 61 * q^2 - 37 * q^3 - 13 * q^4 - 70 * q^5 - 151 * q^6 - 31 * q^7 - 5 * q^8 - 57 * q^9 - 20 * q^10 + 27 * q^11 + 114 * q^12 - 177 * q^13 - 336 * q^14 - 80 * q^15 - 193 * q^16 + 549 * q^17 + 1218 * q^18 + 820 * q^19 - 420 * q^20 - 86 * q^21 - 401 * q^22 - 1402 * q^23 - 3095 * q^24 - 1450 * q^25 - 596 * q^26 - 1630 * q^27 - 1458 * q^28 - 455 * q^29 + 500 * q^30 - 171 * q^31 + 3444 * q^32 + 828 * q^33 + 2434 * q^34 + 1600 * q^35 + 1992 * q^36 + 2229 * q^37 + 3720 * q^38 + 5301 * q^39 + 5320 * q^40 + 1449 * q^41 + 9358 * q^42 + 6698 * q^43 + 6972 * q^44 - 2390 * q^45 + 514 * q^46 - 4711 * q^47 - 15032 * q^48 - 9473 * q^49 - 11800 * q^50 - 12706 * q^51 - 25346 * q^52 - 11587 * q^53 - 26430 * q^54 - 5310 * q^55 - 18060 * q^56 - 7210 * q^57 - 8260 * q^58 + 5790 * q^59 + 19020 * q^60 + 3899 * q^61 + 25138 * q^62 + 19628 * q^63 + 25547 * q^64 + 7190 * q^65 + 14794 * q^66 + 12044 * q^67 + 14942 * q^68 + 6576 * q^69 - 1020 * q^70 - 2911 * q^71 - 9725 * q^72 - 11867 * q^73 - 20546 * q^74 - 11800 * q^75 - 7250 * q^76 - 7341 * q^77 - 12524 * q^78 - 2505 * q^79 - 11740 * q^80 + 3572 * q^81 + 10303 * q^82 + 15168 * q^83 + 28484 * q^84 + 19210 * q^85 + 10689 * q^86 + 20390 * q^87 + 17225 * q^88 + 16490 * q^89 + 30820 * q^90 + 22679 * q^91 + 44334 * q^92 + 27181 * q^93 + 22494 * q^94 - 5620 * q^95 + 31524 * q^96 - 12406 * q^97 - 10138 * q^98 - 11377 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.4.a	\(\chi_{275}(1, \cdot)\)	275.4.a.a	1	1
		275.4.a.b	2
		275.4.a.c	2
		275.4.a.d	3
		275.4.a.e	4
		275.4.a.f	5
		275.4.a.g	5
		275.4.a.h	5
		275.4.a.i	5
		275.4.a.j	6
		275.4.a.k	10
275.4.b	\(\chi_{275}(199, \cdot)\)	275.4.b.a	2	1
		275.4.b.b	4
		275.4.b.c	4
		275.4.b.d	6
		275.4.b.e	8
		275.4.b.f	10
		275.4.b.g	10
275.4.e	\(\chi_{275}(32, \cdot)\)	n/a	104	2
275.4.g	\(\chi_{275}(16, \cdot)\)	n/a	352	4
275.4.h	\(\chi_{275}(26, \cdot)\)	n/a	216	4
275.4.i	\(\chi_{275}(56, \cdot)\)	n/a	296	4
275.4.j	\(\chi_{275}(81, \cdot)\)	n/a	352	4
275.4.k	\(\chi_{275}(36, \cdot)\)	n/a	352	4
275.4.l	\(\chi_{275}(31, \cdot)\)	n/a	352	4
275.4.n	\(\chi_{275}(104, \cdot)\)	n/a	352	4
275.4.t	\(\chi_{275}(14, \cdot)\)	n/a	352	4
275.4.y	\(\chi_{275}(34, \cdot)\)	n/a	304	4
275.4.z	\(\chi_{275}(49, \cdot)\)	n/a	208	4
275.4.ba	\(\chi_{275}(4, \cdot)\)	n/a	352	4
275.4.bb	\(\chi_{275}(9, \cdot)\)	n/a	352	4
275.4.bf	\(\chi_{275}(28, \cdot)\)	n/a	704	8
275.4.bg	\(\chi_{275}(13, \cdot)\)	n/a	704	8
275.4.bl	\(\chi_{275}(17, \cdot)\)	n/a	704	8
275.4.bm	\(\chi_{275}(7, \cdot)\)	n/a	416	8
275.4.bn	\(\chi_{275}(2, \cdot)\)	n/a	704	8
275.4.bo	\(\chi_{275}(87, \cdot)\)	n/a	704	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)