Space of modular forms of level 2057 and weight 4

• Label: 2057.4
• Level: 2057
• Weight: 4
• Dimension: 508438
• Nonzero newspaces: 20
• Sturm bound: 1393920
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(1393920\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2057))\).

	Total	New	Old
Modular forms	525280	512652	12628
Cusp forms	520160	508438	11722
Eisenstein series	5120	4214	906

Trace form

508438 * q - 638 * q^2 - 638 * q^3 - 638 * q^4 - 638 * q^5 - 838 * q^6 - 678 * q^7 - 478 * q^8 - 318 * q^9 - 362 * q^10 - 600 * q^11 - 654 * q^12 - 526 * q^13 - 1258 * q^14 - 1542 * q^15 - 1718 * q^16 - 855 * q^17 - 938 * q^18 + 342 * q^19 + 1214 * q^20 + 926 * q^21 + 560 * q^22 - 1806 * q^23 - 3270 * q^24 - 2106 * q^25 - 2370 * q^26 - 1274 * q^27 - 1154 * q^28 - 578 * q^29 - 794 * q^30 - 1334 * q^31 + 1438 * q^32 - 1110 * q^33 + 149 * q^34 - 94 * q^35 + 1206 * q^36 + 594 * q^37 + 574 * q^38 + 1226 * q^39 - 2954 * q^40 - 18 * q^41 - 3426 * q^42 - 4922 * q^43 - 2930 * q^44 + 1022 * q^45 + 1934 * q^46 + 3242 * q^47 + 8366 * q^48 + 4858 * q^49 + 2514 * q^50 + 107 * q^51 - 2874 * q^52 - 8866 * q^53 - 16146 * q^54 - 3900 * q^55 - 7918 * q^56 - 8346 * q^57 + 2702 * q^58 + 3758 * q^59 + 4766 * q^60 + 882 * q^61 + 7878 * q^62 + 2070 * q^63 + 66 * q^64 + 4122 * q^65 + 1910 * q^66 + 4338 * q^67 + 5667 * q^68 + 6078 * q^69 + 1214 * q^70 + 1434 * q^71 + 138 * q^72 - 10538 * q^73 - 6234 * q^74 - 2474 * q^75 + 630 * q^76 - 5160 * q^77 - 10062 * q^78 - 3150 * q^79 - 15322 * q^80 - 8882 * q^81 - 12974 * q^82 - 4034 * q^83 - 12242 * q^84 + 689 * q^85 - 6222 * q^86 + 11934 * q^87 + 8660 * q^88 + 5498 * q^89 - 2266 * q^90 + 6482 * q^91 - 7106 * q^92 - 9238 * q^93 + 2158 * q^94 + 9810 * q^95 + 6574 * q^96 + 3070 * q^97 + 15438 * q^98 + 2540 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2057))\)

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
2057.4.a	\(\chi_{2057}(1, \cdot)\)	2057.4.a.a	1	1
		2057.4.a.b	1
		2057.4.a.c	1
		2057.4.a.d	1
		2057.4.a.e	3
		2057.4.a.f	3
		2057.4.a.g	4
		2057.4.a.h	10
		2057.4.a.i	10
		2057.4.a.j	12
		2057.4.a.k	19
		2057.4.a.l	19
		2057.4.a.m	20
		2057.4.a.n	20
		2057.4.a.o	20
		2057.4.a.p	20
		2057.4.a.q	40
		2057.4.a.r	40
		2057.4.a.s	44
		2057.4.a.t	44
		2057.4.a.u	52
		2057.4.a.v	52
2057.4.d	\(\chi_{2057}(1937, \cdot)\)	n/a	482	1
2057.4.e	\(\chi_{2057}(727, \cdot)\)	n/a	964	2
2057.4.g	\(\chi_{2057}(511, \cdot)\)	n/a	1728	4
2057.4.h	\(\chi_{2057}(485, \cdot)\)	n/a	1924	4
2057.4.j	\(\chi_{2057}(390, \cdot)\)	n/a	1912	4
2057.4.m	\(\chi_{2057}(188, \cdot)\)	n/a	5280	10
2057.4.n	\(\chi_{2057}(241, \cdot)\)	n/a	3824	8
2057.4.q	\(\chi_{2057}(81, \cdot)\)	n/a	3824	8
2057.4.r	\(\chi_{2057}(67, \cdot)\)	n/a	5920	10
2057.4.v	\(\chi_{2057}(9, \cdot)\)	n/a	7648	16
2057.4.x	\(\chi_{2057}(89, \cdot)\)	n/a	11840	20
2057.4.y	\(\chi_{2057}(69, \cdot)\)	n/a	21120	40
2057.4.ba	\(\chi_{2057}(40, \cdot)\)	n/a	15296	32
2057.4.bc	\(\chi_{2057}(100, \cdot)\)	n/a	23680	40
2057.4.bf	\(\chi_{2057}(16, \cdot)\)	n/a	23680	40
2057.4.bh	\(\chi_{2057}(10, \cdot)\)	n/a	47360	80
2057.4.bi	\(\chi_{2057}(4, \cdot)\)	n/a	47360	80
2057.4.bk	\(\chi_{2057}(15, \cdot)\)	n/a	94720	160
2057.4.bm	\(\chi_{2057}(6, \cdot)\)	n/a	189440	320

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2057))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2057)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 2}\)