Space of modular forms of level 2057, weight 4, and Character 2057.m

• Label: 2057.4.m
• Level: $2057$
• Weight: $4$
• Character orbit: 2057.m
• Rep. character: $\chi_{2057}(188,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $5280$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2057, [\chi])\).

	Total	New	Old
Modular forms	5960	5280	680
Cusp forms	5920	5280	640
Eisenstein series	40	0	40

Trace form

5280 * q + 4 * q^2 - 2132 * q^4 + 24 * q^6 + 52 * q^7 - 36 * q^8 + 47520 * q^9 + 400 * q^10 + 8 * q^11 + 48 * q^12 - 216 * q^13 - 156 * q^14 - 144 * q^15 - 8452 * q^16 + 68 * q^17 + 292 * q^18 - 160 * q^19 + 380 * q^20 + 40 * q^21 - 402 * q^22 + 1476 * q^23 - 3024 * q^24 - 12792 * q^25 + 180 * q^26 + 312 * q^27 + 92 * q^28 + 988 * q^29 - 32 * q^30 - 552 * q^31 - 984 * q^32 + 316 * q^33 + 408 * q^35 - 20324 * q^36 - 1496 * q^37 - 216 * q^38 + 784 * q^39 - 6340 * q^40 + 1736 * q^41 + 1740 * q^42 - 256 * q^43 + 3456 * q^44 + 392 * q^45 - 880 * q^46 + 256 * q^47 + 1396 * q^48 - 26784 * q^49 + 8082 * q^50 + 408 * q^51 - 1104 * q^52 + 2588 * q^53 - 15520 * q^54 - 2968 * q^55 + 438 * q^56 + 584 * q^57 + 6778 * q^58 + 312 * q^59 + 328 * q^60 + 1452 * q^61 - 624 * q^62 + 9992 * q^63 - 45988 * q^64 - 2056 * q^65 - 792 * q^66 + 2088 * q^67 + 816 * q^68 + 1832 * q^69 + 600 * q^70 + 2568 * q^71 - 2432 * q^72 - 1552 * q^73 - 208 * q^74 + 1120 * q^75 + 24018 * q^76 - 5492 * q^77 - 12324 * q^78 + 1508 * q^79 - 1600 * q^80 + 428616 * q^81 + 8 * q^82 + 2808 * q^83 - 5260 * q^84 - 476 * q^85 + 716 * q^86 - 968 * q^87 + 9314 * q^88 + 10056 * q^89 + 13848 * q^90 - 532 * q^91 - 5496 * q^92 - 592 * q^93 + 2248 * q^94 - 10160 * q^95 - 1088 * q^96 + 4080 * q^97 - 5144 * q^98 + 2840 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2057, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2057, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2057, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)