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

• Label: 2057.4.bm
• Level: $2057$
• Weight: $4$
• Character orbit: 2057.bm
• Rep. character: $\chi_{2057}(6,\cdot)$
• Character field: $\Q(\zeta_{880})$
• Dimension: $189440$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.bm (of order \(880\) and degree \(320\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2057 \)
Character field:			\(\Q(\zeta_{880})\)
Sturm bound:			\(792\)

Dimensions

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

	Total	New	Old
Modular forms	190720	190720	0
Cusp forms	189440	189440	0
Eisenstein series	1280	1280	0

Trace form

189440 * q - 312 * q^2 - 240 * q^3 - 328 * q^4 - 328 * q^5 - 312 * q^6 - 312 * q^7 - 312 * q^8 - 240 * q^9 - 352 * q^10 - 1440 * q^11 + 576 * q^12 - 504 * q^13 + 1112 * q^14 - 328 * q^15 - 312 * q^17 - 624 * q^18 - 312 * q^19 - 328 * q^20 - 352 * q^21 - 96 * q^22 - 704 * q^23 - 5112 * q^24 + 568 * q^25 - 328 * q^26 - 888 * q^27 - 312 * q^28 - 312 * q^29 - 312 * q^30 + 1400 * q^31 - 352 * q^32 - 288 * q^34 - 624 * q^35 - 200 * q^36 - 328 * q^37 + 2928 * q^38 - 312 * q^39 - 400 * q^40 - 5112 * q^41 - 4072 * q^42 - 352 * q^43 + 192 * q^44 - 288 * q^45 - 312 * q^46 - 328 * q^47 - 2272 * q^48 + 13496 * q^49 - 312 * q^51 + 14736 * q^52 - 328 * q^53 + 2024 * q^54 - 10752 * q^55 - 288 * q^56 - 26800 * q^57 - 2904 * q^58 - 8 * q^59 + 4792 * q^60 - 312 * q^61 - 312 * q^62 - 13032 * q^63 + 696 * q^64 - 352 * q^65 + 41856 * q^66 - 312 * q^68 + 4336 * q^69 + 25352 * q^70 - 328 * q^71 - 312 * q^72 - 312 * q^73 - 312 * q^74 + 56 * q^75 - 352 * q^76 - 3840 * q^77 - 288 * q^78 + 22568 * q^79 + 7064 * q^80 + 19552 * q^81 - 328 * q^82 - 9952 * q^83 - 312 * q^85 - 5904 * q^86 - 352 * q^87 + 1408 * q^88 - 288 * q^89 - 312 * q^90 + 27896 * q^91 - 20488 * q^92 - 328 * q^93 + 21200 * q^94 - 312 * q^95 - 312 * q^96 + 4280 * q^97 - 352 * q^98 + 50568 * 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.