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Properties

Label 2057.4.r
Level $2057$
Weight $4$
Character orbit 2057.r
Rep. character $\chi_{2057}(67,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $5920$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.r (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2057 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(792\)

Dimensions

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

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

Trace form

\( 5920 q - 14 q^{2} - 2378 q^{4} + 62 q^{8} - 52956 q^{9} + O(q^{10}) \) \( 5920 q - 14 q^{2} - 2378 q^{4} + 62 q^{8} - 52956 q^{9} + 218 q^{13} + 132 q^{15} - 9362 q^{16} - 207 q^{17} - 80 q^{18} + 290 q^{19} + 276 q^{21} + 14854 q^{25} - 66 q^{26} - 336 q^{30} + 98 q^{32} + 1740 q^{33} + 113 q^{34} - 1198 q^{35} + 20764 q^{36} + 718 q^{38} + 108 q^{42} + 1586 q^{43} - 10 q^{47} + 32138 q^{49} - 1060 q^{50} + 2477 q^{51} - 13298 q^{52} - 1570 q^{53} + 3682 q^{55} - 582 q^{59} + 4596 q^{60} - 40754 q^{64} - 6040 q^{66} - 3234 q^{67} - 2939 q^{68} - 660 q^{69} - 12534 q^{70} - 15236 q^{72} - 6226 q^{76} - 6830 q^{77} + 473776 q^{81} + 4186 q^{83} - 192 q^{84} - 2399 q^{85} - 2006 q^{86} - 2868 q^{87} - 2942 q^{89} + 8148 q^{93} - 27940 q^{94} - 2418 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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