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Properties

Label 2057.4.h
Level $2057$
Weight $4$
Character orbit 2057.h
Rep. character $\chi_{2057}(485,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1924$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 2424 1996 428
Cusp forms 2328 1924 404
Eisenstein series 96 72 24

Trace form

\( 1924 q + 4 q^{2} + 4 q^{3} + 20 q^{5} + 28 q^{6} + 4 q^{7} - 28 q^{8} + 64 q^{9} + O(q^{10}) \) \( 1924 q + 4 q^{2} + 4 q^{3} + 20 q^{5} + 28 q^{6} + 4 q^{7} - 28 q^{8} + 64 q^{9} - 108 q^{10} - 96 q^{12} + 132 q^{14} + 92 q^{15} - 28856 q^{16} + 76 q^{17} - 4 q^{19} + 68 q^{20} + 236 q^{23} + 272 q^{24} - 8 q^{25} + 292 q^{26} - 440 q^{27} - 452 q^{28} + 640 q^{29} - 188 q^{31} - 980 q^{32} + 1308 q^{34} + 1624 q^{35} + 1204 q^{36} - 588 q^{37} - 104 q^{39} - 632 q^{40} + 1144 q^{41} + 2056 q^{42} + 112 q^{43} - 64 q^{45} - 1268 q^{46} - 828 q^{48} - 1044 q^{49} + 72 q^{50} - 1540 q^{51} - 792 q^{52} - 1280 q^{53} - 2148 q^{54} - 2332 q^{56} + 468 q^{57} + 168 q^{58} + 872 q^{59} + 2760 q^{60} - 2596 q^{61} - 2732 q^{62} + 4088 q^{63} + 4020 q^{65} + 984 q^{67} - 3868 q^{68} - 4072 q^{69} + 3944 q^{70} + 484 q^{71} + 2752 q^{73} - 2284 q^{74} - 800 q^{75} - 2120 q^{76} - 2952 q^{78} + 548 q^{79} - 4096 q^{80} + 2080 q^{82} + 7856 q^{83} - 11632 q^{84} - 704 q^{85} - 16800 q^{86} + 4308 q^{87} + 17180 q^{90} - 1720 q^{91} + 1092 q^{92} + 2788 q^{93} - 5352 q^{94} + 6708 q^{95} - 4740 q^{96} + 1192 q^{97} + O(q^{100}) \)

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.

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

\( S_{4}^{\mathrm{old}}(2057, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)