Properties

Label 2057.4.bh
Level $2057$
Weight $4$
Character orbit 2057.bh
Rep. character $\chi_{2057}(10,\cdot)$
Character field $\Q(\zeta_{176})$
Dimension $47360$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.bh (of order \(176\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2057 \)
Character field: \(\Q(\zeta_{176})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 47680 47680 0
Cusp forms 47360 47360 0
Eisenstein series 320 320 0

Trace form

\( 47360 q - 88 q^{2} - 160 q^{3} - 72 q^{4} - 72 q^{5} - 88 q^{6} - 88 q^{7} - 88 q^{8} - 160 q^{9} + O(q^{10}) \) \( 47360 q - 88 q^{2} - 160 q^{3} - 72 q^{4} - 72 q^{5} - 88 q^{6} - 88 q^{7} - 88 q^{8} - 160 q^{9} - 88 q^{10} + 1040 q^{11} - 936 q^{12} + 264 q^{13} - 1512 q^{14} - 72 q^{15} - 88 q^{17} - 176 q^{18} - 88 q^{19} - 72 q^{20} - 88 q^{21} - 304 q^{22} + 344 q^{23} - 88 q^{24} - 968 q^{25} - 72 q^{26} - 592 q^{27} - 88 q^{28} - 88 q^{29} - 88 q^{30} - 1800 q^{31} - 88 q^{32} - 72 q^{34} - 176 q^{35} - 200 q^{36} - 72 q^{37} - 728 q^{38} - 88 q^{39} - 88 q^{41} + 3672 q^{42} - 88 q^{43} - 592 q^{44} - 72 q^{45} - 88 q^{46} - 72 q^{47} + 1872 q^{48} - 13896 q^{49} - 88 q^{51} - 176 q^{52} - 72 q^{53} - 2464 q^{54} - 3888 q^{55} - 72 q^{56} + 26400 q^{57} + 2504 q^{58} - 392 q^{59} - 5192 q^{60} - 88 q^{61} - 88 q^{62} - 88 q^{63} - 1096 q^{64} - 88 q^{65} - 8456 q^{66} - 88 q^{68} - 17616 q^{69} - 25752 q^{70} - 72 q^{71} - 88 q^{72} - 88 q^{73} - 88 q^{74} - 456 q^{75} - 88 q^{76} - 2080 q^{77} - 72 q^{78} - 22968 q^{79} + 18136 q^{80} - 19952 q^{81} - 72 q^{82} - 88 q^{83} - 88 q^{85} + 5104 q^{86} - 88 q^{87} - 1808 q^{88} - 72 q^{89} - 88 q^{90} - 18216 q^{91} + 20088 q^{92} - 72 q^{93} - 88 q^{95} - 88 q^{96} - 4680 q^{97} - 88 q^{98} - 50968 q^{99} + O(q^{100}) \)

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

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