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Properties

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 $792$

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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

\( 189440 q - 312 q^{2} - 240 q^{3} - 328 q^{4} - 328 q^{5} - 312 q^{6} - 312 q^{7} - 312 q^{8} - 240 q^{9} + O(q^{10}) \) \( 189440 q - 312 q^{2} - 240 q^{3} - 328 q^{4} - 328 q^{5} - 312 q^{6} - 312 q^{7} - 312 q^{8} - 240 q^{9} - 352 q^{10} - 1440 q^{11} + 576 q^{12} - 504 q^{13} + 1112 q^{14} - 328 q^{15} - 312 q^{17} - 624 q^{18} - 312 q^{19} - 328 q^{20} - 352 q^{21} - 96 q^{22} - 704 q^{23} - 5112 q^{24} + 568 q^{25} - 328 q^{26} - 888 q^{27} - 312 q^{28} - 312 q^{29} - 312 q^{30} + 1400 q^{31} - 352 q^{32} - 288 q^{34} - 624 q^{35} - 200 q^{36} - 328 q^{37} + 2928 q^{38} - 312 q^{39} - 400 q^{40} - 5112 q^{41} - 4072 q^{42} - 352 q^{43} + 192 q^{44} - 288 q^{45} - 312 q^{46} - 328 q^{47} - 2272 q^{48} + 13496 q^{49} - 312 q^{51} + 14736 q^{52} - 328 q^{53} + 2024 q^{54} - 10752 q^{55} - 288 q^{56} - 26800 q^{57} - 2904 q^{58} - 8 q^{59} + 4792 q^{60} - 312 q^{61} - 312 q^{62} - 13032 q^{63} + 696 q^{64} - 352 q^{65} + 41856 q^{66} - 312 q^{68} + 4336 q^{69} + 25352 q^{70} - 328 q^{71} - 312 q^{72} - 312 q^{73} - 312 q^{74} + 56 q^{75} - 352 q^{76} - 3840 q^{77} - 288 q^{78} + 22568 q^{79} + 7064 q^{80} + 19552 q^{81} - 328 q^{82} - 9952 q^{83} - 312 q^{85} - 5904 q^{86} - 352 q^{87} + 1408 q^{88} - 288 q^{89} - 312 q^{90} + 27896 q^{91} - 20488 q^{92} - 328 q^{93} + 21200 q^{94} - 312 q^{95} - 312 q^{96} + 4280 q^{97} - 352 q^{98} + 50568 q^{99} + O(q^{100}) \)

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.