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Properties

Label 1856.4.cm
Level $1856$
Weight $4$
Character orbit 1856.cm
Rep. character $\chi_{1856}(11,\cdot)$
Character field $\Q(\zeta_{112})$
Dimension $34464$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.cm (of order \(112\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1856 \)
Character field: \(\Q(\zeta_{112})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1856, [\chi])\).

Total New Old
Modular forms 34656 34656 0
Cusp forms 34464 34464 0
Eisenstein series 192 192 0

Trace form

\( 34464 q - 48 q^{2} - 48 q^{3} - 56 q^{4} - 56 q^{5} - 56 q^{6} - 40 q^{7} - 48 q^{8} - 56 q^{9} + O(q^{10}) \) \( 34464 q - 48 q^{2} - 48 q^{3} - 56 q^{4} - 56 q^{5} - 56 q^{6} - 40 q^{7} - 48 q^{8} - 56 q^{9} - 48 q^{10} - 48 q^{11} - 48 q^{12} - 56 q^{13} - 48 q^{14} - 40 q^{15} - 40 q^{16} - 408 q^{18} - 48 q^{19} - 40 q^{20} - 48 q^{21} - 56 q^{22} - 40 q^{23} - 40 q^{24} - 40 q^{25} - 48 q^{26} + 480 q^{27} - 48 q^{29} - 96 q^{30} - 96 q^{31} - 48 q^{32} + 264 q^{34} - 56 q^{35} - 40 q^{36} - 48 q^{37} + 11984 q^{38} + 7152 q^{39} - 624 q^{40} - 48 q^{41} - 56 q^{42} - 1664 q^{43} - 9128 q^{44} - 40 q^{45} - 2928 q^{46} - 56 q^{47} - 48 q^{48} - 40 q^{49} - 48 q^{50} + 1024 q^{51} - 3352 q^{52} - 40 q^{53} - 40 q^{54} - 48 q^{55} + 344 q^{56} + 1608 q^{58} - 96 q^{59} - 35016 q^{60} - 48 q^{61} - 7880 q^{62} - 56 q^{64} - 80 q^{65} - 5456 q^{66} - 56 q^{67} + 5992 q^{68} - 48 q^{69} + 1176 q^{70} - 56 q^{71} + 3360 q^{72} - 48 q^{73} - 40 q^{74} + 952 q^{75} - 4336 q^{76} - 3856 q^{77} - 7096 q^{78} - 56 q^{79} + 6264 q^{80} - 40 q^{81} - 40 q^{82} - 40 q^{83} - 48 q^{84} + 5952 q^{85} - 4736 q^{86} + 2528 q^{87} - 6336 q^{88} - 48 q^{89} + 14760 q^{90} + 7144 q^{91} - 10816 q^{92} - 56 q^{93} - 51392 q^{94} - 96 q^{95} - 56 q^{96} - 8112 q^{98} + 168 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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