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Properties

Label 1856.4.co
Level $1856$
Weight $4$
Character orbit 1856.co
Rep. character $\chi_{1856}(5,\cdot)$
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.co (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

\( 34464 q - 56 q^{2} - 56 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 40 q^{7} - 56 q^{8} - 40 q^{9} + O(q^{10}) \) \( 34464 q - 56 q^{2} - 56 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 40 q^{7} - 56 q^{8} - 40 q^{9} - 56 q^{10} - 56 q^{11} - 40 q^{13} - 56 q^{14} - 56 q^{15} - 40 q^{16} - 56 q^{18} - 56 q^{19} - 40 q^{20} - 56 q^{21} - 2400 q^{22} - 40 q^{23} - 40 q^{24} - 40 q^{25} - 56 q^{26} - 56 q^{27} - 1616 q^{28} - 48 q^{29} - 96 q^{30} - 56 q^{32} - 40 q^{34} - 40 q^{35} - 40 q^{36} - 56 q^{37} - 920 q^{38} - 56 q^{39} - 56 q^{40} - 40 q^{42} - 56 q^{43} + 6944 q^{44} - 40 q^{45} - 56 q^{47} - 56 q^{48} - 40 q^{49} - 56 q^{50} - 40 q^{51} + 3272 q^{52} - 40 q^{53} - 40 q^{54} - 56 q^{55} - 2800 q^{56} - 96 q^{57} - 2424 q^{58} - 96 q^{59} + 34216 q^{60} - 56 q^{61} + 88 q^{62} + 10000 q^{63} + 12056 q^{64} - 80 q^{65} - 38360 q^{66} - 8200 q^{67} - 56 q^{68} - 56 q^{69} - 40 q^{71} - 56 q^{72} - 56 q^{73} - 5304 q^{74} - 56 q^{76} - 56 q^{77} + 17144 q^{78} - 56 q^{79} - 40 q^{80} - 40 q^{81} - 40 q^{82} - 40 q^{83} - 56 q^{84} - 56 q^{85} - 96 q^{86} - 48 q^{87} + 6144 q^{88} - 56 q^{89} + 65464 q^{90} - 40 q^{91} - 40 q^{92} + 392 q^{93} - 40 q^{94} + 25800 q^{96} - 56 q^{98} + O(q^{100}) \)

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.