Properties

Label 1856.2.co
Level $1856$
Weight $2$
Character orbit 1856.co
Rep. character $\chi_{1856}(5,\cdot)$
Character field $\Q(\zeta_{112})$
Dimension $11424$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.co (of order \(112\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1856 \)
Character field: \(\Q(\zeta_{112})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1856, [\chi])\).

Total New Old
Modular forms 11616 11616 0
Cusp forms 11424 11424 0
Eisenstein series 192 192 0

Trace form

\( 11424 q - 56 q^{2} - 56 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 40 q^{7} - 56 q^{8} - 40 q^{9} + O(q^{10}) \) \( 11424 q - 56 q^{2} - 56 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 40 q^{7} - 56 q^{8} - 40 q^{9} - 56 q^{10} - 56 q^{11} - 40 q^{13} - 56 q^{14} - 56 q^{15} - 40 q^{16} - 56 q^{18} - 56 q^{19} - 40 q^{20} - 56 q^{21} - 80 q^{22} - 40 q^{23} - 40 q^{24} - 40 q^{25} - 56 q^{26} - 56 q^{27} - 16 q^{28} - 48 q^{29} - 96 q^{30} - 56 q^{32} - 40 q^{34} - 40 q^{35} - 40 q^{36} - 56 q^{37} - 120 q^{38} - 56 q^{39} - 56 q^{40} - 40 q^{42} - 56 q^{43} - 40 q^{45} - 56 q^{47} - 56 q^{48} - 40 q^{49} - 56 q^{50} - 40 q^{51} + 8 q^{52} - 40 q^{53} - 40 q^{54} - 56 q^{55} + 336 q^{56} - 96 q^{57} + 24 q^{58} - 96 q^{59} - 728 q^{60} - 56 q^{61} - 8 q^{62} - 240 q^{63} - 232 q^{64} - 80 q^{65} + 616 q^{66} + 120 q^{67} - 56 q^{68} - 56 q^{69} - 40 q^{71} - 56 q^{72} - 56 q^{73} - 152 q^{74} - 56 q^{76} - 56 q^{77} + 56 q^{78} - 56 q^{79} - 40 q^{80} - 40 q^{81} - 40 q^{82} - 40 q^{83} - 56 q^{84} - 56 q^{85} - 96 q^{86} - 48 q^{87} - 256 q^{88} - 56 q^{89} - 1064 q^{90} - 40 q^{91} - 40 q^{92} + 8 q^{93} - 40 q^{94} - 312 q^{96} - 56 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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