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Properties

Label 1856.2.bl
Level $1856$
Weight $2$
Character orbit 1856.bl
Rep. character $\chi_{1856}(307,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1904$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.bl (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1856 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1936 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

Trace form

\( 1904 q - 8 q^{2} - 8 q^{3} - 16 q^{7} - 8 q^{8} + O(q^{10}) \) \( 1904 q - 8 q^{2} - 8 q^{3} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{14} - 16 q^{16} - 16 q^{17} + 32 q^{18} - 8 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 8 q^{26} - 56 q^{27} - 8 q^{29} - 16 q^{30} - 16 q^{31} - 8 q^{32} - 32 q^{34} - 16 q^{36} - 8 q^{37} - 112 q^{38} - 56 q^{39} - 72 q^{40} - 8 q^{41} - 24 q^{43} + 72 q^{44} - 16 q^{45} + 56 q^{46} - 16 q^{47} - 8 q^{48} - 16 q^{49} - 8 q^{50} - 48 q^{51} + 32 q^{52} - 16 q^{53} - 16 q^{54} - 8 q^{55} + 48 q^{56} - 16 q^{58} - 16 q^{59} + 64 q^{60} - 8 q^{61} - 48 q^{62} - 32 q^{65} - 120 q^{66} + 16 q^{68} - 8 q^{69} + 16 q^{70} - 200 q^{72} - 8 q^{73} - 16 q^{74} + 32 q^{75} + 56 q^{76} - 40 q^{77} + 32 q^{78} - 16 q^{79} - 80 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 8 q^{84} - 48 q^{85} + 128 q^{86} - 120 q^{87} - 176 q^{88} - 8 q^{89} + 304 q^{90} - 96 q^{91} + 16 q^{92} - 16 q^{94} - 16 q^{95} - 72 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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