Properties

Label 1440.2.dz
Level $1440$
Weight $2$
Character orbit 1440.dz
Rep. character $\chi_{1440}(59,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $2272$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.dz (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1440 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

Total New Old
Modular forms 2336 2336 0
Cusp forms 2272 2272 0
Eisenstein series 64 64 0

Trace form

\( 2272 q - 8 q^{4} - 12 q^{5} - 16 q^{6} - 16 q^{9} + O(q^{10}) \) \( 2272 q - 8 q^{4} - 12 q^{5} - 16 q^{6} - 16 q^{9} - 16 q^{10} - 24 q^{11} - 24 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{19} - 12 q^{20} - 16 q^{21} - 16 q^{24} - 4 q^{25} - 24 q^{29} - 40 q^{30} + 8 q^{34} + 64 q^{36} - 16 q^{39} - 4 q^{40} - 24 q^{41} - 8 q^{45} - 32 q^{46} + 144 q^{50} + 32 q^{51} - 16 q^{54} - 16 q^{55} - 24 q^{56} - 24 q^{59} + 36 q^{60} - 8 q^{61} - 32 q^{64} - 24 q^{65} - 64 q^{66} - 16 q^{69} - 4 q^{70} - 24 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{79} - 376 q^{84} + 16 q^{85} - 24 q^{86} + 52 q^{90} - 32 q^{91} + 24 q^{94} + 16 q^{96} + 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

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