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Properties

Label 1440.2.ee
Level $1440$
Weight $2$
Character orbit 1440.ee
Rep. character $\chi_{1440}(173,\cdot)$
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.ee (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

\( 2272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 16 q^{6} + O(q^{10}) \) \( 2272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 16 q^{6} - 16 q^{10} - 24 q^{11} - 8 q^{12} - 4 q^{13} - 8 q^{16} - 16 q^{18} + 72 q^{20} - 16 q^{21} - 4 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{27} - 48 q^{28} + 4 q^{30} - 16 q^{31} - 12 q^{32} - 16 q^{33} - 16 q^{36} - 16 q^{37} - 12 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{42} - 4 q^{43} - 8 q^{45} - 32 q^{46} + 44 q^{48} + 1040 q^{49} - 12 q^{50} - 16 q^{51} - 4 q^{52} - 112 q^{54} - 16 q^{55} - 24 q^{56} - 4 q^{58} + 8 q^{60} - 8 q^{61} - 16 q^{63} - 24 q^{65} - 80 q^{66} - 4 q^{67} + 36 q^{68} + 24 q^{69} + 24 q^{70} - 12 q^{72} + 4 q^{75} + 16 q^{76} - 12 q^{77} + 76 q^{78} - 32 q^{82} - 12 q^{83} - 56 q^{84} - 4 q^{85} - 24 q^{86} + 96 q^{87} - 52 q^{88} - 32 q^{91} - 240 q^{92} + 4 q^{93} - 24 q^{95} + 16 q^{96} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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