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Properties

Label 1440.3.eg
Level $1440$
Weight $3$
Character orbit 1440.eg
Rep. character $\chi_{1440}(13,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $4576$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1440.eg (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1440 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1440, [\chi])\).

Total New Old
Modular forms 4640 4640 0
Cusp forms 4576 4576 0
Eisenstein series 64 64 0

Trace form

\( 4576 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 16 q^{8} + O(q^{10}) \) \( 4576 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 8 q^{12} - 4 q^{13} - 64 q^{14} - 8 q^{16} + 8 q^{18} + 80 q^{20} - 16 q^{21} - 4 q^{22} - 32 q^{24} - 4 q^{25} - 32 q^{26} - 8 q^{27} - 144 q^{28} - 164 q^{30} - 16 q^{31} - 4 q^{32} - 16 q^{33} - 216 q^{35} - 16 q^{36} - 16 q^{37} - 508 q^{38} - 4 q^{40} - 8 q^{41} - 152 q^{42} - 4 q^{43} - 8 q^{45} - 32 q^{46} + 44 q^{48} + 15344 q^{49} - 36 q^{50} - 16 q^{51} - 4 q^{52} - 16 q^{53} - 112 q^{54} - 16 q^{55} - 8 q^{56} - 4 q^{58} + 56 q^{60} - 8 q^{61} + 16 q^{62} - 16 q^{63} - 8 q^{65} - 848 q^{66} - 4 q^{67} - 68 q^{68} - 72 q^{69} + 192 q^{70} - 32 q^{71} + 924 q^{72} + 28 q^{75} - 320 q^{76} - 396 q^{77} + 52 q^{78} - 16 q^{80} + 16 q^{82} - 4 q^{83} - 392 q^{84} - 4 q^{85} - 8 q^{86} - 912 q^{87} + 44 q^{88} - 1344 q^{90} - 32 q^{91} - 360 q^{92} + 28 q^{93} - 8 q^{95} - 560 q^{96} - 8 q^{97} - 376 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

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