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Properties

Label 1792.3.ca
Level $1792$
Weight $3$
Character orbit 1792.ca
Rep. character $\chi_{1792}(5,\cdot)$
Character field $\Q(\zeta_{192})$
Dimension $32640$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.ca (of order \(192\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1792 \)
Character field: \(\Q(\zeta_{192})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1792, [\chi])\).

Total New Old
Modular forms 32896 32896 0
Cusp forms 32640 32640 0
Eisenstein series 256 256 0

Trace form

\( 32640 q - 32 q^{2} - 96 q^{3} - 32 q^{4} - 96 q^{5} - 64 q^{7} - 128 q^{8} - 32 q^{9} + O(q^{10}) \) \( 32640 q - 32 q^{2} - 96 q^{3} - 32 q^{4} - 96 q^{5} - 64 q^{7} - 128 q^{8} - 32 q^{9} - 96 q^{10} - 32 q^{11} - 96 q^{12} - 64 q^{14} - 128 q^{15} - 32 q^{16} - 96 q^{17} - 32 q^{18} - 96 q^{19} - 64 q^{21} - 128 q^{22} - 32 q^{23} - 96 q^{24} - 32 q^{25} - 96 q^{26} - 64 q^{28} - 128 q^{29} - 32 q^{30} - 96 q^{31} - 32 q^{32} - 96 q^{33} - 64 q^{35} - 128 q^{36} - 32 q^{37} - 96 q^{38} - 32 q^{39} - 96 q^{40} - 64 q^{42} - 128 q^{43} - 32 q^{44} - 96 q^{45} - 32 q^{46} - 96 q^{47} - 64 q^{49} - 128 q^{50} - 32 q^{51} - 96 q^{52} - 32 q^{53} - 96 q^{54} - 64 q^{56} - 128 q^{57} - 32 q^{58} - 96 q^{59} - 32 q^{60} - 96 q^{61} - 64 q^{63} - 128 q^{64} - 32 q^{65} - 96 q^{66} - 32 q^{67} - 96 q^{68} - 64 q^{70} - 128 q^{71} - 32 q^{72} - 96 q^{73} - 32 q^{74} - 96 q^{75} - 64 q^{77} - 128 q^{78} - 32 q^{79} - 96 q^{80} - 32 q^{81} - 96 q^{82} - 64 q^{84} - 128 q^{85} - 32 q^{86} - 96 q^{87} - 32 q^{88} - 96 q^{89} - 64 q^{91} - 128 q^{92} - 32 q^{93} - 96 q^{94} - 32 q^{95} - 96 q^{96} - 64 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

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