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Properties

Label 1792.3.bt
Level $1792$
Weight $3$
Character orbit 1792.bt
Rep. character $\chi_{1792}(13,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $16320$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.bt (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1792 \)
Character field: \(\Q(\zeta_{64})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 16448 16448 0
Cusp forms 16320 16320 0
Eisenstein series 128 128 0

Trace form

\( 16320 q - 64 q^{2} - 64 q^{4} - 32 q^{7} - 64 q^{8} - 64 q^{9} + O(q^{10}) \) \( 16320 q - 64 q^{2} - 64 q^{4} - 32 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{11} - 32 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{18} - 32 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{25} - 32 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{32} - 32 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{39} - 32 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{46} - 32 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{53} - 32 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{60} - 32 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{67} - 32 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{74} - 32 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{81} - 32 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{88} - 32 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{95} - 32 q^{98} - 64 q^{99} + O(q^{100}) \)

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.