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Properties

Label 3840.2.dv
Level $3840$
Weight $2$
Character orbit 3840.dv
Rep. character $\chi_{3840}(173,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $24448$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.dv (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3840 \)
Character field: \(\Q(\zeta_{64})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

Total New Old
Modular forms 24704 24704 0
Cusp forms 24448 24448 0
Eisenstein series 256 256 0

Trace form

\( 24448 q - 32 q^{3} - 64 q^{6} - 64 q^{7} + O(q^{10}) \) \( 24448 q - 32 q^{3} - 64 q^{6} - 64 q^{7} - 64 q^{10} - 32 q^{12} - 64 q^{13} - 32 q^{15} - 128 q^{16} - 32 q^{18} - 64 q^{21} - 64 q^{22} - 64 q^{25} - 32 q^{27} - 64 q^{28} - 32 q^{30} - 128 q^{31} - 32 q^{33} - 64 q^{36} - 64 q^{37} - 64 q^{40} - 32 q^{42} - 64 q^{43} - 32 q^{45} - 128 q^{46} - 32 q^{48} - 64 q^{51} - 64 q^{52} - 64 q^{55} - 32 q^{57} - 64 q^{58} - 32 q^{60} - 128 q^{61} - 64 q^{63} + 384 q^{64} - 64 q^{66} - 64 q^{67} + 320 q^{70} - 32 q^{72} - 64 q^{73} - 32 q^{75} - 128 q^{76} - 32 q^{78} - 64 q^{81} - 64 q^{82} - 64 q^{85} - 32 q^{87} - 64 q^{88} - 32 q^{90} - 128 q^{91} - 32 q^{93} - 64 q^{96} - 64 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

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