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Properties

Label 3264.2.dt
Level $3264$
Weight $2$
Character orbit 3264.dt
Rep. character $\chi_{3264}(317,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4576$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3264.dt (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3264 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3264, [\chi])\).

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

Trace form

\( 4576 q - 16 q^{3} + 8 q^{6} - 16 q^{7} - 16 q^{9} + O(q^{10}) \) \( 4576 q - 16 q^{3} + 8 q^{6} - 16 q^{7} - 16 q^{9} - 16 q^{10} - 72 q^{12} - 16 q^{13} + 16 q^{15} - 16 q^{16} + 16 q^{19} - 32 q^{21} + 16 q^{22} + 16 q^{24} - 16 q^{25} - 16 q^{27} - 16 q^{28} - 32 q^{30} + 48 q^{33} - 16 q^{34} - 40 q^{36} - 16 q^{37} - 32 q^{39} - 128 q^{40} - 8 q^{42} - 16 q^{43} + 32 q^{45} - 32 q^{46} - 136 q^{48} - 16 q^{49} + 16 q^{51} - 32 q^{52} + 8 q^{54} + 64 q^{55} - 32 q^{57} + 48 q^{58} - 112 q^{60} + 48 q^{61} - 72 q^{63} + 96 q^{64} + 104 q^{66} + 8 q^{69} - 16 q^{70} - 8 q^{72} - 16 q^{73} - 32 q^{75} - 16 q^{76} - 16 q^{79} - 16 q^{81} - 16 q^{82} - 24 q^{84} - 16 q^{85} - 8 q^{87} + 112 q^{88} - 232 q^{90} - 16 q^{91} - 8 q^{93} + 16 q^{94} + 16 q^{96} + 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3264, [\chi])\) into newform subspaces

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