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Properties

Label 3264.2.fh
Level $3264$
Weight $2$
Character orbit 3264.fh
Rep. character $\chi_{3264}(251,\cdot)$
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.fh (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

\( 4576 q - 8 q^{3} - 32 q^{4} - 8 q^{6} - 16 q^{7} + O(q^{10}) \) \( 4576 q - 8 q^{3} - 32 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{12} - 32 q^{13} - 32 q^{16} - 16 q^{18} - 16 q^{21} - 16 q^{22} - 48 q^{24} - 8 q^{27} - 16 q^{28} + 64 q^{30} - 32 q^{31} - 16 q^{34} - 16 q^{37} - 8 q^{39} + 48 q^{40} - 8 q^{45} - 80 q^{46} - 112 q^{48} + 16 q^{51} - 128 q^{52} - 8 q^{54} - 32 q^{55} - 8 q^{57} + 48 q^{58} + 48 q^{61} - 128 q^{64} - 32 q^{67} - 16 q^{69} - 16 q^{72} - 16 q^{73} + 32 q^{75} - 8 q^{78} - 16 q^{81} - 16 q^{82} - 16 q^{84} + 64 q^{85} - 16 q^{88} + 112 q^{90} + 80 q^{91} - 96 q^{94} - 144 q^{96} - 8 q^{99} + O(q^{100}) \)

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.