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Properties

Label 3264.2.gu
Level $3264$
Weight $2$
Character orbit 3264.gu
Rep. character $\chi_{3264}(59,\cdot)$
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.gu (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

\( 4576 q - 8 q^{3} - 8 q^{6} - 32 q^{7} - 8 q^{9} + O(q^{10}) \) \( 4576 q - 8 q^{3} - 8 q^{6} - 32 q^{7} - 8 q^{9} - 8 q^{12} - 32 q^{16} - 56 q^{18} - 16 q^{19} - 24 q^{21} - 16 q^{22} + 32 q^{24} - 16 q^{25} - 8 q^{27} - 80 q^{28} - 32 q^{30} - 32 q^{31} + 32 q^{34} - 8 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} + 32 q^{42} - 16 q^{43} - 48 q^{45} + 160 q^{46} - 8 q^{48} + 4352 q^{49} - 8 q^{51} - 32 q^{52} - 8 q^{54} - 16 q^{57} + 48 q^{58} + 24 q^{60} - 16 q^{61} - 56 q^{63} - 24 q^{66} - 32 q^{67} + 8 q^{69} - 240 q^{70} - 112 q^{72} - 48 q^{75} - 16 q^{76} - 112 q^{78} + 16 q^{79} - 16 q^{82} - 72 q^{84} - 16 q^{85} - 8 q^{87} - 16 q^{88} - 8 q^{90} - 32 q^{91} - 8 q^{93} + 16 q^{94} - 8 q^{96} - 8 q^{99} + O(q^{100}) \)

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.