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Properties

Label 3264.2.gq
Level $3264$
Weight $2$
Character orbit 3264.gq
Rep. character $\chi_{3264}(379,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2304$
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.gq (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1088 \)
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 2304 2336
Cusp forms 4576 2304 2272
Eisenstein series 64 0 64

Trace form

\( 2304 q - 16 q^{4} + 2304 q^{9} + O(q^{10}) \) \( 2304 q - 16 q^{4} + 2304 q^{9} - 64 q^{14} + 16 q^{16} + 32 q^{19} + 80 q^{32} - 16 q^{36} - 16 q^{40} - 96 q^{46} - 64 q^{48} - 32 q^{51} - 64 q^{56} - 288 q^{58} - 128 q^{59} + 64 q^{61} - 32 q^{62} - 16 q^{64} + 64 q^{66} + 112 q^{68} + 2304 q^{81} + 64 q^{84} - 160 q^{86} + 176 q^{88} + 128 q^{91} + 112 q^{94} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)