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Properties

Label 3264.2.ce
Level $3264$
Weight $2$
Character orbit 3264.ce
Rep. character $\chi_{3264}(1103,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $560$
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.ce (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 816 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 592 1776
Cusp forms 2240 560 1680
Eisenstein series 128 32 96

Trace form

\( 560 q + 4 q^{3} + 16 q^{7} + O(q^{10}) \) \( 560 q + 4 q^{3} + 16 q^{7} + 4 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{37} + 8 q^{39} + 16 q^{45} - 16 q^{49} + 44 q^{51} + 24 q^{57} - 40 q^{61} - 80 q^{63} + 16 q^{67} - 8 q^{69} + 36 q^{75} - 8 q^{85} + 8 q^{87} - 96 q^{91} - 16 q^{97} + 40 q^{99} + O(q^{100}) \)

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.

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

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1632, [\chi])\)\(^{\oplus 2}\)