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Properties

Label 3264.2.bm
Level $3264$
Weight $2$
Character orbit 3264.bm
Rep. character $\chi_{3264}(1007,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
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.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 816 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 296 888
Cusp forms 1120 280 840
Eisenstein series 64 16 48

Trace form

\( 280 q + 8 q^{7} + O(q^{10}) \) \( 280 q + 8 q^{7} - 8 q^{13} + 24 q^{15} - 4 q^{21} + 248 q^{25} - 16 q^{31} - 8 q^{33} + 4 q^{39} - 12 q^{51} + 16 q^{55} + 12 q^{57} + 40 q^{63} + 8 q^{67} - 4 q^{69} - 8 q^{81} - 8 q^{85} + 12 q^{93} - 8 q^{97} + O(q^{100}) \)

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

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