Properties

Label 2736.3.w
Level $2736$
Weight $3$
Character orbit 2736.w
Rep. character $\chi_{2736}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $796$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 1936 804 1132
Cusp forms 1904 796 1108
Eisenstein series 32 8 24

Trace form

\( 796q - 4q^{4} + 4q^{5} + O(q^{10}) \) \( 796q - 4q^{4} + 4q^{5} + 4q^{11} + 52q^{16} + 8q^{17} - 34q^{19} - 80q^{20} + 56q^{26} + 72q^{38} - 4q^{43} - 268q^{44} + 8q^{47} - 5412q^{49} + 80q^{58} + 60q^{61} + 396q^{62} + 224q^{64} - 440q^{68} + 432q^{74} + 4q^{76} - 192q^{77} + 408q^{80} + 300q^{82} + 164q^{83} - 424q^{85} - 192q^{92} + 388q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)