Properties

Label 2736.2.bb
Level $2736$
Weight $2$
Character orbit 2736.bb
Rep. character $\chi_{2736}(379,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $396$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 976 404 572
Cusp forms 944 396 548
Eisenstein series 32 8 24

Trace form

\( 396q - 4q^{4} + 4q^{5} - 8q^{7} + O(q^{10}) \) \( 396q - 4q^{4} + 4q^{5} - 8q^{7} + 4q^{11} - 12q^{16} + 8q^{17} - 10q^{19} + 32q^{20} + 8q^{23} - 32q^{26} + 48q^{35} - 36q^{38} - 4q^{43} + 20q^{44} + 364q^{49} - 8q^{55} + 24q^{58} - 36q^{61} - 44q^{62} + 32q^{64} + 40q^{68} + 40q^{74} + 12q^{76} + 32q^{77} - 40q^{80} - 12q^{82} + 44q^{83} + 8q^{85} + 32q^{92} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

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