Properties

Label 2736.2.x
Level $2736$
Weight $2$
Character orbit 2736.x
Rep. character $\chi_{2736}(685,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 976 360 616
Cusp forms 944 360 584
Eisenstein series 32 0 32

Trace form

\( 360q - 4q^{4} + O(q^{10}) \) \( 360q - 4q^{4} - 8q^{11} + 12q^{14} + 4q^{16} + 16q^{20} + 12q^{22} + 16q^{26} + 24q^{28} - 16q^{29} + 20q^{32} + 32q^{34} - 16q^{37} + 8q^{40} + 40q^{43} - 12q^{44} + 40q^{47} - 360q^{49} - 80q^{50} - 44q^{52} + 16q^{53} + 28q^{56} + 56q^{59} - 36q^{62} - 64q^{64} - 16q^{65} + 8q^{67} + 64q^{68} + 20q^{70} + 72q^{74} + 16q^{77} - 76q^{82} - 40q^{83} - 60q^{86} + 8q^{88} - 80q^{91} - 80q^{92} + 24q^{94} - 32q^{95} - 80q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)