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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

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

Display 100 coefficients 10 coefficients

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

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