↑

Properties

Label 2736.2.y
Level $2736$
Weight $2$
Character orbit 2736.y
Rep. character $\chi_{2736}(1331,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 976 288 688
Cusp forms 944 288 656
Eisenstein series 32 0 32

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 16 q^{16} + 80 q^{22} + 48 q^{28} - 64 q^{34} - 144 q^{40} + 64 q^{43} + 288 q^{49} + 16 q^{52} + 128 q^{55} - 48 q^{58} + 32 q^{67} - 80 q^{82} - 16 q^{88} - 96 q^{91} - 48 q^{94} + O(q^{100}) \)

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

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