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Properties

Label 1512.2.dx
Level $1512$
Weight $2$
Character orbit 1512.dx
Rep. character $\chi_{1512}(85,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1296$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.dx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 1752 1296 456
Cusp forms 1704 1296 408
Eisenstein series 48 0 48

Trace form

\( 1296 q + O(q^{10}) \) \( 1296 q - 18 q^{12} + 42 q^{18} - 42 q^{20} + 36 q^{26} + 48 q^{30} + 30 q^{32} - 24 q^{33} + 24 q^{41} + 30 q^{42} - 48 q^{44} + 18 q^{48} + 156 q^{50} + 54 q^{52} - 54 q^{58} - 186 q^{60} + 6 q^{66} - 78 q^{68} + 168 q^{71} - 42 q^{72} - 180 q^{80} - 30 q^{86} + 72 q^{87} + 30 q^{90} - 114 q^{92} + 54 q^{94} - 156 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)