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Properties

Label 1512.2.dd
Level $1512$
Weight $2$
Character orbit 1512.dd
Rep. character $\chi_{1512}(193,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $432$
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.dd (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1776 432 1344
Cusp forms 1680 432 1248
Eisenstein series 96 0 96

Trace form

\( 432 q + O(q^{10}) \) \( 432 q + 12 q^{15} + 24 q^{17} + 12 q^{21} - 24 q^{23} + 18 q^{29} - 36 q^{39} + 12 q^{41} + 18 q^{45} - 18 q^{47} - 36 q^{49} - 18 q^{61} + 18 q^{63} + 72 q^{65} + 48 q^{69} - 72 q^{75} - 84 q^{77} + 72 q^{81} + 72 q^{89} + 72 q^{93} + 54 q^{95} - 108 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)