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Properties

Label 1728.2.y
Level $1728$
Weight $2$
Character orbit 1728.y
Rep. character $\chi_{1728}(193,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $420$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1728.y (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).

Total New Old
Modular forms 1800 444 1356
Cusp forms 1656 420 1236
Eisenstein series 144 24 120

Trace form

\( 420 q + 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 420 q + 12 q^{5} - 12 q^{9} + 12 q^{13} - 6 q^{17} + 12 q^{21} - 12 q^{25} + 12 q^{29} - 36 q^{33} + 6 q^{37} - 36 q^{41} + 12 q^{45} - 12 q^{49} + 24 q^{53} + 6 q^{57} + 12 q^{61} - 12 q^{65} + 12 q^{69} - 6 q^{73} + 12 q^{77} - 12 q^{81} - 18 q^{85} - 6 q^{89} - 132 q^{93} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)