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Properties

Label 1728.2.bs
Level $1728$
Weight $2$
Character orbit 1728.bs
Rep. character $\chi_{1728}(49,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $840$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1728.bs (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 3552 888 2664
Cusp forms 3360 840 2520
Eisenstein series 192 48 144

Trace form

\( 840 q + 12 q^{3} - 12 q^{5} + O(q^{10}) \) \( 840 q + 12 q^{3} - 12 q^{5} + 12 q^{11} - 12 q^{13} + 24 q^{15} - 12 q^{17} + 6 q^{19} - 12 q^{21} + 12 q^{27} - 12 q^{29} + 24 q^{31} - 24 q^{33} + 6 q^{35} - 6 q^{37} + 12 q^{43} - 12 q^{45} + 24 q^{47} - 24 q^{49} - 6 q^{51} - 24 q^{53} + 48 q^{59} - 12 q^{61} + 24 q^{63} - 24 q^{65} + 12 q^{67} - 12 q^{69} + 96 q^{75} - 12 q^{77} + 24 q^{79} - 24 q^{81} - 48 q^{83} + 18 q^{85} + 6 q^{91} - 12 q^{93} + 24 q^{95} - 24 q^{97} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)