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Properties

Label 2160.2.ek
Level $2160$
Weight $2$
Character orbit 2160.ek
Rep. character $\chi_{2160}(113,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1272$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.ek (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

Total New Old
Modular forms 5328 1320 4008
Cusp forms 5040 1272 3768
Eisenstein series 288 48 240

Trace form

\( 1272 q + 12 q^{3} - 12 q^{5} + 12 q^{7} + O(q^{10}) \) \( 1272 q + 12 q^{3} - 12 q^{5} + 12 q^{7} + 24 q^{11} - 12 q^{13} + 12 q^{15} - 18 q^{17} - 24 q^{21} + 12 q^{23} - 12 q^{25} - 24 q^{27} + 24 q^{31} - 12 q^{33} + 18 q^{35} - 6 q^{37} - 24 q^{41} + 12 q^{43} - 12 q^{45} - 24 q^{47} + 24 q^{51} + 24 q^{55} - 30 q^{57} - 24 q^{61} + 12 q^{63} + 36 q^{65} + 12 q^{67} + 36 q^{71} - 6 q^{73} + 96 q^{75} - 12 q^{77} - 24 q^{81} + 12 q^{83} - 12 q^{85} + 12 q^{87} + 12 q^{91} - 12 q^{93} + 42 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)