↑

Properties

Label 2700.2.bk
Level $2700$
Weight $2$
Character orbit 2700.bk
Rep. character $\chi_{2700}(299,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1920$
Sturm bound $1080$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.bk (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 540 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 3312 1968 1344
Cusp forms 3168 1920 1248
Eisenstein series 144 48 96

Trace form

\( 1920 q + 12 q^{4} - 12 q^{6} + 24 q^{9} + O(q^{10}) \) \( 1920 q + 12 q^{4} - 12 q^{6} + 24 q^{9} + 12 q^{14} - 12 q^{16} - 24 q^{21} - 6 q^{24} + 24 q^{34} - 12 q^{36} - 24 q^{41} + 162 q^{44} - 6 q^{46} + 24 q^{49} + 180 q^{54} - 138 q^{56} - 24 q^{61} + 6 q^{64} - 18 q^{66} + 24 q^{69} + 42 q^{74} - 36 q^{76} + 24 q^{81} + 90 q^{84} + 156 q^{86} + 36 q^{89} + 12 q^{94} + 96 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)