↑

Properties

Label 2268.2.bq
Level $2268$
Weight $2$
Character orbit 2268.bq
Rep. character $\chi_{2268}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $144$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.bq (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

Total New Old
Modular forms 2700 144 2556
Cusp forms 2484 144 2340
Eisenstein series 216 0 216

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 6 q^{11} - 48 q^{17} + 21 q^{23} - 6 q^{29} + 9 q^{35} + 12 q^{41} - 18 q^{47} - 18 q^{49} - 15 q^{53} + 15 q^{59} - 36 q^{61} - 36 q^{65} + 12 q^{71} + 18 q^{73} + 3 q^{77} + 18 q^{79} - 36 q^{85} - 144 q^{89} + 9 q^{91} + 30 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)