↑

Properties

Label 1140.2.ck
Level $1140$
Weight $2$
Character orbit 1140.ck
Rep. character $\chi_{1140}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.ck (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 1512 240 1272
Cusp forms 1368 240 1128
Eisenstein series 144 0 144

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 3 q^{15} - 24 q^{19} - 24 q^{25} + 24 q^{39} + 9 q^{45} + 72 q^{49} + 36 q^{51} - 12 q^{55} + 36 q^{61} + 48 q^{79} + 96 q^{81} - 30 q^{85} - 60 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)