↑

Properties

Label 1140.2.bp
Level $1140$
Weight $2$
Character orbit 1140.bp
Rep. character $\chi_{1140}(197,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 160 848
Cusp forms 912 160 752
Eisenstein series 96 0 96

Trace form

\( 160 q + O(q^{10}) \) \( 160 q + 8 q^{13} - 6 q^{15} + 8 q^{25} - 12 q^{27} - 16 q^{31} + 12 q^{33} - 16 q^{37} + 20 q^{43} + 76 q^{45} - 32 q^{51} + 16 q^{55} - 14 q^{57} - 8 q^{61} + 28 q^{63} + 24 q^{67} + 16 q^{73} + 12 q^{75} + 24 q^{81} + 8 q^{85} + 56 q^{87} + 56 q^{91} + 28 q^{93} + 8 q^{97} + O(q^{100}) \)

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

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