↑

Properties

Label 1288.2.n
Level $1288$
Weight $2$
Character orbit 1288.n
Rep. character $\chi_{1288}(827,\cdot)$
Character field $\Q$
Dimension $144$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1288.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1288, [\chi])\).

Total New Old
Modular forms 196 144 52
Cusp forms 188 144 44
Eisenstein series 8 0 8

Trace form

\( 144 q - 2 q^{2} + 10 q^{4} - 14 q^{6} + 4 q^{8} + 144 q^{9} + O(q^{10}) \) \( 144 q - 2 q^{2} + 10 q^{4} - 14 q^{6} + 4 q^{8} + 144 q^{9} - 6 q^{12} + 18 q^{16} - 4 q^{18} - 8 q^{24} + 144 q^{25} + 26 q^{26} - 24 q^{27} - 22 q^{32} + 48 q^{36} - 30 q^{46} - 26 q^{48} + 144 q^{49} - 86 q^{50} + 14 q^{52} + 2 q^{54} - 22 q^{58} + 24 q^{59} - 50 q^{62} + 40 q^{64} + 32 q^{72} + 82 q^{78} + 144 q^{81} - 82 q^{82} - 50 q^{92} + 90 q^{94} - 182 q^{96} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)