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Properties

Label 1288.2.z
Level $1288$
Weight $2$
Character orbit 1288.z
Rep. character $\chi_{1288}(507,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $352$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1288.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 392 352 40
Cusp forms 376 352 24
Eisenstein series 16 0 16

Trace form

\( 352 q + 12 q^{8} + 176 q^{9} + O(q^{10}) \) \( 352 q + 12 q^{8} + 176 q^{9} - 18 q^{10} + 30 q^{12} - 20 q^{14} + 8 q^{16} - 10 q^{18} - 24 q^{22} - 36 q^{24} - 176 q^{25} + 18 q^{28} + 20 q^{30} + 10 q^{32} - 24 q^{35} - 40 q^{36} - 18 q^{38} + 22 q^{42} - 14 q^{44} + 16 q^{49} + 52 q^{50} - 40 q^{51} - 36 q^{52} + 114 q^{54} + 72 q^{56} + 32 q^{57} - 10 q^{58} - 96 q^{59} + 24 q^{60} + 108 q^{64} - 72 q^{66} - 24 q^{67} + 36 q^{68} - 42 q^{70} - 12 q^{72} - 48 q^{73} - 50 q^{74} - 100 q^{78} - 132 q^{80} - 176 q^{81} - 36 q^{84} - 50 q^{86} - 46 q^{88} + 80 q^{91} - 36 q^{94} - 84 q^{96} - 42 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)