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Properties

Label 1288.2.i
Level $1288$
Weight $2$
Character orbit 1288.i
Rep. character $\chi_{1288}(139,\cdot)$
Character field $\Q$
Dimension $176$
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.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 196 176 20
Cusp forms 188 176 12
Eisenstein series 8 0 8

Trace form

\( 176 q - 12 q^{8} - 176 q^{9} + O(q^{10}) \) \( 176 q - 12 q^{8} - 176 q^{9} - 4 q^{14} + 16 q^{16} - 20 q^{18} + 24 q^{22} + 176 q^{25} - 18 q^{28} - 20 q^{30} - 40 q^{32} + 24 q^{35} - 20 q^{36} + 44 q^{42} - 28 q^{44} - 16 q^{49} + 8 q^{50} - 80 q^{51} - 6 q^{56} - 32 q^{57} + 52 q^{58} + 60 q^{60} - 36 q^{64} - 48 q^{67} - 24 q^{70} + 36 q^{72} - 100 q^{74} + 28 q^{78} + 176 q^{81} - 138 q^{84} - 40 q^{86} - 20 q^{88} - 80 q^{91} + 60 q^{98} + O(q^{100}) \)

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

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