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Properties

Label 1288.2.bo
Level $1288$
Weight $2$
Character orbit 1288.bo
Rep. character $\chi_{1288}(27,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1880$
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.bo (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1960 1960 0
Cusp forms 1880 1880 0
Eisenstein series 80 80 0

Trace form

\( 1880 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 144 q^{9} + O(q^{10}) \) \( 1880 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 144 q^{9} - 44 q^{11} - 13 q^{14} - 8 q^{16} - 32 q^{18} - 44 q^{22} - 208 q^{25} - 23 q^{28} - 50 q^{30} - 36 q^{32} + 2 q^{35} + 71 q^{36} + 103 q^{42} - 44 q^{43} + 59 q^{44} + 8 q^{46} - 18 q^{49} - 89 q^{50} - 60 q^{51} - 30 q^{56} - 60 q^{57} - 105 q^{58} + 14 q^{60} - 4 q^{64} + 4 q^{65} + 4 q^{67} - 46 q^{70} + 86 q^{72} - 31 q^{74} - 222 q^{78} - 184 q^{81} + 31 q^{84} - 54 q^{86} + 91 q^{88} - 12 q^{91} - 238 q^{92} - 17 q^{98} + 52 q^{99} + O(q^{100}) \)

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.