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Properties

Label 1208.2.bl
Level $1208$
Weight $2$
Character orbit 1208.bl
Rep. character $\chi_{1208}(29,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $3000$
Sturm bound $304$

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Defining parameters

Level: \( N \) \(=\) \( 1208 = 2^{3} \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1208.bl (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1208 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(304\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1208, [\chi])\).

Total New Old
Modular forms 3080 3080 0
Cusp forms 3000 3000 0
Eisenstein series 80 80 0

Trace form

\( 3000 q - 15 q^{2} - 15 q^{4} - 40 q^{6} - 40 q^{7} - 15 q^{8} - 40 q^{9} + O(q^{10}) \) \( 3000 q - 15 q^{2} - 15 q^{4} - 40 q^{6} - 40 q^{7} - 15 q^{8} - 40 q^{9} - 30 q^{10} - 35 q^{12} - 5 q^{14} - 40 q^{15} - 15 q^{16} - 40 q^{17} - 180 q^{20} - 55 q^{22} - 50 q^{23} + 105 q^{24} - 40 q^{25} - 45 q^{26} - 40 q^{28} + 75 q^{30} - 40 q^{31} - 80 q^{33} - 30 q^{34} + 90 q^{36} - 40 q^{39} - 85 q^{40} - 40 q^{41} - 260 q^{42} - 70 q^{44} + 5 q^{46} - 40 q^{47} - 235 q^{48} - 40 q^{49} - 10 q^{50} - 55 q^{52} - 30 q^{54} - 40 q^{55} + 15 q^{56} - 70 q^{57} - 165 q^{58} + 40 q^{60} + 20 q^{62} - 40 q^{63} - 15 q^{64} - 40 q^{65} - 45 q^{66} - 55 q^{68} + 60 q^{70} - 60 q^{71} + 15 q^{72} - 40 q^{73} - 60 q^{74} - 25 q^{76} - 30 q^{78} + 360 q^{79} - 45 q^{80} - 40 q^{81} - 10 q^{82} - 170 q^{84} - 190 q^{86} - 150 q^{87} + 125 q^{88} - 40 q^{89} - 70 q^{90} + 25 q^{92} - 55 q^{94} - 90 q^{95} + 35 q^{96} - 200 q^{97} - 25 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1208, [\chi])\) into newform subspaces

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