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Properties

Label 1208.2.x
Level $1208$
Weight $2$
Character orbit 1208.x
Rep. character $\chi_{1208}(461,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $600$
Sturm bound $304$

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Defining parameters

Level: \( N \) \(=\) \( 1208 = 2^{3} \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1208.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1208 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(304\)

Dimensions

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

Total New Old
Modular forms 616 616 0
Cusp forms 600 600 0
Eisenstein series 16 16 0

Trace form

\( 600 q - 10 q^{2} - 10 q^{4} + 15 q^{6} - 10 q^{7} - 16 q^{8} + 140 q^{9} + O(q^{10}) \) \( 600 q - 10 q^{2} - 10 q^{4} + 15 q^{6} - 10 q^{7} - 16 q^{8} + 140 q^{9} + 7 q^{10} + 12 q^{12} - 12 q^{14} - 10 q^{15} + 6 q^{16} - 6 q^{17} - 35 q^{18} - 22 q^{20} + 22 q^{22} + 19 q^{24} + 136 q^{25} + 22 q^{26} + 11 q^{28} - 92 q^{30} - 22 q^{31} - 60 q^{32} - 28 q^{33} + 3 q^{34} - 99 q^{36} - 26 q^{38} + 6 q^{39} + 55 q^{40} - 6 q^{41} - 23 q^{42} + 34 q^{44} - 36 q^{46} - 6 q^{47} - 28 q^{48} - 160 q^{49} - 40 q^{50} + 36 q^{52} + 7 q^{54} - 26 q^{55} - 8 q^{56} + 28 q^{57} - 27 q^{58} + 9 q^{60} - 13 q^{62} + 30 q^{63} + 8 q^{64} - 26 q^{65} - 24 q^{66} + 63 q^{68} + 73 q^{70} - 22 q^{71} - 46 q^{72} + 10 q^{73} + 41 q^{74} + 22 q^{76} + 17 q^{78} + 90 q^{79} + 9 q^{80} - 152 q^{81} - 3 q^{82} + 71 q^{84} - 25 q^{86} + 100 q^{87} + 52 q^{88} - 6 q^{89} + 25 q^{90} - 2 q^{92} + 15 q^{94} - 16 q^{95} + 28 q^{96} - 46 q^{97} + 16 q^{98} + O(q^{100}) \)

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.