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Properties

Label 1208.2.b
Level $1208$
Weight $2$
Character orbit 1208.b
Rep. character $\chi_{1208}(605,\cdot)$
Character field $\Q$
Dimension $150$
Sturm bound $304$

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Defining parameters

Level: \( N \) \(=\) \( 1208 = 2^{3} \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1208.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(304\)

Dimensions

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

Total New Old
Modular forms 154 150 4
Cusp forms 150 150 0
Eisenstein series 4 0 4

Trace form

\( 150 q + 6 q^{8} - 150 q^{9} + O(q^{10}) \) \( 150 q + 6 q^{8} - 150 q^{9} - 2 q^{10} - 2 q^{12} - 8 q^{14} - 16 q^{16} - 4 q^{17} + 10 q^{18} + 2 q^{20} + 8 q^{22} + 26 q^{24} - 146 q^{25} - 2 q^{26} + 4 q^{28} - 8 q^{30} + 12 q^{31} + 10 q^{32} + 8 q^{33} + 2 q^{34} - 16 q^{36} + q^{38} - 16 q^{39} + 5 q^{40} - 4 q^{41} + 8 q^{42} + 11 q^{44} + 6 q^{46} - 4 q^{47} - 12 q^{48} + 150 q^{49} + 25 q^{50} - 6 q^{52} - 2 q^{54} + 16 q^{55} - 32 q^{56} - 8 q^{57} - 33 q^{58} - 24 q^{60} - 32 q^{62} - 40 q^{63} - 18 q^{64} + 16 q^{65} - 6 q^{66} - 33 q^{68} + 42 q^{70} + 32 q^{71} + 6 q^{72} - 20 q^{73} - 6 q^{74} + 28 q^{76} - 12 q^{78} + 11 q^{80} + 142 q^{81} - 12 q^{82} + 74 q^{84} - 10 q^{86} - 2 q^{88} - 4 q^{89} + 20 q^{90} - 48 q^{92} + 15 q^{94} + 56 q^{95} + 62 q^{96} - 4 q^{97} - 16 q^{98} + O(q^{100}) \)

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.