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Properties

Label 1208.2.m
Level $1208$
Weight $2$
Character orbit 1208.m
Rep. character $\chi_{1208}(723,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $300$
Sturm bound $304$

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Defining parameters

Level: \( N \) \(=\) \( 1208 = 2^{3} \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1208.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1208 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(304\)

Dimensions

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

Total New Old
Modular forms 308 308 0
Cusp forms 300 300 0
Eisenstein series 8 8 0

Trace form

\( 300 q - 3 q^{6} - 12 q^{8} - 300 q^{9} + O(q^{10}) \) \( 300 q - 3 q^{6} - 12 q^{8} - 300 q^{9} - 7 q^{10} + 6 q^{11} + 6 q^{12} - 8 q^{16} - 2 q^{17} - 13 q^{18} - 24 q^{19} - 16 q^{20} + 20 q^{22} + 140 q^{25} + 6 q^{30} + 15 q^{32} + 12 q^{33} - 17 q^{34} - 6 q^{35} - 19 q^{36} - 14 q^{38} - 30 q^{40} + 24 q^{42} + 6 q^{43} + 6 q^{44} - 48 q^{46} + 57 q^{48} - 132 q^{49} + 8 q^{50} + 12 q^{51} - 3 q^{52} + 18 q^{54} - 9 q^{56} - 2 q^{58} - 56 q^{59} + 8 q^{62} + 24 q^{64} - 60 q^{66} - 66 q^{68} + 38 q^{72} - 18 q^{74} + 96 q^{75} - 28 q^{76} + 92 q^{78} + 16 q^{80} + 284 q^{81} - 42 q^{82} - 122 q^{84} + 72 q^{86} - 46 q^{88} - 6 q^{89} - 9 q^{90} - 28 q^{91} + 26 q^{94} + 66 q^{96} + 30 q^{97} - 4 q^{98} - 54 q^{99} + O(q^{100}) \)

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.