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Properties

Label 1287.2.dw
Level $1287$
Weight $2$
Character orbit 1287.dw
Rep. character $\chi_{1287}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1312$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1287.dw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1287 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1287, [\chi])\).

Total New Old
Modular forms 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312 q - 3 q^{3} + 314 q^{4} - 9 q^{6} - 9 q^{7} + 3 q^{9} + O(q^{10}) \) \( 1312 q - 3 q^{3} + 314 q^{4} - 9 q^{6} - 9 q^{7} + 3 q^{9} - 12 q^{10} - 30 q^{12} - 3 q^{13} - 14 q^{14} - 27 q^{15} - 318 q^{16} - 22 q^{17} - 36 q^{18} - 18 q^{19} + 39 q^{20} + 30 q^{21} - 24 q^{22} + 8 q^{23} - 9 q^{24} - 154 q^{25} + 12 q^{26} - 24 q^{27} - 30 q^{28} - 52 q^{29} + 23 q^{30} - 24 q^{33} - 12 q^{34} + 51 q^{35} + 75 q^{36} - 18 q^{37} + 6 q^{38} + 14 q^{39} - 22 q^{40} - 9 q^{41} - 19 q^{42} + 8 q^{43} + 6 q^{45} - 18 q^{46} - 29 q^{48} - 137 q^{49} + 12 q^{50} - 8 q^{51} + 25 q^{52} - 8 q^{53} - 3 q^{55} - 50 q^{56} + 18 q^{57} - 18 q^{60} + 3 q^{61} - 34 q^{62} - 51 q^{63} + 276 q^{64} + 20 q^{65} - 105 q^{66} - 24 q^{67} + 40 q^{68} + 63 q^{69} - 75 q^{70} + 102 q^{71} - 219 q^{72} + 51 q^{74} - 61 q^{75} - 48 q^{76} - 42 q^{77} - 76 q^{78} - 18 q^{79} + 144 q^{80} - 77 q^{81} - 14 q^{82} + 27 q^{83} - 9 q^{84} + 60 q^{86} + 6 q^{87} + 100 q^{88} - 18 q^{89} - 24 q^{90} - 8 q^{91} - 16 q^{92} - 12 q^{93} - 29 q^{94} + 38 q^{95} + 27 q^{96} - 9 q^{97} - 42 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1287, [\chi])\) into newform subspaces

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