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Properties

Label 1287.2.dj
Level $1287$
Weight $2$
Character orbit 1287.dj
Rep. character $\chi_{1287}(194,\cdot)$
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.dj (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

\( 1312 q - 12 q^{3} - 166 q^{4} - 36 q^{9} + O(q^{10}) \) \( 1312 q - 12 q^{3} - 166 q^{4} - 36 q^{9} - 36 q^{12} - 5 q^{13} - 18 q^{14} + 138 q^{16} - 48 q^{23} + 142 q^{25} + 12 q^{27} - 120 q^{29} - 20 q^{30} + 80 q^{36} + 144 q^{38} + 55 q^{39} + 30 q^{40} - 70 q^{42} - 50 q^{48} + 134 q^{49} + 60 q^{51} - 5 q^{52} - 52 q^{55} - 108 q^{56} - 10 q^{61} + 192 q^{64} + 74 q^{66} - 420 q^{68} + 30 q^{69} - 30 q^{74} - 100 q^{75} - 72 q^{77} - 104 q^{78} - 10 q^{79} - 100 q^{81} - 8 q^{82} + 4 q^{88} + 380 q^{90} - 76 q^{91} + 36 q^{92} - 10 q^{94} - 30 q^{95} + O(q^{100}) \)

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.