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Properties

Label 1287.2.dp
Level $1287$
Weight $2$
Character orbit 1287.dp
Rep. character $\chi_{1287}(248,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1152$
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.dp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 1152 224
Cusp forms 1312 1152 160
Eisenstein series 64 0 64

Trace form

\( 1152 q - 6 q^{3} + 144 q^{4} - 6 q^{5} + 10 q^{6} + 14 q^{9} + O(q^{10}) \) \( 1152 q - 6 q^{3} + 144 q^{4} - 6 q^{5} + 10 q^{6} + 14 q^{9} - 6 q^{11} + 56 q^{12} - 12 q^{15} + 144 q^{16} - 20 q^{18} + 60 q^{19} + 24 q^{20} + 6 q^{22} + 36 q^{23} - 30 q^{24} - 150 q^{25} + 6 q^{27} + 6 q^{31} + 8 q^{33} + 12 q^{34} - 38 q^{36} - 12 q^{37} + 18 q^{38} + 12 q^{42} + 40 q^{45} + 24 q^{47} - 110 q^{48} - 144 q^{49} - 10 q^{51} + 24 q^{55} - 168 q^{56} - 140 q^{57} + 36 q^{58} - 180 q^{59} - 36 q^{60} + 30 q^{63} - 288 q^{64} + 120 q^{66} - 36 q^{67} - 74 q^{69} + 24 q^{70} - 150 q^{72} - 48 q^{75} - 186 q^{77} - 40 q^{78} + 94 q^{81} - 36 q^{82} + 126 q^{86} + 66 q^{88} + 80 q^{90} + 414 q^{92} + 12 q^{93} + 240 q^{95} + 140 q^{96} - 60 q^{97} + 58 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)