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Properties

Label 1287.2.dl
Level $1287$
Weight $2$
Character orbit 1287.dl
Rep. character $\chi_{1287}(82,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $544$
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.dl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
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 1408 576 832
Cusp forms 1280 544 736
Eisenstein series 128 32 96

Trace form

\( 544 q + 9 q^{2} - 69 q^{4} - 9 q^{7} + O(q^{10}) \) \( 544 q + 9 q^{2} - 69 q^{4} - 9 q^{7} - 4 q^{10} - 6 q^{11} - 11 q^{13} - 8 q^{14} + 39 q^{16} + 7 q^{17} + 3 q^{19} + 45 q^{20} - 17 q^{22} - 2 q^{23} + 96 q^{25} + 54 q^{26} + 39 q^{28} - 16 q^{29} + 48 q^{32} + 10 q^{35} - 9 q^{37} - 46 q^{38} - 72 q^{40} - 9 q^{41} - 8 q^{43} + 27 q^{46} - 45 q^{49} - 78 q^{50} + 57 q^{52} + 2 q^{53} - 25 q^{55} + 134 q^{56} + 93 q^{58} - 18 q^{59} - 15 q^{61} + 19 q^{62} - 68 q^{64} - 18 q^{65} + 48 q^{67} - 40 q^{68} + 105 q^{71} - 35 q^{74} - 258 q^{76} + 108 q^{77} - 132 q^{79} - 21 q^{80} + 39 q^{82} + 45 q^{85} - 77 q^{88} + 162 q^{89} - 37 q^{91} - 74 q^{92} - 11 q^{94} - 37 q^{95} + 72 q^{97} - 90 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)