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Properties

Label 1287.2.cr
Level $1287$
Weight $2$
Character orbit 1287.cr
Rep. character $\chi_{1287}(289,\cdot)$
Character field $\Q(\zeta_{15})$
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.cr (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 544 q + 3 q^{2} + 63 q^{4} + 12 q^{5} - 3 q^{7} + 20 q^{8} + O(q^{10}) \) \( 544 q + 3 q^{2} + 63 q^{4} + 12 q^{5} - 3 q^{7} + 20 q^{8} + 20 q^{10} + 6 q^{11} - 11 q^{13} + 32 q^{14} + 55 q^{16} + 19 q^{17} + 9 q^{19} + 17 q^{20} + 23 q^{22} + 2 q^{23} - 144 q^{25} - 14 q^{26} - 27 q^{28} + 26 q^{29} + 8 q^{31} + 28 q^{32} - 132 q^{34} + 34 q^{35} - 15 q^{37} - 2 q^{38} + 41 q^{41} + 56 q^{43} + 12 q^{44} + 45 q^{46} - 46 q^{47} + 39 q^{49} + 24 q^{50} - 55 q^{52} + 58 q^{53} + 31 q^{55} - 46 q^{56} + 3 q^{58} + 2 q^{59} - 39 q^{61} + 23 q^{62} - 116 q^{64} - 14 q^{65} - 84 q^{67} + 114 q^{68} - 50 q^{70} + 27 q^{71} + 30 q^{73} + 81 q^{74} + 78 q^{76} - 20 q^{77} - 52 q^{79} - 51 q^{80} - q^{82} - 78 q^{83} + 3 q^{85} - 40 q^{86} + 71 q^{88} + 6 q^{89} - 43 q^{91} - 22 q^{92} - 51 q^{94} + 23 q^{95} - 2 q^{97} - 14 q^{98} + O(q^{100}) \)

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

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