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Properties

Label 1287.2.q
Level $1287$
Weight $2$
Character orbit 1287.q
Rep. character $\chi_{1287}(235,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 704 240 464
Cusp forms 640 240 400
Eisenstein series 64 0 64

Trace form

\( 240 q - 2 q^{2} - 64 q^{4} - 2 q^{5} + 10 q^{7} + 14 q^{8} + O(q^{10}) \) \( 240 q - 2 q^{2} - 64 q^{4} - 2 q^{5} + 10 q^{7} + 14 q^{8} + 16 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 64 q^{16} + 24 q^{17} + 10 q^{19} - 8 q^{20} + 4 q^{22} - 20 q^{23} - 70 q^{25} - 54 q^{28} - 10 q^{29} - 30 q^{31} - 64 q^{32} - 44 q^{34} + 20 q^{35} + 30 q^{37} - 18 q^{38} + 30 q^{40} + 26 q^{41} + 62 q^{44} + 46 q^{46} - 16 q^{47} - 22 q^{49} + 84 q^{50} - 18 q^{52} + 28 q^{53} - 2 q^{55} - 32 q^{56} + 22 q^{58} - 24 q^{59} - 18 q^{61} - 16 q^{62} - 168 q^{64} - 32 q^{65} + 36 q^{67} - 2 q^{68} - 128 q^{70} + 6 q^{71} - 100 q^{73} - 120 q^{74} + 92 q^{76} - 32 q^{77} + 22 q^{79} + 158 q^{80} + 66 q^{82} - 10 q^{83} - 82 q^{85} - 58 q^{86} + 78 q^{88} - 56 q^{89} + 8 q^{91} + 30 q^{92} - 8 q^{94} - 2 q^{95} + 116 q^{97} + 100 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)