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Properties

Label 2646.2.v
Level $2646$
Weight $2$
Character orbit 2646.v
Rep. character $\chi_{2646}(295,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $738$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

Total New Old
Modular forms 3120 738 2382
Cusp forms 2928 738 2190
Eisenstein series 192 0 192

Trace form

\( 738 q - 6 q^{5} + 6 q^{6} - 3 q^{8} + 12 q^{9} + O(q^{10}) \) \( 738 q - 6 q^{5} + 6 q^{6} - 3 q^{8} + 12 q^{9} + 9 q^{11} - 3 q^{12} + 6 q^{15} + 12 q^{17} + 6 q^{18} + 12 q^{20} - 9 q^{22} - 24 q^{23} - 18 q^{25} - 36 q^{26} + 27 q^{27} + 42 q^{29} - 36 q^{30} - 18 q^{31} - 45 q^{33} - 9 q^{34} + 18 q^{36} - 12 q^{38} + 42 q^{39} - 39 q^{41} - 9 q^{43} - 6 q^{44} + 12 q^{45} - 72 q^{47} - 6 q^{48} + 36 q^{50} + 36 q^{51} + 96 q^{53} + 75 q^{57} + 66 q^{59} + 18 q^{60} + 18 q^{61} + 24 q^{62} - 369 q^{64} + 66 q^{65} + 27 q^{67} + 24 q^{68} + 78 q^{69} - 24 q^{71} - 24 q^{72} + 18 q^{73} + 66 q^{74} + 108 q^{75} + 18 q^{76} - 36 q^{78} - 72 q^{79} - 12 q^{80} + 48 q^{81} - 72 q^{85} - 69 q^{86} - 96 q^{87} + 18 q^{88} + 69 q^{89} + 18 q^{90} - 6 q^{92} - 30 q^{93} - 36 q^{94} + 30 q^{95} + 6 q^{96} + 27 q^{97} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)