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Properties

Label 2646.2.x
Level $2646$
Weight $2$
Character orbit 2646.x
Rep. character $\chi_{2646}(373,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $720$
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.x (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
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 720 2400
Cusp forms 2928 720 2208
Eisenstein series 192 0 192

Trace form

\( 720 q - 6 q^{6} + 24 q^{9} + O(q^{10}) \) \( 720 q - 6 q^{6} + 24 q^{9} + 24 q^{11} + 24 q^{15} - 48 q^{17} + 6 q^{23} + 36 q^{26} - 6 q^{29} - 18 q^{30} + 36 q^{33} - 6 q^{36} - 78 q^{39} + 12 q^{41} + 12 q^{45} - 18 q^{47} - 18 q^{51} + 30 q^{53} - 18 q^{54} + 30 q^{57} - 30 q^{59} + 36 q^{60} + 36 q^{61} + 48 q^{62} - 360 q^{64} + 132 q^{65} + 72 q^{66} + 36 q^{68} + 60 q^{69} - 48 q^{71} + 24 q^{72} + 36 q^{73} - 18 q^{74} + 6 q^{75} - 72 q^{78} + 72 q^{79} + 12 q^{80} + 48 q^{81} - 144 q^{85} + 48 q^{86} + 66 q^{87} - 144 q^{89} - 66 q^{92} + 12 q^{93} + 36 q^{94} - 210 q^{95} - 60 q^{99} + O(q^{100}) \)

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

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