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Properties

Label 2646.2.bk
Level $2646$
Weight $2$
Character orbit 2646.bk
Rep. character $\chi_{2646}(289,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $672$
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.bk (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 6192 672 5520
Cusp forms 5904 672 5232
Eisenstein series 288 0 288

Trace form

\( 672 q + 56 q^{4} + 8 q^{5} + 2 q^{7} + O(q^{10}) \) \( 672 q + 56 q^{4} + 8 q^{5} + 2 q^{7} - 2 q^{13} + 2 q^{14} + 56 q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} - 30 q^{23} - 112 q^{25} - 16 q^{26} + 2 q^{28} - 16 q^{29} - 2 q^{31} - 14 q^{35} + 26 q^{37} + 24 q^{38} - 6 q^{41} - 2 q^{43} - 78 q^{46} + 78 q^{47} + 14 q^{49} - 8 q^{50} - 10 q^{52} + 156 q^{53} - 30 q^{55} - 4 q^{56} - 30 q^{58} - 22 q^{59} + 188 q^{61} + 44 q^{62} - 112 q^{64} - 14 q^{65} - 14 q^{67} - 84 q^{68} - 14 q^{71} + 28 q^{73} + 12 q^{74} + 4 q^{76} - 34 q^{77} - 8 q^{79} + 24 q^{80} + 212 q^{83} - 8 q^{86} - 106 q^{89} + 16 q^{91} - 6 q^{92} - 12 q^{94} + 26 q^{95} - 2 q^{97} + 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)