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Properties

Label 2646.2.cd
Level $2646$
Weight $2$
Character orbit 2646.cd
Rep. character $\chi_{2646}(5,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $6048$
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.cd (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{126})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 18288 6048 12240
Cusp forms 18000 6048 11952
Eisenstein series 288 0 288

Trace form

\( 6048 q + 24 q^{6} + O(q^{10}) \) \( 6048 q + 24 q^{6} - 6 q^{14} - 6 q^{21} + 144 q^{23} - 78 q^{29} + 18 q^{30} + 54 q^{35} - 48 q^{36} + 30 q^{39} + 144 q^{42} - 72 q^{47} - 18 q^{49} - 24 q^{50} - 18 q^{51} + 540 q^{53} + 54 q^{54} + 12 q^{56} + 234 q^{57} + 90 q^{59} + 36 q^{60} + 24 q^{63} - 504 q^{64} + 84 q^{65} - 48 q^{69} + 18 q^{70} - 18 q^{74} + 216 q^{75} + 78 q^{77} + 6 q^{84} - 90 q^{87} + 18 q^{91} + 18 q^{92} + 288 q^{93} + 18 q^{95} - 216 q^{98} - 252 q^{99} + O(q^{100}) \)

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

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