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Properties

Label 2646.2.bx
Level $2646$
Weight $2$
Character orbit 2646.bx
Rep. character $\chi_{2646}(269,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $888$
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.bx (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 6192 888 5304
Cusp forms 5904 888 5016
Eisenstein series 288 0 288

Trace form

\( 888 q - 74 q^{4} - 10 q^{7} + O(q^{10}) \) \( 888 q - 74 q^{4} - 10 q^{7} + 6 q^{10} + 74 q^{16} - 12 q^{19} + 10 q^{22} + 72 q^{25} - 8 q^{28} - 24 q^{31} + 94 q^{37} - 22 q^{40} - 36 q^{43} - 54 q^{49} - 24 q^{52} + 560 q^{55} + 76 q^{58} - 68 q^{61} + 148 q^{64} + 22 q^{67} + 44 q^{70} + 120 q^{73} + 2 q^{79} + 24 q^{82} + 128 q^{85} - 2 q^{88} + 176 q^{91} + 104 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)