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Properties

Label 1638.2.ez
Level $1638$
Weight $2$
Character orbit 1638.ez
Rep. character $\chi_{1638}(359,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.ez (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 1408 160 1248
Cusp forms 1280 160 1120
Eisenstein series 128 0 128

Trace form

\( 160 q + O(q^{10}) \) \( 160 q + 80 q^{16} + 16 q^{19} + 32 q^{31} + 32 q^{37} - 16 q^{46} + 64 q^{55} - 16 q^{58} + 64 q^{61} - 48 q^{67} - 32 q^{73} - 32 q^{76} + 32 q^{79} - 32 q^{85} + 80 q^{91} + 32 q^{94} + 256 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)