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Properties

Label 1638.2.fb
Level $1638$
Weight $2$
Character orbit 1638.fb
Rep. character $\chi_{1638}(431,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
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.fb (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 144 1264
Cusp forms 1280 144 1136
Eisenstein series 128 0 128

Trace form

\( 144 q - 8 q^{7} + O(q^{10}) \) \( 144 q - 8 q^{7} + 72 q^{16} + 8 q^{19} + 40 q^{31} + 40 q^{37} - 120 q^{43} + 32 q^{46} + 56 q^{49} + 8 q^{52} - 32 q^{55} + 32 q^{58} - 128 q^{61} + 160 q^{67} - 16 q^{73} + 32 q^{76} + 32 q^{79} + 112 q^{85} - 16 q^{91} + 32 q^{94} + 168 q^{97} + O(q^{100}) \)

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

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