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Properties

Label 1638.2.fh
Level $1638$
Weight $2$
Character orbit 1638.fh
Rep. character $\chi_{1638}(73,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
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.fh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 192 1216
Cusp forms 1280 192 1088
Eisenstein series 128 0 128

Trace form

\( 192 q + 8 q^{7} + O(q^{10}) \) \( 192 q + 8 q^{7} - 4 q^{11} - 4 q^{14} + 96 q^{16} + 12 q^{19} - 8 q^{22} - 4 q^{28} + 8 q^{29} - 12 q^{31} + 72 q^{35} - 8 q^{37} - 4 q^{44} + 4 q^{46} + 36 q^{47} - 16 q^{50} + 12 q^{52} - 12 q^{53} - 24 q^{58} + 12 q^{61} - 36 q^{65} + 8 q^{67} + 12 q^{68} - 56 q^{70} - 56 q^{71} + 84 q^{73} + 40 q^{74} + 24 q^{79} - 32 q^{85} + 36 q^{86} - 12 q^{89} - 8 q^{91} + 48 q^{92} + 36 q^{94} + 8 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)