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Properties

Label 1638.2.ea
Level $1638$
Weight $2$
Character orbit 1638.ea
Rep. character $\chi_{1638}(677,\cdot)$
Character field $\Q(\zeta_{6})$
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.ea (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 192 496
Cusp forms 656 192 464
Eisenstein series 32 0 32

Trace form

\( 192 q + 96 q^{4} + 4 q^{9} + O(q^{10}) \) \( 192 q + 96 q^{4} + 4 q^{9} + 12 q^{14} + 12 q^{15} - 96 q^{16} - 36 q^{17} + 28 q^{21} + 12 q^{24} + 192 q^{25} + 54 q^{27} - 12 q^{29} + 14 q^{30} + 8 q^{36} - 12 q^{41} - 22 q^{42} - 24 q^{45} - 12 q^{46} - 24 q^{49} + 48 q^{50} - 2 q^{51} - 48 q^{53} - 4 q^{57} + 24 q^{58} - 60 q^{59} - 12 q^{60} + 36 q^{61} + 36 q^{62} - 40 q^{63} - 192 q^{64} - 48 q^{66} - 72 q^{68} + 12 q^{77} + 12 q^{79} - 52 q^{81} + 44 q^{84} + 96 q^{87} + 12 q^{89} + 54 q^{90} - 36 q^{92} - 80 q^{93} + 132 q^{95} + 12 q^{96} - 60 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)