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Properties

Label 3648.2.cs
Level $3648$
Weight $2$
Character orbit 3648.cs
Rep. character $\chi_{3648}(257,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $936$
Sturm bound $1280$

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Defining parameters

Level: \( N \) \(=\) \( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3648.cs (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

Total New Old
Modular forms 3984 984 3000
Cusp forms 3696 936 2760
Eisenstein series 288 48 240

Trace form

\( 936 q - 12 q^{9} + O(q^{10}) \) \( 936 q - 12 q^{9} - 6 q^{21} - 24 q^{25} - 30 q^{33} + 6 q^{45} - 408 q^{49} - 12 q^{57} + 72 q^{61} + 18 q^{69} - 24 q^{73} - 36 q^{81} - 72 q^{85} + 30 q^{93} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)