Properties

Label 3648.2.cj
Level $3648$
Weight $2$
Character orbit 3648.cj
Rep. character $\chi_{3648}(419,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4608$
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.cj (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 5152 4608 544
Cusp forms 5088 4608 480
Eisenstein series 64 0 64

Trace form

\( 4608 q + O(q^{10}) \) \( 4608 q + 80 q^{24} + 160 q^{30} + 160 q^{36} + 80 q^{42} - 96 q^{52} + 128 q^{55} - 288 q^{58} + 256 q^{67} - 48 q^{78} - 160 q^{82} - 224 q^{84} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)