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Properties

Label 3648.2.v
Level $3648$
Weight $2$
Character orbit 3648.v
Rep. character $\chi_{3648}(1103,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 1312 288 1024
Cusp forms 1248 288 960
Eisenstein series 64 0 64

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 24 q^{27} + 48 q^{39} + 32 q^{43} + 288 q^{49} + 40 q^{51} + 64 q^{55} + 64 q^{67} - 48 q^{91} - 48 q^{93} - 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)