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Properties

Label 3648.2.ch
Level $3648$
Weight $2$
Character orbit 3648.ch
Rep. character $\chi_{3648}(229,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2304$
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.ch (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
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 2304 2848
Cusp forms 5088 2304 2784
Eisenstein series 64 0 64

Trace form

\( 2304 q + O(q^{10}) \) \( 2304 q + 32 q^{22} + 32 q^{44} - 96 q^{52} + 128 q^{55} - 224 q^{56} + 256 q^{59} - 96 q^{62} + 64 q^{63} + 64 q^{67} - 96 q^{68} + 256 q^{71} - 224 q^{74} + 128 q^{75} - 96 q^{78} + 160 q^{82} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)