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Properties

Label 3648.2.by
Level $3648$
Weight $2$
Character orbit 3648.by
Rep. character $\chi_{3648}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 2624 320 2304
Cusp forms 2496 320 2176
Eisenstein series 128 0 128

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 16 q^{15} - 8 q^{19} - 96 q^{31} + 48 q^{35} - 320 q^{49} - 8 q^{51} - 32 q^{61} - 48 q^{67} + 64 q^{69} - 48 q^{79} + 160 q^{81} - 80 q^{83} - 16 q^{85} - 48 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)