Properties

Label 3648.2.ep
Level $3648$
Weight $2$
Character orbit 3648.ep
Rep. character $\chi_{3648}(67,\cdot)$
Character field $\Q(\zeta_{144})$
Dimension $15360$
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.ep (of order \(144\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{144})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 30912 15360 15552
Cusp forms 30528 15360 15168
Eisenstein series 384 0 384

Trace form

\( 15360 q + O(q^{10}) \) \( 15360 q + 480 q^{34} + 240 q^{38} - 240 q^{40} - 432 q^{50} + 96 q^{51} + 48 q^{54} + 288 q^{68} - 288 q^{70} + O(q^{100}) \)

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

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