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Properties

Label 3825.2.do
Level $3825$
Weight $2$
Character orbit 3825.do
Rep. character $\chi_{3825}(8,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $2880$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 3825 = 3^{2} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3825.do (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1275 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3825, [\chi])\).

Total New Old
Modular forms 8768 2880 5888
Cusp forms 8512 2880 5632
Eisenstein series 256 0 256

Trace form

\( 2880 q - 720 q^{4} + 16 q^{13} - 720 q^{16} + 32 q^{22} + 8 q^{25} - 64 q^{28} - 64 q^{37} + 64 q^{52} + 16 q^{55} - 72 q^{58} + 160 q^{61} - 720 q^{64} + 64 q^{67} - 288 q^{70} - 360 q^{73} + 160 q^{79}+ \cdots + 88 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3825, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)