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Properties

Label 3600.3.bn
Level $3600$
Weight $3$
Character orbit 3600.bn
Rep. character $\chi_{3600}(1349,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.bn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).

Total New Old
Modular forms 2928 576 2352
Cusp forms 2832 576 2256
Eisenstein series 96 0 96

Trace form

\( 576 q + O(q^{10}) \) \( 576 q - 112 q^{16} + 128 q^{19} + 144 q^{34} - 112 q^{46} + 4032 q^{49} - 128 q^{61} - 96 q^{64} - 32 q^{76} - 1024 q^{79} + 64 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)