↑

Properties

Label 3600.3.cc
Level $3600$
Weight $3$
Character orbit 3600.cc
Rep. character $\chi_{3600}(751,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $456$
Sturm bound $2160$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 2952 456 2496
Cusp forms 2808 456 2352
Eisenstein series 144 0 144

Trace form

\( 456 q - 12 q^{9} + O(q^{10}) \) \( 456 q - 12 q^{9} + 72 q^{17} - 24 q^{21} - 72 q^{29} - 36 q^{33} - 36 q^{41} + 1596 q^{49} + 144 q^{53} - 180 q^{57} - 48 q^{69} - 72 q^{73} + 144 q^{77} - 372 q^{81} + 288 q^{89} - 96 q^{93} + 180 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)