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Properties

Label 3600.3.cz
Level $3600$
Weight $3$
Character orbit 3600.cz
Rep. character $\chi_{3600}(193,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $856$
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.cz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 5904 872 5032
Cusp forms 5616 856 4760
Eisenstein series 288 16 272

Trace form

\( 856 q - 4 q^{3} - 2 q^{7} + O(q^{10}) \) \( 856 q - 4 q^{3} - 2 q^{7} + 4 q^{11} + 2 q^{13} + 8 q^{17} + 24 q^{21} - 2 q^{23} + 188 q^{27} + 4 q^{31} - 14 q^{33} + 8 q^{37} - 4 q^{41} - 2 q^{43} - 146 q^{47} + 392 q^{51} + 8 q^{53} - 64 q^{57} - 4 q^{61} - 246 q^{63} - 2 q^{67} - 1136 q^{71} + 8 q^{73} - 194 q^{77} - 40 q^{81} - 2 q^{83} + 202 q^{87} + 16 q^{91} - 14 q^{93} + 2 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)