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Properties

Label 3600.3.fy
Level $3600$
Weight $3$
Character orbit 3600.fy
Rep. character $\chi_{3600}(97,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5728$
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.fy (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 23232 5792 17440
Cusp forms 22848 5728 17120
Eisenstein series 384 64 320

Trace form

\( 5728 q + 16 q^{3} - 8 q^{5} + 8 q^{7} - 20 q^{9} + O(q^{10}) \) \( 5728 q + 16 q^{3} - 8 q^{5} + 8 q^{7} - 20 q^{9} + 6 q^{11} - 8 q^{13} + 64 q^{15} - 32 q^{17} + 40 q^{19} - 12 q^{21} + 8 q^{23} - 8 q^{25} + 208 q^{27} - 10 q^{29} + 6 q^{31} - 34 q^{33} + 32 q^{35} - 32 q^{37} + 20 q^{39} - 6 q^{41} + 8 q^{43} + 34 q^{45} - 136 q^{47} + 32 q^{51} - 32 q^{53} + 132 q^{55} - 84 q^{57} + 10 q^{59} - 6 q^{61} - 226 q^{63} - 104 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{71} - 32 q^{73} + 48 q^{75} - 204 q^{77} + 10 q^{79} - 12 q^{81} + 8 q^{83} - 8 q^{85} + 222 q^{87} - 40 q^{89} + 24 q^{91} - 34 q^{93} + 58 q^{95} - 8 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)