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Properties

Label 3600.3.eu
Level $3600$
Weight $3$
Character orbit 3600.eu
Rep. character $\chi_{3600}(641,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2864$
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.eu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 11616 2896 8720
Cusp forms 11424 2864 8560
Eisenstein series 192 32 160

Trace form

\( 2864 q + 6 q^{3} - 12 q^{5} + 8 q^{7} - 6 q^{9} + O(q^{10}) \) \( 2864 q + 6 q^{3} - 12 q^{5} + 8 q^{7} - 6 q^{9} + 9 q^{11} - 3 q^{13} - 25 q^{15} + 12 q^{19} + 21 q^{21} + 9 q^{23} - 4 q^{25} - 186 q^{27} - 9 q^{29} + 3 q^{31} + 12 q^{33} - 12 q^{37} + 24 q^{39} - 9 q^{41} + 8 q^{43} + 17 q^{45} + 441 q^{47} - 9696 q^{49} + 52 q^{51} - 34 q^{55} - 12 q^{57} + 9 q^{59} - 3 q^{61} - 285 q^{63} + 132 q^{65} + 3 q^{67} + 12 q^{69} - 12 q^{73} - 47 q^{75} - 9 q^{77} + 3 q^{79} + 474 q^{81} + 9 q^{83} - 29 q^{85} - 236 q^{87} - 282 q^{91} - 34 q^{93} - 711 q^{95} - 3 q^{97} - 146 q^{99} + O(q^{100}) \)

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

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