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Properties

Label 900.3.t
Level $900$
Weight $3$
Character orbit 900.t
Rep. character $\chi_{900}(151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $444$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 744 468 276
Cusp forms 696 444 252
Eisenstein series 48 24 24

Trace form

\( 444 q + q^{2} + q^{4} - 5 q^{6} - 14 q^{8} + 8 q^{9} + O(q^{10}) \) \( 444 q + q^{2} + q^{4} - 5 q^{6} - 14 q^{8} + 8 q^{9} - 14 q^{12} + 2 q^{13} - 38 q^{14} - 3 q^{16} - 16 q^{17} - 20 q^{18} + 14 q^{21} + 9 q^{22} + 83 q^{24} + 40 q^{26} + 36 q^{28} + 26 q^{29} + 61 q^{32} + 2 q^{33} - 5 q^{34} - 5 q^{36} + 8 q^{37} + 93 q^{38} + 54 q^{41} + 12 q^{42} + 258 q^{44} + 80 q^{46} - 183 q^{48} + 1304 q^{49} - 40 q^{52} - 136 q^{53} - 49 q^{54} + 86 q^{56} + 108 q^{57} + 38 q^{58} - 6 q^{61} + 408 q^{62} - 254 q^{64} - 468 q^{66} - 103 q^{68} + 46 q^{69} + 21 q^{72} + 32 q^{73} + 304 q^{74} - 33 q^{76} + 150 q^{77} - 176 q^{78} - 32 q^{81} + 194 q^{82} - 80 q^{84} - 25 q^{86} - 75 q^{88} + 104 q^{89} + 378 q^{92} + 230 q^{93} + 154 q^{94} - 416 q^{96} - 58 q^{97} - 158 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)