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Properties

Label 900.3.x
Level $900$
Weight $3$
Character orbit 900.x
Rep. character $\chi_{900}(91,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1472 608 864
Cusp forms 1408 592 816
Eisenstein series 64 16 48

Trace form

\( 592 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 6 q^{8} + O(q^{10}) \) \( 592 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 6 q^{8} + 13 q^{10} + 6 q^{13} - 39 q^{14} + 57 q^{16} + 26 q^{17} - 7 q^{20} - 112 q^{22} - 46 q^{25} - 50 q^{26} + 83 q^{28} - 14 q^{29} - 2 q^{32} + 85 q^{34} - 291 q^{38} - 90 q^{40} + 106 q^{41} - 70 q^{44} + 89 q^{46} - 3904 q^{49} - 93 q^{50} - 204 q^{52} - 180 q^{53} - 54 q^{56} - 18 q^{58} - 26 q^{61} + 242 q^{62} + 12 q^{64} - 168 q^{65} - 390 q^{68} + 72 q^{70} - 50 q^{73} - 320 q^{74} - 160 q^{76} - 336 q^{77} - 408 q^{80} - 182 q^{82} + 56 q^{85} - 159 q^{86} - 808 q^{88} - 384 q^{89} + 178 q^{92} + 329 q^{94} + 294 q^{97} + 608 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)