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Properties

Label 900.4.br
Level $900$
Weight $4$
Character orbit 900.br
Rep. character $\chi_{900}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4288$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 4352 4352 0
Cusp forms 4288 4288 0
Eisenstein series 64 64 0

Trace form

\( 4288 q - 9 q^{2} - 3 q^{4} - 24 q^{5} - 22 q^{6} - 12 q^{9} + O(q^{10}) \) \( 4288 q - 9 q^{2} - 3 q^{4} - 24 q^{5} - 22 q^{6} - 12 q^{9} + 48 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} + 476 q^{18} + 219 q^{20} - 174 q^{21} - 35 q^{22} + 106 q^{24} - 8 q^{25} - 396 q^{28} - 18 q^{29} - 368 q^{30} - 1404 q^{32} - 120 q^{33} - 19 q^{34} + 196 q^{36} - 24 q^{37} - 57 q^{38} - 129 q^{40} - 18 q^{41} - 1112 q^{42} + 726 q^{45} - 44 q^{46} - 2807 q^{48} + 100336 q^{49} + 1587 q^{50} - 259 q^{52} - 1153 q^{54} - 3096 q^{56} - 1096 q^{57} + 29 q^{58} - 503 q^{60} - 6 q^{61} - 12 q^{64} - 720 q^{65} + 3322 q^{66} - 408 q^{68} + 624 q^{69} + 1626 q^{70} - 4684 q^{72} - 24 q^{73} - 6318 q^{74} - 136 q^{76} - 18 q^{77} - 188 q^{78} - 924 q^{81} + 3213 q^{84} - 258 q^{85} + 8331 q^{86} - 1067 q^{88} + 9397 q^{90} + 9453 q^{92} - 4868 q^{93} + 2449 q^{94} - 2623 q^{96} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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