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Properties

Label 1900.3.bz
Level $1900$
Weight $3$
Character orbit 1900.bz
Rep. character $\chi_{1900}(159,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4768$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.bz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 5 q^{2} - 3 q^{4} - 8 q^{5} - 19 q^{6} - 50 q^{8} + 1758 q^{9} + O(q^{10}) \) \( 4768 q - 5 q^{2} - 3 q^{4} - 8 q^{5} - 19 q^{6} - 50 q^{8} + 1758 q^{9} - 5 q^{10} - 20 q^{12} - 10 q^{13} - 45 q^{14} - 3 q^{16} - 10 q^{17} - 112 q^{20} - 60 q^{21} - 155 q^{22} + 80 q^{24} - 8 q^{25} - 116 q^{26} - 85 q^{28} - 6 q^{29} - 288 q^{30} - 10 q^{33} + 13 q^{34} - 49 q^{36} - 40 q^{37} - 25 q^{38} - 188 q^{40} - 6 q^{41} - 185 q^{42} + 175 q^{44} - 168 q^{45} - 28 q^{46} - 5 q^{48} + 31968 q^{49} - 354 q^{50} - 5 q^{52} - 10 q^{53} - 166 q^{54} - 600 q^{56} - 890 q^{58} + 304 q^{60} - 6 q^{61} + 320 q^{62} - 522 q^{64} + 164 q^{65} - 95 q^{66} - 96 q^{69} - 312 q^{70} - 320 q^{72} - 10 q^{73} + 194 q^{74} + 16 q^{76} - 2000 q^{77} + 40 q^{78} - 33 q^{80} + 4626 q^{81} - 700 q^{84} + 36 q^{85} - 129 q^{86} - 1340 q^{88} - 6 q^{89} + 313 q^{90} + 345 q^{92} + 792 q^{94} + 102 q^{96} - 10 q^{97} - 270 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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