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Properties

Label 1500.4.bb
Level $1500$
Weight $4$
Character orbit 1500.bb
Rep. character $\chi_{1500}(59,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $17920$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1500.bb (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1500 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1500, [\chi])\).

Total New Old
Modular forms 18080 18080 0
Cusp forms 17920 17920 0
Eisenstein series 160 160 0

Trace form

\( 17920 q - 40 q^{4} - 20 q^{6} - 40 q^{9} + O(q^{10}) \) \( 17920 q - 40 q^{4} - 20 q^{6} - 40 q^{9} - 40 q^{10} - 20 q^{12} - 80 q^{13} - 220 q^{16} - 25 q^{18} + 230 q^{21} - 40 q^{22} - 15 q^{24} - 80 q^{25} + 600 q^{28} - 20 q^{30} - 40 q^{33} - 40 q^{34} + 2180 q^{36} - 1400 q^{37} - 40 q^{40} + 1410 q^{42} - 40 q^{45} - 40 q^{46} - 3075 q^{48} - 213700 q^{49} + 110 q^{52} - 1905 q^{54} - 13720 q^{58} - 785 q^{60} - 80 q^{61} - 40 q^{64} + 3055 q^{66} - 40 q^{69} + 3390 q^{70} - 20 q^{72} - 80 q^{73} - 30 q^{76} + 2910 q^{78} - 800 q^{81} - 50 q^{82} + 1695 q^{84} + 4360 q^{85} - 2020 q^{88} + 605 q^{90} - 50 q^{93} + 9620 q^{94} - 155 q^{96} - 9380 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces

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