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Properties

Label 1875.2.x
Level $1875$
Weight $2$
Character orbit 1875.x
Rep. character $\chi_{1875}(2,\cdot)$
Character field $\Q(\zeta_{500})$
Dimension $49600$
Sturm bound $500$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1875.x (of order \(500\) and degree \(200\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1875 \)
Character field: \(\Q(\zeta_{500})\)
Sturm bound: \(500\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1875, [\chi])\).

Total New Old
Modular forms 50400 50400 0
Cusp forms 49600 49600 0
Eisenstein series 800 800 0

Trace form

\( 49600 q - 200 q^{3} - 400 q^{4} - 200 q^{6} - 400 q^{7} - 200 q^{9} + O(q^{10}) \) \( 49600 q - 200 q^{3} - 400 q^{4} - 200 q^{6} - 400 q^{7} - 200 q^{9} - 400 q^{10} - 200 q^{12} - 400 q^{13} - 200 q^{15} - 400 q^{16} - 200 q^{18} - 400 q^{19} - 200 q^{21} - 400 q^{22} - 200 q^{24} - 400 q^{25} - 200 q^{27} - 400 q^{28} - 200 q^{30} - 400 q^{31} - 200 q^{33} - 400 q^{34} - 200 q^{36} - 400 q^{37} - 200 q^{39} - 400 q^{40} - 200 q^{42} - 400 q^{43} - 200 q^{45} - 400 q^{46} - 200 q^{48} - 400 q^{49} - 200 q^{51} - 400 q^{52} - 200 q^{54} - 400 q^{55} - 200 q^{57} - 400 q^{58} - 200 q^{60} - 400 q^{61} - 200 q^{63} - 400 q^{64} - 200 q^{66} - 400 q^{67} - 200 q^{69} - 400 q^{70} - 200 q^{72} - 400 q^{73} - 200 q^{75} - 400 q^{76} - 200 q^{78} - 400 q^{79} - 200 q^{81} - 400 q^{82} - 200 q^{84} - 400 q^{85} - 200 q^{87} - 400 q^{88} - 200 q^{90} - 400 q^{91} - 200 q^{93} - 400 q^{94} - 200 q^{96} - 400 q^{97} - 200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1875, [\chi])\) into newform subspaces

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