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Properties

Label 1875.4.r
Level $1875$
Weight $4$
Character orbit 1875.r
Rep. character $\chi_{1875}(32,\cdot)$
Character field $\Q(\zeta_{100})$
Dimension $17760$
Sturm bound $1000$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.r (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 375 \)
Character field: \(\Q(\zeta_{100})\)
Sturm bound: \(1000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1875, [\chi])\).

Total New Old
Modular forms 30400 18240 12160
Cusp forms 29600 17760 11840
Eisenstein series 800 480 320

Trace form

\( 17760 q + 40 q^{3} + 80 q^{4} - 120 q^{6} + 80 q^{7} + 40 q^{9} + O(q^{10}) \) \( 17760 q + 40 q^{3} + 80 q^{4} - 120 q^{6} + 80 q^{7} + 40 q^{9} + 40 q^{12} + 80 q^{13} - 240 q^{16} + 40 q^{18} + 200 q^{19} - 120 q^{21} - 640 q^{22} + 50 q^{24} + 40 q^{27} - 640 q^{28} - 240 q^{31} + 40 q^{33} + 2720 q^{34} - 120 q^{36} + 80 q^{37} + 2480 q^{39} + 740 q^{42} + 80 q^{43} - 240 q^{46} - 6150 q^{48} + 100 q^{49} - 90 q^{51} + 240 q^{52} - 3730 q^{54} + 600 q^{57} + 80 q^{58} - 240 q^{61} + 2460 q^{63} - 2800 q^{64} - 120 q^{66} + 800 q^{67} + 3120 q^{69} + 9560 q^{72} + 2960 q^{73} - 180 q^{76} + 6510 q^{78} + 2240 q^{79} - 120 q^{81} + 9800 q^{82} - 1880 q^{84} - 4060 q^{87} - 4600 q^{88} - 240 q^{91} - 2640 q^{93} - 19240 q^{94} - 2040 q^{96} - 12940 q^{97} + 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1875, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1875, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)