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Properties

Label 1875.4.o
Level $1875$
Weight $4$
Character orbit 1875.o
Rep. character $\chi_{1875}(49,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $4480$
Sturm bound $1000$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.o (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(1000\)

Dimensions

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

Total New Old
Modular forms 15200 4480 10720
Cusp forms 14800 4480 10320
Eisenstein series 400 0 400

Trace form

\( 4480 q + 210 q^{8} + O(q^{10}) \) \( 4480 q + 210 q^{8} - 140 q^{11} - 180 q^{16} + 320 q^{17} + 60 q^{19} + 290 q^{22} - 1560 q^{23} - 720 q^{24} - 360 q^{28} - 80 q^{29} - 690 q^{31} + 480 q^{33} + 480 q^{34} + 1030 q^{37} + 2490 q^{38} + 480 q^{41} - 1020 q^{42} - 1330 q^{44} - 1080 q^{46} - 1720 q^{47} + 52920 q^{49} + 2040 q^{51} - 3720 q^{52} - 5170 q^{53} + 10560 q^{56} - 12070 q^{58} + 1640 q^{59} + 720 q^{61} + 8830 q^{62} - 180 q^{63} + 6270 q^{64} + 18120 q^{67} + 4640 q^{71} + 1890 q^{72} + 840 q^{73} + 7600 q^{76} + 1120 q^{77} - 1080 q^{79} - 3600 q^{82} + 9380 q^{83} + 5640 q^{84} + 6100 q^{86} + 2280 q^{87} + 2030 q^{88} + 13350 q^{89} - 7920 q^{91} - 11230 q^{92} - 17100 q^{93} - 1380 q^{94} - 6450 q^{96} - 3870 q^{97} - 7020 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)