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Properties

Label 1875.4.b
Level $1875$
Weight $4$
Character orbit 1875.b
Rep. character $\chi_{1875}(1249,\cdot)$
Character field $\Q$
Dimension $240$
Sturm bound $1000$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1000\)

Dimensions

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

Total New Old
Modular forms 780 240 540
Cusp forms 720 240 480
Eisenstein series 60 0 60

Trace form

\( 240 q - 960 q^{4} - 2160 q^{9} + O(q^{10}) \) \( 240 q - 960 q^{4} - 2160 q^{9} + 3840 q^{16} + 180 q^{19} - 120 q^{21} + 440 q^{26} - 260 q^{29} + 180 q^{31} + 40 q^{34} + 8640 q^{36} - 420 q^{39} - 460 q^{41} + 2580 q^{44} - 2220 q^{46} - 12480 q^{49} - 420 q^{56} - 580 q^{61} - 16380 q^{64} - 380 q^{74} - 2880 q^{76} + 2520 q^{79} + 19440 q^{81} + 1920 q^{84} + 4980 q^{86} + 3340 q^{89} + 900 q^{91} - 3720 q^{94} + 3480 q^{96} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)