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Properties

Label 1875.4.e
Level $1875$
Weight $4$
Character orbit 1875.e
Rep. character $\chi_{1875}(182,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $928$
Sturm bound $1000$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1000\)

Dimensions

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

Total New Old
Modular forms 1560 992 568
Cusp forms 1440 928 512
Eisenstein series 120 64 56

Trace form

\( 928 q + 8 q^{6} + O(q^{10}) \) \( 928 q + 8 q^{6} - 13296 q^{16} + 8 q^{21} + 376 q^{31} - 504 q^{36} + 16 q^{46} - 2852 q^{51} - 2144 q^{61} - 1600 q^{66} + 4672 q^{76} - 1272 q^{81} - 6104 q^{91} + 1224 q^{96} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)