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Properties

Label 1875.2.i
Level $1875$
Weight $2$
Character orbit 1875.i
Rep. character $\chi_{1875}(124,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
Sturm bound $500$

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Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1875.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(500\)

Dimensions

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

Total New Old
Modular forms 1120 320 800
Cusp forms 880 320 560
Eisenstein series 240 0 240

Trace form

\( 320 q + 80 q^{4} + 80 q^{9} + O(q^{10}) \) \( 320 q + 80 q^{4} + 80 q^{9} - 80 q^{16} + 40 q^{26} - 40 q^{29} + 60 q^{34} - 80 q^{36} + 40 q^{41} - 320 q^{49} + 40 q^{61} + 80 q^{64} - 40 q^{74} - 80 q^{81} + 60 q^{89} - 90 q^{94} + 90 q^{96} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1875, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)