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Properties

Label 2500.2.s
Level $2500$
Weight $2$
Character orbit 2500.s
Rep. character $\chi_{2500}(21,\cdot)$
Character field $\Q(\zeta_{125})$
Dimension $6300$
Sturm bound $750$

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Defining parameters

Level: \( N \) \(=\) \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2500.s (of order \(125\) and degree \(100\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 625 \)
Character field: \(\Q(\zeta_{125})\)
Sturm bound: \(750\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2500, [\chi])\).

Total New Old
Modular forms 37800 6300 31500
Cusp forms 37200 6300 30900
Eisenstein series 600 0 600

Trace form

\( 6300 q + O(q^{10}) \) \( 6300 q - 50 q^{23} - 200 q^{25} - 150 q^{45} + 125 q^{47} - 100 q^{71} + 150 q^{91} - 100 q^{93} + 50 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2500, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2500, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2500, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1250, [\chi])\)\(^{\oplus 2}\)