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Properties

Label 2500.2.o
Level $2500$
Weight $2$
Character orbit 2500.o
Rep. character $\chi_{2500}(49,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $760$
Sturm bound $750$

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Defining parameters

Level: \( N \) \(=\) \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2500.o (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(750\)

Dimensions

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

Total New Old
Modular forms 7800 760 7040
Cusp forms 7200 760 6440
Eisenstein series 600 0 600

Trace form

\( 760 q + O(q^{10}) \) \( 760 q + 5 q^{11} - 5 q^{17} - 10 q^{19} + 30 q^{23} - 10 q^{29} - 10 q^{31} + 15 q^{33} - 10 q^{37} + 20 q^{39} + 15 q^{41} - 80 q^{47} + 210 q^{49} - 20 q^{51} + 30 q^{53} + 15 q^{59} + 20 q^{61} + 20 q^{63} - 5 q^{67} - 110 q^{69} + 95 q^{71} - 60 q^{73} - 20 q^{77} - 20 q^{79} - 5 q^{81} - 10 q^{83} - 55 q^{87} + 15 q^{89} - 120 q^{91} + 100 q^{93} + 25 q^{97} + 30 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2500, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1250, [\chi])\)\(^{\oplus 2}\)