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Properties

Label 1250.2.h
Level $1250$
Weight $2$
Character orbit 1250.h
Rep. character $\chi_{1250}(49,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $760$
Sturm bound $375$

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Defining parameters

Level: \( N \) \(=\) \( 1250 = 2 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1250.h (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(375\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1250, [\chi])\).

Total New Old
Modular forms 3960 760 3200
Cusp forms 3560 760 2800
Eisenstein series 400 0 400

Trace form

\( 760 q + O(q^{10}) \) \( 760 q - 10 q^{11} + 40 q^{12} + 10 q^{17} + 20 q^{19} + 20 q^{22} + 60 q^{23} + 10 q^{24} - 30 q^{26} + 10 q^{28} + 20 q^{29} - 10 q^{31} - 30 q^{33} + 50 q^{34} - 10 q^{37} + 20 q^{39} - 30 q^{41} - 10 q^{42} - 20 q^{46} + 220 q^{47} - 10 q^{48} + 210 q^{49} - 20 q^{51} + 30 q^{59} - 40 q^{61} + 20 q^{63} + 10 q^{67} + 220 q^{69} + 50 q^{71} + 50 q^{74} - 10 q^{76} + 40 q^{77} + 170 q^{78} + 40 q^{79} - 50 q^{81} + 200 q^{82} + 50 q^{83} + 30 q^{84} + 20 q^{87} - 10 q^{88} + 90 q^{89} + 240 q^{91} - 10 q^{92} + 100 q^{93} - 20 q^{97} - 40 q^{98} + 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1250, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1250, [\chi])\) into lower level spaces

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