Properties

Label 1050.2.n
Level 1050
Weight 2
Character orbit n
Rep. character \(\chi_{1050}(211,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 128
Sturm bound 480

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1050.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1050, [\chi])\).

Total New Old
Modular forms 992 128 864
Cusp forms 928 128 800
Eisenstein series 64 0 64

Trace form

\( 128q - 4q^{2} - 32q^{4} - 4q^{5} - 4q^{8} - 32q^{9} + O(q^{10}) \) \( 128q - 4q^{2} - 32q^{4} - 4q^{5} - 4q^{8} - 32q^{9} - 4q^{10} - 24q^{13} - 8q^{15} - 32q^{16} - 8q^{17} + 16q^{18} + 24q^{19} + 16q^{20} - 4q^{21} + 12q^{22} + 24q^{23} + 16q^{25} - 24q^{26} + 16q^{30} + 16q^{32} + 24q^{33} + 36q^{34} - 8q^{35} - 32q^{36} + 4q^{37} - 4q^{40} - 24q^{41} - 32q^{43} - 4q^{45} - 4q^{46} + 48q^{47} + 128q^{49} - 20q^{50} + 32q^{51} - 24q^{52} - 12q^{53} + 128q^{55} - 40q^{57} - 8q^{58} - 48q^{59} - 8q^{60} + 24q^{61} - 32q^{62} - 32q^{64} - 36q^{65} - 8q^{68} - 16q^{69} - 4q^{70} + 16q^{71} - 4q^{72} - 8q^{73} - 24q^{74} - 32q^{75} - 16q^{76} + 48q^{77} + 32q^{79} - 4q^{80} - 32q^{81} - 40q^{82} + 24q^{83} - 4q^{84} + 4q^{85} + 24q^{87} - 8q^{88} - 12q^{89} - 4q^{90} - 8q^{91} - 16q^{92} - 40q^{95} + 32q^{97} - 4q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database