Properties

Label 1050.2.bv
Level 1050
Weight 2
Character orbit bv
Rep. character \(\chi_{1050}(73,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 640
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3968 640 3328
Cusp forms 3712 640 3072
Eisenstein series 256 0 256

Trace form

\( 640q - 24q^{5} + 12q^{7} + O(q^{10}) \) \( 640q - 24q^{5} + 12q^{7} - 12q^{10} - 8q^{15} - 80q^{16} + 72q^{22} - 72q^{23} + 16q^{25} + 32q^{28} + 160q^{29} - 32q^{30} - 12q^{33} + 80q^{35} + 160q^{36} + 16q^{37} + 48q^{38} - 4q^{42} - 112q^{43} + 24q^{47} + 144q^{53} + 16q^{57} - 36q^{58} + 240q^{59} - 32q^{65} + 48q^{67} - 116q^{70} + 24q^{73} + 48q^{75} + 32q^{78} - 24q^{80} - 80q^{81} + 192q^{82} - 16q^{85} - 60q^{87} - 4q^{88} - 16q^{92} + 32q^{93} - 104q^{95} - 16q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database