Properties

Label 1050.2.w
Level 1050
Weight 2
Character orbit w
Rep. character \(\chi_{1050}(169,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 112
Sturm bound 480

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Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1050.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 112 880
Cusp forms 928 112 816
Eisenstein series 64 0 64

Trace form

\( 112q + 28q^{4} + 28q^{9} + O(q^{10}) \) \( 112q + 28q^{4} + 28q^{9} + 8q^{15} - 28q^{16} + 24q^{19} + 4q^{21} + 20q^{22} + 40q^{23} - 28q^{25} - 16q^{26} + 40q^{29} + 16q^{30} + 40q^{33} - 24q^{34} + 8q^{35} - 28q^{36} - 16q^{41} + 4q^{46} + 80q^{47} - 112q^{49} - 16q^{50} - 32q^{51} - 40q^{53} - 48q^{55} - 48q^{59} - 8q^{60} - 64q^{61} + 28q^{64} + 16q^{65} + 80q^{67} - 16q^{69} - 4q^{70} - 16q^{71} + 80q^{73} + 16q^{74} + 16q^{76} - 80q^{77} + 32q^{79} - 28q^{81} - 120q^{83} - 4q^{84} + 96q^{85} + 40q^{87} - 72q^{89} + 8q^{91} - 8q^{95} - 120q^{97} + O(q^{100}) \)

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