Properties

Label 1050.2.z
Level 1050
Weight 2
Character orbit z
Rep. character \(\chi_{1050}(209,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 320
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.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
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 992 320 672
Cusp forms 928 320 608
Eisenstein series 64 0 64

Trace form

\( 320q - 80q^{4} + O(q^{10}) \) \( 320q - 80q^{4} + 28q^{15} - 80q^{16} + 12q^{21} + 20q^{22} - 10q^{28} + 8q^{30} + 28q^{39} - 12q^{46} + 28q^{49} + 24q^{51} + 8q^{60} - 50q^{63} - 80q^{64} - 78q^{70} + 56q^{79} - 52q^{81} - 18q^{84} + 96q^{85} - 20q^{88} + 52q^{91} - 32q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database