Properties

Label 1050.2.bl
Level 1050
Weight 2
Character orbit bl
Rep. character \(\chi_{1050}(59,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640q + 80q^{4} + O(q^{10}) \) \( 640q + 80q^{4} + 6q^{10} + 20q^{15} + 80q^{16} - 12q^{21} + 40q^{22} - 6q^{25} + 10q^{28} + 10q^{30} - 18q^{31} + 150q^{33} + 32q^{39} - 6q^{40} + 114q^{45} + 12q^{46} - 28q^{49} + 12q^{51} + 10q^{60} + 50q^{63} - 160q^{64} - 48q^{66} - 90q^{70} + 120q^{73} - 144q^{75} + 28q^{79} - 44q^{81} + 18q^{84} - 72q^{85} - 10q^{88} - 52q^{91} - 48q^{94} - 64q^{99} + O(q^{100}) \)

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