Properties

Label 1050.2.br
Level 1050
Weight 2
Character orbit br
Rep. character \(\chi_{1050}(79,\cdot)\)
Character field \(\Q(\zeta_{30})\)
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.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 320 1664
Cusp forms 1856 320 1536
Eisenstein series 128 0 128

Trace form

\( 320q - 40q^{4} + 4q^{5} - 8q^{6} - 40q^{9} + O(q^{10}) \) \( 320q - 40q^{4} + 4q^{5} - 8q^{6} - 40q^{9} + 2q^{10} + 12q^{11} - 4q^{15} + 40q^{16} + 40q^{17} - 8q^{19} + 8q^{20} - 40q^{22} + 60q^{23} + 16q^{24} + 6q^{25} + 10q^{28} - 48q^{29} + 16q^{30} + 6q^{31} + 32q^{34} + 40q^{35} - 80q^{36} - 2q^{40} - 72q^{41} - 10q^{42} + 8q^{44} - 4q^{45} - 12q^{46} - 12q^{49} - 16q^{50} + 40q^{53} - 4q^{54} - 20q^{55} - 24q^{59} + 8q^{60} + 16q^{61} - 120q^{62} - 20q^{63} + 80q^{64} + 32q^{65} + 16q^{66} + 32q^{69} + 86q^{70} - 64q^{71} + 40q^{73} - 32q^{74} + 8q^{75} + 64q^{76} - 12q^{79} + 4q^{80} + 40q^{81} + 40q^{83} + 112q^{85} - 24q^{86} + 10q^{88} + 4q^{90} - 68q^{91} - 16q^{94} - 28q^{95} + 4q^{96} + 20q^{97} - 80q^{98} - 16q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database