Properties

Label 1050.2.bs
Level 1050
Weight 2
Character orbit bs
Rep. character \(\chi_{1050}(23,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1280
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
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 1280 2688
Cusp forms 3712 1280 2432
Eisenstein series 256 0 256

Trace form

\( 1280q - 4q^{7} + O(q^{10}) \) \( 1280q - 4q^{7} - 4q^{10} + 24q^{15} - 160q^{16} + 8q^{18} - 56q^{22} + 8q^{25} + 72q^{27} + 16q^{28} + 12q^{30} + 20q^{33} + 8q^{37} + 40q^{39} + 40q^{42} + 64q^{43} - 52q^{45} + 16q^{55} + 136q^{57} + 28q^{58} - 8q^{60} - 12q^{63} + 16q^{67} - 280q^{69} - 68q^{70} - 8q^{72} + 56q^{73} + 152q^{75} + 16q^{78} + 64q^{82} - 60q^{84} - 32q^{85} - 76q^{87} - 12q^{88} - 160q^{90} - 84q^{93} - 64q^{97} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database