Properties

Label 1050.2.bk
Level 1050
Weight 2
Character orbit bk
Rep. character \(\chi_{1050}(113,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 480
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.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480q - 8q^{3} + O(q^{10}) \) \( 480q - 8q^{3} + 8q^{12} - 8q^{15} + 120q^{16} + 8q^{18} + 80q^{19} + 32q^{22} + 200q^{25} - 8q^{27} + 32q^{33} + 80q^{34} + 40q^{37} + 40q^{39} + 16q^{40} - 16q^{43} + 40q^{45} + 8q^{48} + 32q^{55} - 32q^{57} + 16q^{58} - 40q^{60} + 32q^{63} - 160q^{67} - 8q^{70} - 8q^{72} - 112q^{73} - 32q^{75} - 192q^{78} - 160q^{79} + 80q^{81} - 64q^{82} - 8q^{85} - 120q^{87} - 8q^{88} - 40q^{90} - 96q^{93} - 16q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database