Properties

Label 1050.2.bh
Level 1050
Weight 2
Character orbit bh
Rep. character \(\chi_{1050}(13,\cdot)\)
Character field \(\Q(\zeta_{20})\)
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.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 320 1664
Cusp forms 1856 320 1536
Eisenstein series 128 0 128

Trace form

\( 320q - 12q^{7} + O(q^{10}) \) \( 320q - 12q^{7} + 8q^{15} + 80q^{16} + 24q^{22} + 48q^{23} + 8q^{25} - 8q^{28} + 80q^{29} + 32q^{30} - 8q^{35} + 80q^{36} + 56q^{37} + 4q^{42} + 160q^{43} - 144q^{53} + 8q^{57} + 24q^{58} + 12q^{63} + 32q^{65} + 44q^{70} - 32q^{78} + 80q^{81} - 56q^{85} + 16q^{88} - 32q^{92} - 32q^{93} + 80q^{95} + 16q^{98} + O(q^{100}) \)

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