Properties

Label 1050.2.bf
Level 1050
Weight 2
Character orbit bf
Rep. character \(\chi_{1050}(107,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 192
Sturm bound 480

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1050.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1056 192 864
Cusp forms 864 192 672
Eisenstein series 192 0 192

Trace form

\( 192q - 16q^{6} - 4q^{7} + O(q^{10}) \) \( 192q - 16q^{6} - 4q^{7} + 96q^{16} + 8q^{18} - 24q^{21} + 24q^{22} + 72q^{27} - 4q^{28} + 16q^{31} + 20q^{33} + 48q^{36} + 8q^{37} + 40q^{42} + 64q^{43} - 48q^{46} - 24q^{57} + 28q^{58} - 8q^{61} + 88q^{63} + 16q^{67} - 8q^{72} + 56q^{73} - 16q^{76} + 16q^{78} - 8q^{81} - 16q^{82} - 76q^{87} - 12q^{88} - 24q^{91} - 84q^{93} - 8q^{96} - 104q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database