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Properties

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

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

Display 100 coefficients 10 coefficients

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

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