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Properties

Label 1050.2.bh
Level $1050$
Weight $2$
Character orbit 1050.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

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

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)