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Properties

Label 1050.2.bv
Level $1050$
Weight $2$
Character orbit 1050.bv
Rep. character $\chi_{1050}(73,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $640$
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3968 640 3328
Cusp forms 3712 640 3072
Eisenstein series 256 0 256

Trace form

\( 640 q - 24 q^{5} + 12 q^{7} + O(q^{10}) \) \( 640 q - 24 q^{5} + 12 q^{7} - 12 q^{10} - 8 q^{15} - 80 q^{16} + 72 q^{22} - 72 q^{23} + 16 q^{25} + 32 q^{28} + 160 q^{29} - 32 q^{30} - 12 q^{33} + 80 q^{35} + 160 q^{36} + 16 q^{37} + 48 q^{38} - 4 q^{42} - 112 q^{43} + 24 q^{47} + 144 q^{53} + 16 q^{57} - 36 q^{58} + 240 q^{59} - 32 q^{65} + 48 q^{67} - 116 q^{70} + 24 q^{73} + 48 q^{75} + 32 q^{78} - 24 q^{80} - 80 q^{81} + 192 q^{82} - 16 q^{85} - 60 q^{87} - 4 q^{88} - 16 q^{92} + 32 q^{93} - 104 q^{95} - 16 q^{98} + O(q^{100}) \)

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

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