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Properties

Label 1050.2.bs
Level $1050$
Weight $2$
Character orbit 1050.bs
Rep. character $\chi_{1050}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1280$
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
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 1280 2688
Cusp forms 3712 1280 2432
Eisenstein series 256 0 256

Trace form

\( 1280 q - 4 q^{7} + O(q^{10}) \) \( 1280 q - 4 q^{7} - 4 q^{10} + 24 q^{15} - 160 q^{16} + 8 q^{18} - 56 q^{22} + 8 q^{25} + 72 q^{27} + 16 q^{28} + 12 q^{30} + 20 q^{33} + 8 q^{37} + 40 q^{39} + 40 q^{42} + 64 q^{43} - 52 q^{45} + 16 q^{55} + 136 q^{57} + 28 q^{58} - 8 q^{60} - 12 q^{63} + 16 q^{67} - 280 q^{69} - 68 q^{70} - 8 q^{72} + 56 q^{73} + 152 q^{75} + 16 q^{78} + 64 q^{82} - 60 q^{84} - 32 q^{85} - 76 q^{87} - 12 q^{88} - 160 q^{90} - 84 q^{93} - 64 q^{97} + O(q^{100}) \)

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

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