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Properties

Label 1050.2.w
Level $1050$
Weight $2$
Character orbit 1050.w
Rep. character $\chi_{1050}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $112$
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.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 112 880
Cusp forms 928 112 816
Eisenstein series 64 0 64

Trace form

\( 112 q + 28 q^{4} + 28 q^{9} + O(q^{10}) \) \( 112 q + 28 q^{4} + 28 q^{9} + 8 q^{15} - 28 q^{16} + 24 q^{19} + 4 q^{21} + 20 q^{22} + 40 q^{23} - 28 q^{25} - 16 q^{26} + 40 q^{29} + 16 q^{30} + 40 q^{33} - 24 q^{34} + 8 q^{35} - 28 q^{36} - 16 q^{41} + 4 q^{46} + 80 q^{47} - 112 q^{49} - 16 q^{50} - 32 q^{51} - 40 q^{53} - 48 q^{55} - 48 q^{59} - 8 q^{60} - 64 q^{61} + 28 q^{64} + 16 q^{65} + 80 q^{67} - 16 q^{69} - 4 q^{70} - 16 q^{71} + 80 q^{73} + 16 q^{74} + 16 q^{76} - 80 q^{77} + 32 q^{79} - 28 q^{81} - 120 q^{83} - 4 q^{84} + 96 q^{85} + 40 q^{87} - 72 q^{89} + 8 q^{91} - 8 q^{95} - 120 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)