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Properties

Label 1050.2.n
Level $1050$
Weight $2$
Character orbit 1050.n
Rep. character $\chi_{1050}(211,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $128$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 128 864
Cusp forms 928 128 800
Eisenstein series 64 0 64

Trace form

\( 128 q - 4 q^{2} - 32 q^{4} - 4 q^{5} - 4 q^{8} - 32 q^{9} + O(q^{10}) \) \( 128 q - 4 q^{2} - 32 q^{4} - 4 q^{5} - 4 q^{8} - 32 q^{9} - 4 q^{10} - 24 q^{13} - 8 q^{15} - 32 q^{16} - 8 q^{17} + 16 q^{18} + 24 q^{19} + 16 q^{20} - 4 q^{21} + 12 q^{22} + 24 q^{23} + 16 q^{25} - 24 q^{26} + 16 q^{30} + 16 q^{32} + 24 q^{33} + 36 q^{34} - 8 q^{35} - 32 q^{36} + 4 q^{37} - 4 q^{40} - 24 q^{41} - 32 q^{43} - 4 q^{45} - 4 q^{46} + 48 q^{47} + 128 q^{49} - 20 q^{50} + 32 q^{51} - 24 q^{52} - 12 q^{53} + 128 q^{55} - 40 q^{57} - 8 q^{58} - 48 q^{59} - 8 q^{60} + 24 q^{61} - 32 q^{62} - 32 q^{64} - 36 q^{65} - 8 q^{68} - 16 q^{69} - 4 q^{70} + 16 q^{71} - 4 q^{72} - 8 q^{73} - 24 q^{74} - 32 q^{75} - 16 q^{76} + 48 q^{77} + 32 q^{79} - 4 q^{80} - 32 q^{81} - 40 q^{82} + 24 q^{83} - 4 q^{84} + 4 q^{85} + 24 q^{87} - 8 q^{88} - 12 q^{89} - 4 q^{90} - 8 q^{91} - 16 q^{92} - 40 q^{95} + 32 q^{97} - 4 q^{98} + O(q^{100}) \)

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

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