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Properties

Label 1050.2.bg
Level $1050$
Weight $2$
Character orbit 1050.bg
Rep. character $\chi_{1050}(121,\cdot)$
Character field $\Q(\zeta_{15})$
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.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 320 q + 40 q^{4} + 4 q^{5} + 8 q^{6} - 12 q^{7} + 40 q^{9} + O(q^{10}) \) \( 320 q + 40 q^{4} + 4 q^{5} + 8 q^{6} - 12 q^{7} + 40 q^{9} + 2 q^{10} - 12 q^{11} - 4 q^{15} + 40 q^{16} + 24 q^{17} - 8 q^{19} - 8 q^{20} - 32 q^{22} + 12 q^{23} + 16 q^{24} - 6 q^{25} + 22 q^{28} - 48 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{33} + 32 q^{34} + 40 q^{35} - 80 q^{36} + 16 q^{37} + 16 q^{38} + 2 q^{40} + 72 q^{41} + 6 q^{42} + 144 q^{43} + 8 q^{44} + 4 q^{45} + 12 q^{46} - 40 q^{47} - 12 q^{49} + 16 q^{50} + 72 q^{53} - 4 q^{54} - 12 q^{55} + 16 q^{57} - 28 q^{58} - 24 q^{59} - 8 q^{60} - 16 q^{61} + 72 q^{62} + 20 q^{63} - 80 q^{64} - 16 q^{65} - 16 q^{66} - 16 q^{67} - 16 q^{68} + 32 q^{69} + 22 q^{70} + 64 q^{71} - 24 q^{73} - 32 q^{74} + 8 q^{75} - 64 q^{76} + 80 q^{77} - 32 q^{78} - 12 q^{79} + 4 q^{80} + 40 q^{81} - 64 q^{82} + 88 q^{83} - 96 q^{85} + 24 q^{86} + 28 q^{87} - 14 q^{88} - 4 q^{90} + 68 q^{91} + 16 q^{92} + 32 q^{93} - 16 q^{94} + 68 q^{95} - 4 q^{96} + 60 q^{97} + 32 q^{98} - 16 q^{99} + O(q^{100}) \)

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

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