Properties

Label 1050.2.bg
Level 1050
Weight 2
Character orbit 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

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

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database