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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into irreducible Hecke orbits

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

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