Properties

Label 1050.2.w
Level 1050
Weight 2
Character orbit 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

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

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

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