Properties

Label 1575.2.ek
Level 1575
Weight 2
Character orbit ek
Rep. character \(\chi_{1575}(2,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3776
Sturm bound 480

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.ek (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\(3776q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3776q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut -\mathstrut 30q^{14} \) \(\mathstrut -\mathstrut 26q^{15} \) \(\mathstrut -\mathstrut 442q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 48q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 36q^{28} \) \(\mathstrut -\mathstrut 60q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 60q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 40q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 50q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 34q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 102q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 98q^{48} \) \(\mathstrut -\mathstrut 96q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 48q^{52} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 84q^{55} \) \(\mathstrut -\mathstrut 18q^{56} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 36q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 134q^{63} \) \(\mathstrut -\mathstrut 80q^{64} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut -\mathstrut 30q^{66} \) \(\mathstrut +\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 110q^{69} \) \(\mathstrut +\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 36q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 96q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 72q^{77} \) \(\mathstrut -\mathstrut 154q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut -\mathstrut 48q^{83} \) \(\mathstrut -\mathstrut 260q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 18q^{87} \) \(\mathstrut -\mathstrut 32q^{88} \) \(\mathstrut -\mathstrut 150q^{89} \) \(\mathstrut -\mathstrut 76q^{90} \) \(\mathstrut -\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 132q^{92} \) \(\mathstrut -\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 10q^{94} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 102q^{96} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 48q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.