Properties

Label 1575.2.em
Level 1575
Weight 2
Character orbit em
Rep. character \(\chi_{1575}(23,\cdot)\)
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.em (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

\( 3776q - 8q^{3} - 20q^{4} - 24q^{5} - 24q^{6} - 8q^{7} - 10q^{9} + O(q^{10}) \) \( 3776q - 8q^{3} - 20q^{4} - 24q^{5} - 24q^{6} - 8q^{7} - 10q^{9} - 16q^{10} - 18q^{11} - 36q^{12} - 16q^{13} - 30q^{14} - 26q^{15} + 884q^{16} - 18q^{17} - 20q^{19} - 48q^{20} - 12q^{21} - 24q^{22} + 8q^{25} - 8q^{27} - 36q^{28} - 60q^{29} - 20q^{30} - 12q^{31} + 24q^{33} - 20q^{34} - 40q^{36} - 16q^{37} + 70q^{39} - 8q^{40} - 36q^{41} - 28q^{42} - 16q^{43} + 48q^{45} - 12q^{46} - 98q^{48} - 96q^{50} - 16q^{51} + 24q^{52} - 10q^{54} - 84q^{55} - 18q^{56} + 8q^{57} + 4q^{58} - 132q^{60} - 12q^{61} + 16q^{63} - 80q^{64} + 42q^{66} - 16q^{67} + 216q^{68} - 110q^{69} - 28q^{70} + 36q^{72} - 16q^{73} - 96q^{75} - 16q^{76} - 216q^{77} - 154q^{78} - 20q^{79} + 36q^{80} - 6q^{81} - 12q^{82} - 48q^{83} + 100q^{84} - 16q^{85} - 18q^{86} + 18q^{87} + 16q^{88} + 150q^{89} - 76q^{90} - 24q^{91} - 132q^{92} + 28q^{93} - 20q^{94} + 114q^{96} - 16q^{97} - 48q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database