Properties

Label 75.2.l
Level 75
Weight 2
Character orbit l
Rep. character \(\chi_{75}(2,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 64
Newforms 1
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 75.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(75, [\chi])\).

Total New Old
Modular forms 96 96 0
Cusp forms 64 64 0
Eisenstein series 32 32 0

Trace form

\( 64q - 10q^{3} - 20q^{4} - 6q^{6} - 20q^{7} - 10q^{9} + O(q^{10}) \) \( 64q - 10q^{3} - 20q^{4} - 6q^{6} - 20q^{7} - 10q^{9} - 20q^{10} - 10q^{12} - 20q^{13} - 10q^{15} - 8q^{16} - 10q^{18} - 6q^{21} + 20q^{22} + 40q^{25} - 10q^{27} + 40q^{28} - 10q^{30} - 12q^{31} - 10q^{33} + 20q^{34} - 22q^{36} - 20q^{37} + 30q^{39} - 20q^{40} + 90q^{42} - 20q^{43} + 70q^{45} - 12q^{46} + 100q^{48} - 16q^{51} + 20q^{52} + 120q^{54} - 20q^{55} + 70q^{57} - 20q^{58} + 50q^{60} - 12q^{61} - 20q^{63} - 100q^{64} - 30q^{66} - 60q^{67} - 80q^{69} - 100q^{70} - 150q^{72} - 60q^{73} - 90q^{75} - 64q^{76} - 80q^{78} - 60q^{79} + 14q^{81} - 60q^{82} - 130q^{84} + 60q^{85} - 60q^{87} + 20q^{88} - 70q^{90} - 12q^{91} - 20q^{93} + 260q^{94} + 42q^{96} + 120q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.2.l.a \(64\) \(0.599\) None \(0\) \(-10\) \(0\) \(-20\)