Properties

Label 150.2.l
Level 150
Weight 2
Character orbit l
Rep. character \(\chi_{150}(17,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 80
Newforms 1
Sturm bound 60
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(150, [\chi])\).

Total New Old
Modular forms 272 80 192
Cusp forms 208 80 128
Eisenstein series 64 0 64

Trace form

\( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} - 4q^{10} - 4q^{12} - 8q^{15} + 20q^{16} - 8q^{18} - 40q^{19} - 36q^{22} - 104q^{25} + 4q^{27} - 16q^{28} + 12q^{30} + 4q^{33} - 40q^{34} - 24q^{37} - 40q^{39} - 8q^{40} - 4q^{42} - 24q^{43} - 72q^{45} - 4q^{48} - 12q^{55} - 64q^{57} + 20q^{58} + 24q^{60} + 64q^{63} + 96q^{67} + 140q^{69} + 76q^{70} + 8q^{72} + 100q^{73} + 132q^{75} + 100q^{78} + 80q^{79} - 40q^{81} + 96q^{82} + 60q^{84} + 32q^{85} + 80q^{87} + 4q^{88} + 52q^{90} + 12q^{93} - 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.2.l.a \(80\) \(1.198\) None \(0\) \(4\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)