Properties

Label 150.2.h
Level 150
Weight 2
Character orbit h
Rep. character \(\chi_{150}(19,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 24
Newforms 2
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 136 24 112
Cusp forms 104 24 80
Eisenstein series 32 0 32

Trace form

\(24q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 20q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 14q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 32q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut -\mathstrut 6q^{36} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 44q^{41} \) \(\mathstrut +\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 8q^{50} \) \(\mathstrut +\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 60q^{62} \) \(\mathstrut +\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 22q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 4q^{80} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut +\mathstrut 40q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 50q^{97} \) \(\mathstrut +\mathstrut 80q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.h.a \(8\) \(1.198\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
150.2.h.b \(16\) \(1.198\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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