Properties

Label 150.2.g
Level 150
Weight 2
Character orbit g
Rep. character \(\chi_{150}(31,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 16
Newforms 3
Sturm bound 60
Trace bound 2

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(2\)
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 16 120
Cusp forms 104 16 88
Eisenstein series 32 0 32

Trace form

\(16q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 36q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 8q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 24q^{41} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 12q^{52} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 24q^{57} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 32q^{67} \) \(\mathstrut +\mathstrut 12q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut 28q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 16q^{77} \) \(\mathstrut +\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 44q^{82} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 14q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 2q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 4q^{90} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 14q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.g.a \(4\) \(1.198\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(5\) \(6\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
150.2.g.b \(4\) \(1.198\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(5\) \(8\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
150.2.g.c \(8\) \(1.198\) 8.0.1064390625.3 None \(2\) \(-2\) \(-4\) \(-2\) \(q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

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