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

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

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

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