Properties

Label 150.2.g
Level $150$
Weight $2$
Character orbit 150.g
Rep. character $\chi_{150}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $3$
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: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.2.g.a 150.g 25.d $4$ $1.198$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
150.2.g.b 150.g 25.d $4$ $1.198$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(5\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
150.2.g.c 150.g 25.d $8$ $1.198$ 8.0.1064390625.3 None \(2\) \(-2\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

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