Properties

Label 150.2.h
Level $150$
Weight $2$
Character orbit 150.h
Rep. character $\chi_{150}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $2$
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: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.2.h.a 150.h 25.e $8$ $1.198$ \(\Q(\zeta_{20})\) None 150.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
150.2.h.b 150.h 25.e $16$ $1.198$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 150.2.h.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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