Properties

Label 150.2.a
Level $150$
Weight $2$
Character orbit 150.a
Rep. character $\chi_{150}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(150))\).

Total New Old
Modular forms 42 3 39
Cusp forms 19 3 16
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim
\(+\)\(+\)\(-\)$-$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} - q^{3} + 3 q^{4} + q^{6} + 4 q^{7} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q + q^{2} - q^{3} + 3 q^{4} + q^{6} + 4 q^{7} + q^{8} + 3 q^{9} + 4 q^{11} - q^{12} - 2 q^{13} + 3 q^{16} - 6 q^{17} + q^{18} - 4 q^{19} - 8 q^{21} + q^{24} - 14 q^{26} - q^{27} + 4 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} - 10 q^{34} + 3 q^{36} - 2 q^{37} - 4 q^{38} - 10 q^{39} - 2 q^{41} - 4 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{46} - q^{48} + 3 q^{49} + 2 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} + 4 q^{57} - 6 q^{58} + 20 q^{59} - 6 q^{61} + 8 q^{62} + 4 q^{63} + 3 q^{64} + 4 q^{66} + 4 q^{67} - 6 q^{68} + 8 q^{69} + 24 q^{71} + q^{72} - 2 q^{73} - 6 q^{74} - 4 q^{76} + 2 q^{78} + 8 q^{79} + 3 q^{81} - 6 q^{82} - 12 q^{83} - 8 q^{84} + 12 q^{86} + 6 q^{87} - 2 q^{89} + 16 q^{91} - 8 q^{93} + 16 q^{94} + q^{96} - 2 q^{97} + 9 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(150))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
150.2.a.a 150.a 1.a $1$ $1.198$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
150.2.a.b 150.a 1.a $1$ $1.198$ \(\Q\) None \(1\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
150.2.a.c 150.a 1.a $1$ $1.198$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)