Properties

Label 150.4.a
Level $150$
Weight $4$
Character orbit 150.a
Rep. character $\chi_{150}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $9$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(120\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(150))\).

Total New Old
Modular forms 102 9 93
Cusp forms 78 9 69
Eisenstein series 24 0 24

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
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
Plus space\(+\)\(6\)
Minus space\(-\)\(3\)

Trace form

\( 9 q + 2 q^{2} - 3 q^{3} + 36 q^{4} - 6 q^{6} - 12 q^{7} + 8 q^{8} + 81 q^{9} + 68 q^{11} - 12 q^{12} - 6 q^{13} + 48 q^{14} + 144 q^{16} + 198 q^{17} + 18 q^{18} + 200 q^{19} + 12 q^{21} - 240 q^{23} - 24 q^{24}+ \cdots + 612 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(150))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
150.4.a.a 150.a 1.a $1$ $8.850$ \(\Q\) None 150.4.a.a \(-2\) \(-3\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-q^{7}+\cdots\)
150.4.a.b 150.a 1.a $1$ $8.850$ \(\Q\) None 30.4.a.b \(-2\) \(-3\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+4q^{7}+\cdots\)
150.4.a.c 150.a 1.a $1$ $8.850$ \(\Q\) None 150.4.a.c \(-2\) \(3\) \(0\) \(-23\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-23q^{7}+\cdots\)
150.4.a.d 150.a 1.a $1$ $8.850$ \(\Q\) None 30.4.c.a \(-2\) \(3\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2q^{7}+\cdots\)
150.4.a.e 150.a 1.a $1$ $8.850$ \(\Q\) None 30.4.a.a \(2\) \(-3\) \(0\) \(-32\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2^{5}q^{7}+\cdots\)
150.4.a.f 150.a 1.a $1$ $8.850$ \(\Q\) None 30.4.c.a \(2\) \(-3\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots\)
150.4.a.g 150.a 1.a $1$ $8.850$ \(\Q\) None 150.4.a.c \(2\) \(-3\) \(0\) \(23\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+23q^{7}+\cdots\)
150.4.a.h 150.a 1.a $1$ $8.850$ \(\Q\) None 150.4.a.a \(2\) \(3\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+q^{7}+\cdots\)
150.4.a.i 150.a 1.a $1$ $8.850$ \(\Q\) None 6.4.a.a \(2\) \(3\) \(0\) \(16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+2^{4}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(150))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(150)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)