Properties

Label 4.9.b
Level $4$
Weight $9$
Character orbit 4.b
Rep. character $\chi_{4}(3,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $4$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(4, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3 q - 4 q^{2} + 144 q^{4} + 166 q^{5} - 2496 q^{6} + 11456 q^{8} - 285 q^{9} - 29064 q^{10} + 49920 q^{12} - 11418 q^{13} - 34944 q^{14} - 52992 q^{16} + 82822 q^{17} + 173436 q^{18} - 338144 q^{20} - 279552 q^{21}+ \cdots + 16078076 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.9.b.a 4.b 4.b $1$ $1.630$ \(\Q\) \(\Q(\sqrt{-1}) \) 4.9.b.a \(16\) \(0\) \(-1054\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
4.9.b.b 4.b 4.b $2$ $1.630$ \(\Q(\sqrt{-39}) \) None 4.9.b.b \(-20\) \(0\) \(1220\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\)