Properties

Label 22.2.c
Level $22$
Weight $2$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $4$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(22, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

Trace form

\( 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} - 4 q^{13} + 2 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - 8 q^{18} - 5 q^{19} - 6 q^{20} - 12 q^{21}+ \cdots - 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.2.c.a 22.c 11.c $4$ $0.176$ \(\Q(\zeta_{10})\) None 22.2.c.a \(-1\) \(-4\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)