Properties

Label 55.2.g
Level $55$
Weight $2$
Character orbit 55.g
Rep. character $\chi_{55}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

Total New Old
Modular forms 32 16 16
Cusp forms 16 16 0
Eisenstein series 16 0 16

Trace form

\( 16 q - 6 q^{2} - 4 q^{3} - 8 q^{4} + 6 q^{6} - 4 q^{7} + 2 q^{8} - 10 q^{9} + 8 q^{10} - 2 q^{11} - 12 q^{12} + 2 q^{13} + 6 q^{15} - 16 q^{16} - 12 q^{17} + 14 q^{18} + 14 q^{19} - 4 q^{20} - 32 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.g.a 55.g 11.c $8$ $0.439$ 8.0.159390625.1 None 55.2.g.a \(-4\) \(1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
55.2.g.b 55.g 11.c $8$ $0.439$ 8.0.13140625.1 None 55.2.g.b \(-2\) \(-5\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)