Properties

Label 5.6.a
Level $5$
Weight $6$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(5))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

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

\(5\)Dim
\(-\)\(1\)

Trace form

\( q + 2 q^{2} - 4 q^{3} - 28 q^{4} + 25 q^{5} - 8 q^{6} + 192 q^{7} - 120 q^{8} - 227 q^{9} + 50 q^{10} - 148 q^{11} + 112 q^{12} + 286 q^{13} + 384 q^{14} - 100 q^{15} + 656 q^{16} - 1678 q^{17} - 454 q^{18}+ \cdots + 33596 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.6.a.a 5.a 1.a $1$ $0.802$ \(\Q\) None 5.6.a.a \(2\) \(-4\) \(25\) \(192\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)