Properties

Label 5.10.a
Level $5$
Weight $10$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $5$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(5))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 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.

\(5\)TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(2\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(0\)\(1\)
\(-\)\(3\)\(2\)\(1\)\(2\)\(2\)\(0\)\(1\)\(0\)\(1\)

Trace form

\( 3 q - 18 q^{2} + 146 q^{3} + 596 q^{4} + 625 q^{5} - 4424 q^{6} + 5942 q^{7} - 12600 q^{8} - 4181 q^{9} - 1250 q^{10} - 22224 q^{11} + 227152 q^{12} - 914 q^{13} - 474288 q^{14} + 233750 q^{15} - 144112 q^{16}+ \cdots - 1654739152 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\) 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
5.10.a.a 5.a 1.a $1$ $2.575$ \(\Q\) None 5.10.a.a \(-8\) \(-114\) \(-625\) \(4242\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b 5.a 1.a $2$ $2.575$ \(\Q(\sqrt{1009}) \) None 5.10.a.b \(-10\) \(260\) \(1250\) \(1700\) $-$ $\mathrm{SU}(2)$ \(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)