Properties

Label 2.10.a
Level $2$
Weight $10$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(2))\).

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.

\(2\)Dim
\(-\)\(1\)

Trace form

\( q + 16 q^{2} - 156 q^{3} + 256 q^{4} + 870 q^{5} - 2496 q^{6} - 952 q^{7} + 4096 q^{8} + 4653 q^{9} + 13920 q^{10} - 56148 q^{11} - 39936 q^{12} + 178094 q^{13} - 15232 q^{14} - 135720 q^{15} + 65536 q^{16}+ \cdots - 261256644 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.10.a.a 2.a 1.a $1$ $1.030$ \(\Q\) None 2.10.a.a \(16\) \(-156\) \(870\) \(-952\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)