Properties

Label 4.22.a
Level $4$
Weight $22$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(4))\).

Total New Old
Modular forms 12 2 10
Cusp forms 9 2 7
Eisenstein series 3 0 3

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
\(-\)\(2\)

Trace form

\( 2 q + 65640 q^{3} + 13689324 q^{5} - 260508080 q^{7} + 12461535162 q^{9} + 145435963320 q^{11} + 1428900417340 q^{13} + 6819782714352 q^{15} + 1840620576420 q^{17} - 16780743928568 q^{19} - 192357511002048 q^{21}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.22.a.a 4.a 1.a $2$ $11.179$ \(\Q(\sqrt{2161}) \) None 4.22.a.a \(0\) \(65640\) \(13689324\) \(-260508080\) $-$ $\mathrm{SU}(2)$ \(q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(4)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)