Properties

Label 6.22.a
Level $6$
Weight $22$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $22$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(22\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(6))\).

Total New Old
Modular forms 23 3 20
Cusp forms 19 3 16
Eisenstein series 4 0 4

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

\(2\)\(3\)FrickeDim
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q + 1024 q^{2} + 59049 q^{3} + 3145728 q^{4} + 16153674 q^{5} - 60466176 q^{6} - 1636375008 q^{7} + 1073741824 q^{8} + 10460353203 q^{9} - 37617076224 q^{10} - 98395423908 q^{11} + 61917364224 q^{12}+ \cdots - 34\!\cdots\!08 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(6))\) 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 3
6.22.a.a 6.a 1.a $1$ $16.769$ \(\Q\) None 6.22.a.a \(-1024\) \(59049\) \(26444550\) \(166115864\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}+26444550q^{5}+\cdots\)
6.22.a.b 6.a 1.a $1$ $16.769$ \(\Q\) None 6.22.a.b \(1024\) \(-59049\) \(12954174\) \(-479513104\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}-3^{10}q^{3}+2^{20}q^{4}+12954174q^{5}+\cdots\)
6.22.a.c 6.a 1.a $1$ $16.769$ \(\Q\) None 6.22.a.c \(1024\) \(59049\) \(-23245050\) \(-1322977768\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}-23245050q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(6)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)