Properties

Label 222.2.a
Level $222$
Weight $2$
Character orbit 222.a
Rep. character $\chi_{222}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $76$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 222 = 2 \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 222.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(76\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(222))\).

Total New Old
Modular forms 42 5 37
Cusp forms 35 5 30
Eisenstein series 7 0 7

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

\(2\)\(3\)\(37\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(1\)\(0\)\(1\)\(1\)\(0\)\(1\)\(0\)\(0\)\(0\)
\(+\)\(+\)\(-\)\(-\)\(9\)\(2\)\(7\)\(8\)\(2\)\(6\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(7\)\(1\)\(6\)\(6\)\(1\)\(5\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(4\)\(0\)\(4\)\(3\)\(0\)\(3\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(5\)\(1\)\(4\)\(4\)\(1\)\(3\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(5\)\(0\)\(5\)\(4\)\(0\)\(4\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(8\)\(0\)\(8\)\(7\)\(0\)\(7\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)\(1\)\(2\)\(2\)\(1\)\(1\)\(1\)\(0\)\(1\)
Plus space\(+\)\(18\)\(0\)\(18\)\(15\)\(0\)\(15\)\(3\)\(0\)\(3\)
Minus space\(-\)\(24\)\(5\)\(19\)\(20\)\(5\)\(15\)\(4\)\(0\)\(4\)

Trace form

\( 5 q - q^{2} - q^{3} + 5 q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + 5 q^{9} - 2 q^{10} + 4 q^{11} - q^{12} + 6 q^{13} + 6 q^{15} + 5 q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} - 8 q^{21} + 4 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(222))\) 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 37
222.2.a.a 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.a \(-1\) \(-1\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+3q^{7}+\cdots\)
222.2.a.b 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.b \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
222.2.a.c 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.c \(-1\) \(1\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
222.2.a.d 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.d \(1\) \(-1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
222.2.a.e 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.e \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(222))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(222)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 2}\)