Properties

Label 37.2.a
Level $37$
Weight $2$
Character orbit 37.a
Rep. character $\chi_{37}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $6$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(37))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

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

\(37\)TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)\(0\)\(0\)\(0\)
\(-\)\(2\)\(2\)\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)

Trace form

\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 6 q^{6} - 2 q^{7} + 4 q^{9} + 4 q^{10} - 2 q^{11} - 8 q^{12} - 6 q^{13} + 2 q^{14} + 6 q^{15} + 6 q^{17} - 12 q^{18} + 2 q^{19} - 4 q^{20} + 2 q^{21} + 10 q^{22} + 8 q^{23}+ \cdots - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 37
37.2.a.a 37.a 1.a $1$ $0.295$ \(\Q\) None 37.2.a.a \(-2\) \(-3\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
37.2.a.b 37.a 1.a $1$ $0.295$ \(\Q\) None 37.2.a.b \(0\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)