Properties

Label 38.2.a
Level $38$
Weight $2$
Character orbit 38.a
Rep. character $\chi_{38}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $10$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(38))\).

Total New Old
Modular forms 7 2 5
Cusp forms 4 2 2
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.

\(2\)\(19\)FrickeDim
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} + 4 q^{15} + 2 q^{16} + 6 q^{17} - 4 q^{20} - 4 q^{21} + 8 q^{22} + 2 q^{23} - 2 q^{24} + 6 q^{25} - 6 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(38))\) 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 19
38.2.a.a 38.a 1.a $1$ $0.303$ \(\Q\) None 38.2.a.a \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
38.2.a.b 38.a 1.a $1$ $0.303$ \(\Q\) None 38.2.a.b \(1\) \(-1\) \(-4\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(38))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(38)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)