Properties

Label 38.6.a
Level $38$
Weight $6$
Character orbit 38.a
Rep. character $\chi_{38}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $30$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(38))\).

Total New Old
Modular forms 27 7 20
Cusp forms 23 7 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.

\(2\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7 q + 4 q^{2} - 4 q^{3} + 112 q^{4} + 22 q^{5} + 8 q^{6} + 194 q^{7} + 64 q^{8} + 221 q^{9} + 200 q^{10} + 320 q^{11} - 64 q^{12} + 1338 q^{13} + 80 q^{14} + 1868 q^{15} + 1792 q^{16} - 1316 q^{17} + 628 q^{18}+ \cdots + 324236 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(38))\) 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
38.6.a.a 38.a 1.a $1$ $6.095$ \(\Q\) None 38.6.a.a \(-4\) \(-6\) \(31\) \(-27\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
38.6.a.b 38.a 1.a $1$ $6.095$ \(\Q\) None 38.6.a.b \(4\) \(-14\) \(-45\) \(-121\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
38.6.a.c 38.a 1.a $2$ $6.095$ \(\Q(\sqrt{1441}) \) None 38.6.a.c \(-8\) \(3\) \(-45\) \(114\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
38.6.a.d 38.a 1.a $3$ $6.095$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 38.6.a.d \(12\) \(13\) \(81\) \(228\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(38))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(38)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)