Properties

Label 38.2.c
Level $38$
Weight $2$
Character orbit 38.c
Rep. character $\chi_{38}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(38, [\chi])\).

Total New Old
Modular forms 14 6 8
Cusp forms 6 6 0
Eisenstein series 8 0 8

Trace form

\( 6 q - q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 6 q^{14} + 14 q^{15} - 3 q^{16} + 6 q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{20}+ \cdots + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.2.c.a 38.c 19.c $2$ $0.303$ \(\Q(\sqrt{-3}) \) None 38.2.c.a \(1\) \(-1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
38.2.c.b 38.c 19.c $4$ $0.303$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 38.2.c.b \(-2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)