Properties

Label 54.4.c
Level $54$
Weight $4$
Character orbit 54.c
Rep. character $\chi_{54}(19,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 54.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(54, [\chi])\).

Total New Old
Modular forms 66 6 60
Cusp forms 42 6 36
Eisenstein series 24 0 24

Trace form

\( 6 q - 2 q^{2} - 12 q^{4} - 18 q^{5} + 12 q^{7} + 16 q^{8} - 39 q^{11} - 24 q^{13} - 100 q^{14} - 48 q^{16} + 78 q^{17} + 210 q^{19} - 72 q^{20} - 18 q^{22} + 264 q^{23} - 219 q^{25} + 392 q^{26} - 96 q^{28}+ \cdots - 2604 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.4.c.a 54.c 9.c $2$ $3.186$ \(\Q(\sqrt{-3}) \) None 18.4.c.a \(2\) \(0\) \(-9\) \(31\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b 54.c 9.c $4$ $3.186$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None 18.4.c.b \(-4\) \(0\) \(-9\) \(-19\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)