Properties

Label 108.3.g
Level $108$
Weight $3$
Character orbit 108.g
Rep. character $\chi_{108}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

Total New Old
Modular forms 90 4 86
Cusp forms 54 4 50
Eisenstein series 36 0 36

Trace form

\( 4 q - 9 q^{5} - q^{7} + 36 q^{11} + 5 q^{13} + 2 q^{19} - 99 q^{23} + 13 q^{25} + 63 q^{29} - 7 q^{31} - 64 q^{37} + 18 q^{41} - 46 q^{43} + 81 q^{47} - 51 q^{49} + 90 q^{55} - 126 q^{59} + 41 q^{61} - 171 q^{65}+ \cdots - 196 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.3.g.a 108.g 9.d $4$ $2.943$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 36.3.g.a \(0\) \(0\) \(-9\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(108, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)