Properties

Label 108.6.e
Level $108$
Weight $6$
Character orbit 108.e
Rep. character $\chi_{108}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(108, [\chi])\).

Total New Old
Modular forms 198 10 188
Cusp forms 162 10 152
Eisenstein series 36 0 36

Trace form

\( 10 q + 21 q^{5} + 29 q^{7} - 177 q^{11} - 181 q^{13} - 2280 q^{17} - 832 q^{19} - 399 q^{23} - 4778 q^{25} + 6033 q^{29} + 2759 q^{31} - 37146 q^{35} - 15172 q^{37} + 18435 q^{41} + 1469 q^{43} + 25155 q^{47}+ \cdots + 40541 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.6.e.a 108.e 9.c $10$ $17.321$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 36.6.e.a \(0\) \(0\) \(21\) \(29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1}+\beta _{7})q^{5}+(6\beta _{1}+\beta _{2}+\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

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