Properties

Label 108.2.e
Level $108$
Weight $2$
Character orbit 108.e
Rep. character $\chi_{108}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

Total New Old
Modular forms 54 2 52
Cusp forms 18 2 16
Eisenstein series 36 0 36

Trace form

\( 2q + 3q^{5} + q^{7} + O(q^{10}) \) \( 2q + 3q^{5} + q^{7} + 3q^{11} + q^{13} - 12q^{17} - 8q^{19} - 3q^{23} - 4q^{25} + 3q^{29} - 5q^{31} + 6q^{35} + 4q^{37} + 3q^{41} + q^{43} - 9q^{47} + 6q^{49} + 12q^{53} + 18q^{55} - 3q^{59} + 13q^{61} - 3q^{65} + 7q^{67} + 24q^{71} - 20q^{73} - 3q^{77} - 11q^{79} - 9q^{83} - 18q^{85} - 12q^{89} + 2q^{91} - 12q^{95} - 11q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.2.e.a \(2\) \(0.862\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)