Properties

Label 108.4.e
Level $108$
Weight $4$
Character orbit 108.e
Rep. character $\chi_{108}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

Total New Old
Modular forms 126 6 120
Cusp forms 90 6 84
Eisenstein series 36 0 36

Trace form

\( 6q - 6q^{5} - 6q^{7} + O(q^{10}) \) \( 6q - 6q^{5} - 6q^{7} - 51q^{11} + 12q^{13} + 222q^{17} + 30q^{19} - 210q^{23} - 3q^{25} - 456q^{29} + 48q^{31} + 1104q^{35} - 96q^{37} - 897q^{41} + 129q^{43} - 522q^{47} - 225q^{49} + 2208q^{53} - 216q^{55} - 453q^{59} - 402q^{61} - 1110q^{65} - 213q^{67} - 120q^{71} + 750q^{73} - 1128q^{77} + 552q^{79} + 612q^{83} + 1188q^{85} + 924q^{89} - 264q^{91} + 2184q^{95} + 93q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.4.e.a \(6\) \(6.372\) 6.0.6831243.2 None \(0\) \(0\) \(-6\) \(-6\) \(q+(-2+2\beta _{1}+\beta _{5})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

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