Properties

Label 108.4.h
Level $108$
Weight $4$
Character orbit 108.h
Rep. character $\chi_{108}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 120 40 80
Cusp forms 96 32 64
Eisenstein series 24 8 16

Trace form

\( 32 q + 3 q^{2} - q^{4} + 6 q^{5} - 20 q^{10} - 2 q^{13} + 78 q^{14} - q^{16} + 234 q^{20} + 15 q^{22} + 198 q^{25} - 132 q^{28} - 78 q^{29} - 687 q^{32} - 191 q^{34} - 8 q^{37} - 891 q^{38} + 34 q^{40}+ \cdots + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.4.h.a 108.h 36.h $8$ $6.372$ 8.0.\(\cdots\).1 None 36.4.h.a \(3\) \(0\) \(-66\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
108.4.h.b 108.h 36.h $24$ $6.372$ None 36.4.h.b \(0\) \(0\) \(72\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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