Properties

Label 108.6.h
Level $108$
Weight $6$
Character orbit 108.h
Rep. character $\chi_{108}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
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 192 64 128
Cusp forms 168 56 112
Eisenstein series 24 8 16

Trace form

\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} + O(q^{10}) \) \( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.6.h.a 108.h 36.h $56$ $17.321$ None \(3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{6}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)