Properties

Label 108.2.h
Level $108$
Weight $2$
Character orbit 108.h
Rep. character $\chi_{108}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
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 48 16 32
Cusp forms 24 8 16
Eisenstein series 24 8 16

Trace form

\( 8 q + 3 q^{2} - q^{4} + 6 q^{5} + O(q^{10}) \) \( 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97} + O(q^{100}) \)

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.h.a $8$ $0.862$ 8.0.170772624.1 None \(3\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{4}+\cdots\)

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

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