Properties

Label 108.5.d
Level $108$
Weight $5$
Character orbit 108.d
Rep. character $\chi_{108}(55,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $90$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(108, [\chi])\).

Total New Old
Modular forms 78 32 46
Cusp forms 66 32 34
Eisenstein series 12 0 12

Trace form

\( 32 q + 14 q^{4} + O(q^{10}) \) \( 32 q + 14 q^{4} - 26 q^{10} - 176 q^{13} - 118 q^{16} + 1122 q^{22} + 4368 q^{25} + 2154 q^{28} - 1016 q^{34} + 3280 q^{37} - 3542 q^{40} - 1788 q^{46} - 8800 q^{49} - 2948 q^{52} - 9092 q^{58} - 4400 q^{61} + 5738 q^{64} + 12522 q^{70} + 8320 q^{73} - 41472 q^{76} - 38396 q^{82} - 8032 q^{85} + 18774 q^{88} + 48084 q^{94} + 7936 q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.5.d.a 108.d 4.b $16$ $11.164$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{7}+\cdots)q^{5}+\cdots\)
108.5.d.b 108.d 4.b $16$ $11.164$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{7}+\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)