Properties

Label 912.1.cb
Level $912$
Weight $1$
Character orbit 912.cb
Rep. character $\chi_{912}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 912.cb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(912, [\chi])\).

Total New Old
Modular forms 96 18 78
Cusp forms 24 6 18
Eisenstein series 72 12 60

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q - 3 q^{13} + 3 q^{19} - 3 q^{21} + 3 q^{27} + 3 q^{43} - 3 q^{49} + 6 q^{61} - 6 q^{63} + 3 q^{67} - 3 q^{73} - 6 q^{75} - 6 q^{79} - 6 q^{91} + 6 q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.1.cb.a 912.cb 57.l $6$ $0.455$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)