Properties

Label 945.2.dd
Level $945$
Weight $2$
Character orbit 945.dd
Rep. character $\chi_{945}(169,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $648$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.dd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 888 648 240
Cusp forms 840 648 192
Eisenstein series 48 0 48

Trace form

\( 648 q + 6 q^{5} + 6 q^{9} + O(q^{10}) \) \( 648 q + 6 q^{5} + 6 q^{9} - 6 q^{11} + 18 q^{15} + 90 q^{20} - 18 q^{25} + 36 q^{31} - 96 q^{36} + 24 q^{39} - 24 q^{41} - 168 q^{44} - 102 q^{45} - 144 q^{50} + 120 q^{51} - 72 q^{54} - 156 q^{59} - 186 q^{60} + 324 q^{64} - 108 q^{65} + 276 q^{66} - 48 q^{69} + 168 q^{71} - 180 q^{74} - 84 q^{75} - 36 q^{79} - 180 q^{80} + 18 q^{81} + 24 q^{84} - 12 q^{86} - 60 q^{89} - 138 q^{90} - 36 q^{95} - 96 q^{96} - 132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.dd.a 945.dd 135.p $648$ $7.546$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)