Properties

Label 945.2.dk
Level $945$
Weight $2$
Character orbit 945.dk
Rep. character $\chi_{945}(157,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1680$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.dk (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 945 \)
Character field: \(\Q(\zeta_{36})\)
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 1776 1776 0
Cusp forms 1680 1680 0
Eisenstein series 96 96 0

Trace form

\( 1680 q - 6 q^{2} - 18 q^{3} - 18 q^{5} - 36 q^{6} - 12 q^{7} - 12 q^{8} + O(q^{10}) \) \( 1680 q - 6 q^{2} - 18 q^{3} - 18 q^{5} - 36 q^{6} - 12 q^{7} - 12 q^{8} - 18 q^{10} - 36 q^{11} - 18 q^{12} - 24 q^{15} - 12 q^{16} - 18 q^{17} - 6 q^{18} - 24 q^{21} - 24 q^{22} - 54 q^{23} - 6 q^{25} - 72 q^{26} - 24 q^{28} - 42 q^{30} - 36 q^{31} + 138 q^{32} - 18 q^{33} - 42 q^{35} - 84 q^{36} - 12 q^{37} - 18 q^{38} - 18 q^{40} + 84 q^{42} - 24 q^{43} - 18 q^{45} - 24 q^{46} - 18 q^{47} - 72 q^{50} - 12 q^{51} - 18 q^{52} - 42 q^{53} + 24 q^{56} - 60 q^{57} - 6 q^{58} - 198 q^{60} + 72 q^{61} - 54 q^{63} + 138 q^{65} - 36 q^{66} - 6 q^{67} - 234 q^{68} - 12 q^{70} - 24 q^{71} - 30 q^{72} - 18 q^{75} + 144 q^{76} - 156 q^{77} - 84 q^{78} - 36 q^{80} + 12 q^{81} - 36 q^{82} - 24 q^{85} + 96 q^{86} - 18 q^{87} - 6 q^{88} + 162 q^{90} - 12 q^{91} - 180 q^{92} - 150 q^{93} + 54 q^{95} - 36 q^{96} - 120 q^{98} + O(q^{100}) \)

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.dk.a 945.dk 945.ck $1680$ $7.546$ None \(-6\) \(-18\) \(-18\) \(-12\) $\mathrm{SU}(2)[C_{36}]$