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Properties

Label 945.2.di
Level $945$
Weight $2$
Character orbit 945.di
Rep. character $\chi_{945}(13,\cdot)$
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.di (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

\( 1680 q - 24 q^{2} - 12 q^{7} - 12 q^{8} + O(q^{10}) \) \( 1680 q - 24 q^{2} - 12 q^{7} - 12 q^{8} - 36 q^{11} - 24 q^{15} - 48 q^{16} - 24 q^{18} - 24 q^{21} - 24 q^{22} - 24 q^{25} - 24 q^{28} - 168 q^{30} - 132 q^{32} + 12 q^{35} + 24 q^{36} - 12 q^{37} - 60 q^{42} - 24 q^{43} - 24 q^{46} + 72 q^{50} - 48 q^{51} - 168 q^{53} - 228 q^{56} + 48 q^{57} - 24 q^{58} - 36 q^{60} - 54 q^{63} - 96 q^{65} - 24 q^{67} - 12 q^{70} - 24 q^{71} - 264 q^{72} + 132 q^{77} + 24 q^{78} - 60 q^{81} - 24 q^{85} - 264 q^{86} + 48 q^{88} - 12 q^{91} - 144 q^{92} - 168 q^{93} + 36 q^{95} - 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.di.a 945.di 945.ci $1680$ $7.546$ None \(-24\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{36}]$